Wikiversity:Colloquium

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== 'Wikidata item' link is moving, finally. ==

Hello everyone, I previously wrote on the 27th September to advise that the ''Wikidata item'' sitelink will change places in the sidebar menu, moving from the '''General''' section into the '''In Other Projects''' section. The scheduled rollout date of 04.10.2024 was delayed due to a necessary request for Mobile/MinervaNeue skin. I am happy to inform that the global rollout can now proceed and will occur later today, 22.10.2024 at 15:00 UTC-2. [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Please let us know]] if you notice any problems or bugs after this change. There should be no need for null-edits or purging cache for the changes to occur. Kind regards, -[[m:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] 11:28, 22 October 2024 (UTC)
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:Hi @[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]]: I Just noticed your post above, and it is timely.
:I have been participating in the English WikiUniversity for a few years, much less often recently. I seems like something in the way the site displays is different, but I cannot put my finger on it. Your posting gave me a clue. Can you please tell me where  the link to wikidata items has moved to? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:23, 11 December 2024 (UTC)
::Hello @[[User:Ottawahitech|Ottawahitech]], sure, I would be happy to. The button/sitelink name didn't change, just its position. You should find it in the sidebar-menu under the section '''In other projects''' (where the links to all other Wikimedia Projects are displayed). If you do not see it, please reach out to us on the [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Move Wikidata item - Discussion page]]. Thank you, -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 09:24, 12 December 2024 (UTC)
:::@[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]], thank you for responding. I intend to followup on the ''Move Wikidata item - Discussion page'' as per your post above by putting it on my ever growing todo list.
:::I don't know about others on this wiki, as I said I have not been visiting here frequently, but for me the constant changes are a big distraction. I have been around wikimedia projects since 2007, so why do I have to spend so much time learning and re-learning how to find what I came here for? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:41, 12 December 2024 (UTC)
::::Hi @[[User:Ottawahitech|Ottawahitech]], thanks for you thoughts. Your input whether positive or critical helps us understand the impacts to editors so we welcome your further thoughts when you reach us in your To Do List :)
::::I can't speak about the other changes you've experienced here but I do hope they are made with a spirit of improvement for the community as a whole. -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 10:43, 16 December 2024 (UTC)
:::::@[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]]: 
:::::Re: '''Your input whether positive or critical helps us understand the impacts to editors'''
:::::Today I (finally)  checked [[Move Wikidata item - Discussion page]] and discovered that it is a talkpage on META where, unfortunately, I am infinitely blocked, so cannot participate. Even so, I proceeded to try and see what others are saying and immediately came to the conclusion that the few who actually participated in that discussin viewed the change  negatively. It must be disheartening for developers to meet such a hostile attitude from the community. Please don't take it personally, this is a common phenomena in  wikimedia community wide discussions , IMIO.
:::::I further checked the [https://pageviews.wmcloud.org/?project=meta.wikimedia.org&amp;platform=all-access&amp;agent=user&amp;redirects=0&amp;range=latest-90&amp;pages=Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link page view statistcics] which showed there were only  828 pageviews in the last 90 days, and what's worse [https://meta.wikimedia.org/w/index.php?title=Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link&amp;action=info#mw-pageinfo-watchers the page has &quot;Fewer than 30 watchers&quot;]. 
:::::Since [[META:User:Danny Benjafield (WMDE)|your userpage on META]] says that you are the: &quot;Community Communications Manager Wikidata Integrations Team&quot;, may I ask how this apparent apathy is being addressed by your own management?
:::::I apologize if my post is not welcome on the Wikiversity:Colloquium, as i said I am  a rather infrequent visitor to this wiki. I probably would not have followed up if you did not assure us that our feedback positive or negative is sought. Cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 20:49, 3 January 2025 (UTC)
::::::Dear @[[User:Ottawahitech|Ottawahitech]], I am so so sorry for leaving you on read for these last months, I have no excuse other than reading your comment and then getting lost before making a reply.
::::::The team I am working with, [[m:Wikidata_For_Wikimedia_Projects|Wikidata for Wikimedia Projects]] is a new development team, so I think management has allowed a certain amount of elbow room or leeway for us to make small changes whilst developing our confidence tackling the MediaWiki codebase with onboarding tasks that won't 'rock the boat' too much. We certainly expected some pushback or resistance to moving the Wikidata item as editors are so used to where it previously resided. Now it has been some time and hopefully the communities have gotten used to the change.
::::::Please do not apologise, your comments are always welcome, critical or not, as a new team I think we certainly &quot;fly under the radar&quot; to an extent and I hope that changes as we continue to work on projects that deepen the integrations between Wikidata and the other sibling projects. Once again, my sincere apologies for the delay in this reply. -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 13:59, 1 April 2025 (UTC)

== Wikiversity - Newsletters ==

Hello All,

I wanted to create a newsletter on Wikiversity, which would highlight what is going on in certain months and events on Wikiversity; which would bolster engagement by many people. This would be on the website and would have its dedicated 'Newsletter' tab.

I hope you acknowledge this idea. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:05, 8 December 2024 (UTC)

:@[[User:RockTransport|RockTransport]], What sort of things do you plan to include in your newsletter? Will they be different than what is currently in [[Main Page/News]]? Just curious.
:I am also wondering about your motive which I think is: to bolster engagement by many people. I am asking because I wonder if others who are currently active here also think this I is desirable? Have you asked them? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:34, 11 December 2024 (UTC)
::Not yet, which was why I was asking this on the colloquium. I plan to include things that many people have created on Wikiversity over the month, as it is a monthly newsletter. It would be somewhere on the website here. It will be more frequent that the ones seen on [[Main Page/News]]. We will include people's resources to essentially promote them. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 06:50, 12 December 2024 (UTC)
:::@[[User:RockTransport|RockTransport]], I Think what you are saying is that ''Main Page/News'' does not update frequently enough? 
:::If this is the reason, why not start small by simply increasing the frequency of posting news on the main page, instead of trying to start a newsletter?
:::If there is more, can you articulate what else is missing. Thanks in advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:51, 12 December 2024 (UTC)
::::I meant going to detail into topics covered in that month, rather than just giving a few points. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 16:53, 12 December 2024 (UTC)
:::::What sort of details did you have in mind? You can pick one of the links provided in [[Main Page/News]] to illustrate. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:29, 16 December 2024 (UTC)
::::::I'm thinking of the community entering their projects, and discussing those in the newsletter. It depends on what they want, though. There would be a dedicated page for giving the information about their projects [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:24, 16 December 2024 (UTC)
:::::::I might start working on this soon, depending on the projects being created on Wikiversity. @[[User:Ottawahitech|Ottawahitech]] @[[User:Atcovi|Atcovi]] [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:25, 17 December 2024 (UTC)
::::::::I'd recommend you start off with putting this under a userspace page (something like [[User:RockTransport/Wikiversity Newsletter]]), and drafting what you desire. Let us know once it's done, and the community can provide their input. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 18:30, 17 December 2024 (UTC)
:::::::::I will try and make one for this month. This is supposed to be a monthly newsletter, showcasing the different projects mentioned there. Users can put their projects, and we will document them on the newsletter. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:33, 17 December 2024 (UTC)
:::::::::I am hoping for it to be released by January 2025. There's no rush to get it done; it's still in it's planning stage. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:43, 17 December 2024 (UTC)
::::I '''might''' be able to icnrease the frequency there, but it doesn't go into detail about these topics. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:30, 18 December 2024 (UTC)
:Where you are going to get the audience for your website and Wikiversity newsletter? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:38, 18 December 2024 (UTC)
::It's on Wikiversity, not on an outside platform. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:51, 18 December 2024 (UTC)
::The audience will be Wikiversity contributors. There will be a dedicated page for it on Wikiversity. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:55, 18 December 2024 (UTC)
:::Hi @[[User:RockTransport|RockTransport]], Just wondering if there is a progress on the wikiversity newsletter? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 18:09, 6 January 2025 (UTC)
::::There is progress, I just need to find some topics to cover about. [[User:RockTransport|''Rock Transport'']] 😊 ([[User_talk:RockTransport|Talk page]])  18:26, 6 January 2025 (UTC)
::::Also, if you wanted to see the work being done on the page, go to [[User:RockTransport/Wikiversity Newsletter|this page]]. I haven't worked on it that much lately, but I am constantly working on it. [[User:RockTransport|''Rock Transport'']] 😊 ([[User_talk:RockTransport|Talk page]])  18:38, 6 January 2025 (UTC)

== &lt;s&gt;Degrees&lt;/s&gt; (Certificates (see below)) ==

Why does Wikiversity not provide degrees? I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal. But anyway, why is that? Wikiversity is about opening doors, i.e., removing obstacles. So, what kind of an obstacle was a paper? Was a certain body of knowledge that you learned well?! Because Wikiversity is not accredited for that? Yes, and do we need official US accreditation? We cannot create our system so that the learners who learn here and would like to continue their science career have a recognizable degree they can continue? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:19, 18 December 2024 (UTC)

:&quot;I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal.&quot; Was it? Becoming a degree-granting institution is an extremely high bar in the United States, but what is even the point in becoming a degree-granting institution in... Malawi? Tonga? Somewhere else where the servers aren't located or the WMF aren't incorporated? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:53, 18 December 2024 (UTC)
::I ment certificates. The question is the recognazibility of a certificate. I am not talking here about equal certification, which is provided by governmental institucians to universities, rather on Wikiversity own certification, which might may advocate itself over the time. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:05, 19 December 2024 (UTC)
::: We could issue certificates in some residing in certain jurisdictions probably (?). To my knowledge, there is no legal prohibition federally against doing this in the USA as long as no misrepresentation happens. Although some states might prohibit it (?). Degrees are likely different (at least with respect to accreditation). Please let me know if you believe I am likely incorrect in my understanding. I asked an LLM this prompt, &quot;is there any prohibition legally in USA for a DAO (decentralized autonomous organization or wiki community related to learning, teaching, and research) from issuing certifications or certificates to those who go through learning materials and educational resources that might be on a decentralized or nonprofit wiki that has an active community?&quot; (i won't post the specific result, but I wrote and engineered that prompt myself). The LLM output seemed to indicate my understanding noted here is correct, but LLM's are sometimes wrong. what do you or others think about this? [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:49, 25 December 2024 (UTC)
:From [https://web.archive.org/web/20170703053134/https://wikimediafoundation.org/wiki/Meetings/November_13,_2005 the WMF Board] (repeated at [[WV:WWIN]]):
:&lt;blockquote&gt;&quot;[[Wikiversity:Original proposal|Wikiversity proposal]] not approved, but we will approve it if [[Wikiversity:Approved Wikiversity project proposal|some changes are made]]... The board recommend rewriting the proposal to ''exclude credentials'', exclude online-courses and clarify the concept of elearning platform.&quot;&lt;/blockquote&gt;
:That is, Wikiversity was prevented from creation until it was codified '''not''' to provide credentials. It is not just ''U.S.'' credentials, but credentials period.
:I see you were around for [[Wikiversity:Community Review/Wikimedia Ethics:Ethical Breaching Experiments|the Reckoning]], so I imagine you are aware of the potential consequences of challenging such a clear policy so explicitly. I worry the community would not withstand another round. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:24, 2 January 2025 (UTC)
::That said, I see nothing wrong with a cute badge of some sort (emulating barnstars) for completion of a resource (perhaps supervised/signed off by the resource creators). Even if there is no pretention of &quot;credentials&quot;, who doesn't like a trophy? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:19, 2 January 2025 (UTC)
:::[[:w:Gamification|Gamification]] is quite different than granting certificates and degrees. And ''even'' if Wikiversity grants certificates, half the battle is getting others to recognize the legitimacy of the certificate. Otherwise people will just think of Wikiversity as a [[:w:diploma mill|diploma mill]] especially if this conversation steers towards purposely issuing certificates in far flung countries for the sole purpose of skirting around the rules. And that's something I don't want to be associated with if Wikiversity goes down that path. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:24, 2 January 2025 (UTC)

== Citation system ==

How is being maintained citation system on en.wv. I mean, is it completly the same as on English Wikipedia? Do we update it according to English Wikipedia? How we do that? Are the templates like [[Template:Cite book|Cite book]] based on Lua? I dont see any invoke word.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 16:20, 2 January 2025 (UTC)

:I was just working on references in [[WikiJournal Preprints/Mobility-aware Scheduling in Fog Computing: Analysis and Challenges]]. And I agree with you. The citation system is so outdated compared to en.wp. Just the fact that I have to do extra clicks to access {{tl|cite journal}} is bizarre. Are there efforts to sync updates to the current citation version on en.wp? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:35, 2 January 2025 (UTC)
::Not mine, I am just wondering if there is an easy system how to take over citation aparatus. I havent investigated the citation system on English Wikipedia yet, but on the first glance it looks like a very complicated environment. So in the following days Ill be looking on it if its a way to overtake it or if it would be easier to create own citation system.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 22:00, 2 January 2025 (UTC)

== Proposal: citation templates for VisualEditor ==

@[[User:OhanaUnited|OhanaUnited]] [[Wikiversity:Colloquium#Citation system|pointed above]], that they had a hard time to create citations via VisualEditor I believe. I think its because of missing map in [[MediaWiki:Cite-tool-definition.json]] ([[phab:T219551|see also]]). And the question is, which citation templates the editor should list. So I would propose the same as on en.wp, i.e. [[Template:Cite book|Cite book]], [[Template:Cite journal|journal]], [[Template:Cite news|news]], and [[Template:Cite web|web]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 13:38, 3 January 2025 (UTC)

:I support those four templates (book, journal, news, web). Another part of me wonders if we should include other use cases like AV media, thesis and report. But they may have limited usage and will only clutter the screen. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 04:55, 7 January 2025 (UTC)
::Sure and thesis could be cited by Cite book. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 06:53, 7 January 2025 (UTC)
::[[Wikiversity:Request custodian action#Edit MediaWiki page|Requested Custodian action]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:01, 7 January 2025 (UTC)

== Wikiversity Newsletter - Topics? ==

Hello,
For the newsletter concept on Wikiversity, for Wikiversitans (which can be seen above), I was wondering if there were any recently added or updated resources on Wikiversity that this newsletter could add.
Kind regards,
Rock [[User:RockTransport|''Rock Transport'']] 😊 ([[User_talk:RockTransport|Talk page]])  18:13, 9 January 2025 (UTC)

== Wikiversity page view statistics ==

I remember seeing [[recent topics/threads]] here wondering about page view statistics for this project. So I wonder if anyone else here is as curious as I am about the following page view which compares wikiversity to other wikimedia projects
https://pageviews.wmcloud.org/siteviews/?platform=all-access&amp;source=pageviews&amp;agent=user&amp;range=latest-30&amp;sites=all-projects
cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 20:05, 15 January 2025 (UTC)

:It does look interesting, but I haven't viewed it in depth yet. [[User:RockTransport|''Rock Transport'']] 😊 ([[User_talk:RockTransport|Talk page]])  17:24, 19 January 2025 (UTC)

== Launching! Join Us for Wiki Loves Ramadan 2025! ==

Dear All,

We’re happy to announce the launch of [[m:Wiki Loves Ramadan 2025|Wiki Loves Ramadan 2025]], an annual international campaign dedicated to celebrating and preserving Islamic cultures and history through the power of Wikipedia. As an active contributor to the Local Wikipedia, you are specially invited to participate in the launch. 

This year’s campaign will be launched for you to join us write, edit, and improve articles that showcase the richness and diversity of Islamic traditions, history, and culture.

* Topic: [[m:Event:Wiki Loves Ramadan 2025 Campaign Launch|Wiki Loves Ramadan 2025 Campaign Launch]]
* When: Jan 19, 2025 
* Time: 16:00 Universal Time UTC and runs throughout Ramadan (starting February 25, 2025).
* Join Zoom Meeting: https://us02web.zoom.us/j/88420056597?pwd=NdrpqIhrwAVPeWB8FNb258n7qngqqo.1 
* Zoom meeting hosted by [[m:Wikimedia Bangladesh|Wikimedia Bangladesh]]

To get started, visit the [[m:Wiki Loves Ramadan 2025|campaign page]] for details, resources, and guidelines: Wiki Loves Ramadan 2025.

Add [[m:Wiki Loves Ramadan 2025/Participant|your community here]], and organized Wiki Loves Ramadan 2025 in your local language.

Whether you’re a first-time editor or an experienced Wikipedian, your contributions matter. Together, we can ensure Islamic cultures and traditions are well-represented and accessible to all.

Feel free to invite your community and friends too. Kindly reach out if you have any questions or need support as you prepare to participate.

Let’s make Wiki Loves Ramadan 2025 a success!

For the [[m:Wiki Loves Ramadan 2025/Team|International Team]] 12:08, 16 January 2025 (UTC)
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== Deletion of talk pages ==

I wonder if there are any policies here that define when talkpages are deleted?

Thanks in advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:30, 17 January 2025 (UTC)

:I'm not too sure if there are any topics about this. [[User:RockTransport|''Rock Transport'']] 😊 ([[User_talk:RockTransport|Talk page]])  19:37, 17 January 2025 (UTC)
::Let me explain why I am asking about deletion:
::I have recently posted a question on a WV talk-page. The page was empty when I arrived, so had to be created, or recreated as it turns out because when I tried to post I received this box that said the page had been deleted by @[[User:Guy vandegrift|Guy vandegrift]] as a test page. I then Went ahead and recreated the page by posting at:
::[[Wikiversity talk:Wikidebate/Guy vandegrift#Do we need dialogues?]].
::However a bit later I remembered a discussion on the English Wikiquote Village Pump which was started by a contributor who was active there a long time ago who apparently was looking for their own contributions. It turned out that the history of the contributions had disappeared when the page was deleted and then re-created by another contributor who's became, at least according to the View history, the &quot;owner&quot; of all the previous contributions. Here is the ENWQ-VP discussion: https://en.wikiquote.org/wiki/Wikiquote:Village_pump#Now_this_is_contrary_to_the_spirit_of_Wikipedia.
::I believe deletions of old pages that seem unimportant to new users of the English Wikversity may become problematic in the future. I know that at least one  [[User:MathXplore|new admin]] has been added in the last  couple of years, but I am not sure how  many of the experienced admins are still active, so I don't know who makes deletion decisions here.. History is crucial to maintain when people are no longeraround.
::It would be nice for the ENWV-community  to understand how and what files/contributions are deleted.
::note: @[[User:Koavf|Koavf]] @[[User:Juandev|Juandev]], @[[User:OhanaUnited|OhanaUnited]] as recent participants in the Colloquium I wonder if you have any knowledge to contribute?
::Thanks advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:20, 18 January 2025 (UTC)
:::This project is generally pretty policy-lite, so deleting talk pages is probably ad hoc and left to best judgement. I have personally deleted one content page here but kept the talk page to document why it was deleted (this is common on en.wikt). —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:47, 18 January 2025 (UTC)
::::I was looking up some old history (2002) on the English Wikipedia associated with a particular user (Roadrunner) and  happened to see a talk-page that was deleted in 2021 that this user had contributed content to:
::::https://en.wikipedia.org/wiki/Talk%3AImmediate_Action_Unit
::::This page is no longer public as a result of: 
::::https://en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/Immediate_Action_Unit
::::So it appears that on the English Wikipedia talkpages were still being deleted along with their associated page as recently as 2021, I think? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 19:52, 31 January 2025 (UTC)
::: Please read [[Wikiversity:Deletions]] (especially [[WV:CSD]]) for the deletion of (talk) pages. No.8 of [[WV:CSD]] is specific for talk pages. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 23:09, 18 January 2025 (UTC)
::::@[[User:MathXplore|MathXplore]], I think @[[User:Ottawahitech|Ottawahitech]] is referring to user talk pages (correct me if I'm wrong). Do we have any policies related to this? [[User:RockTransport|''Rock Transport'']] 😊 ([[User_talk:RockTransport|Talk page]])  08:02, 19 January 2025 (UTC)
::::: [[Wikiversity:Deletions]] (including [[WV:CSD]]) apply for all namespaces. Therefore, the same rule will be applied to user talk pages. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 11:59, 19 January 2025 (UTC)
::::::@[[User:MathXplore|MathXplore]], thanks for clarifying. [[User:RockTransport|''Rock Transport'']] 😊 ([[User_talk:RockTransport|Talk page]])  17:28, 19 January 2025 (UTC)
:::@[[User:Koavf|Koavf]], Thanks for this important tid-bit : {{green|I have personally deleted one content page here but kept the talk page to document why it was deleted (this is common on en.wikt).}}
:::This is a great habit IMIO. Do you happen to know if other WV-admins know how to not delete a talk-page when they delete its counterpart? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 20:05, 26 January 2025 (UTC)
::::I don't know that they do, but it's a fairly simple process when you're deleting pages. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:26, 26 January 2025 (UTC)

== Research Guidelines for the new Wiki of Government Efficiency ==

[[User:Jaredscribe/Department_of_Government_Efficiency]]

Before I move this original research project to mainspace, I invite a colloquy on my proposed
[[User:Jaredscribe/Department_of_Government_Efficiency#Research_Guidelines_and_Scholarly_Ethics|Research_Guidelines_and_Scholarly_Ethics]], and will entertain suggested improvements.

All may constructively contribute;  those who do so competently, are invited to edit after they declare and disclose.
[[User_talk:Jaredscribe/Department_of_Government_Efficiency#Declare_your_Interests_and_Disclose_Potential_Conflicts]] 


Thanks in advance for your consideration and informed opinions on how to make this work.  [[User:Jaredscribe|Jaredscribe]] ([[User talk:Jaredscribe|discuss]] • [[Special:Contributions/Jaredscribe|contribs]]) 07:05, 20 January 2025 (UTC)

== Mentors ==

With respect to [https://en.wikiversity.org/w/index.php?title=User_talk%3AUsername142857&amp;diff=2692853&amp;oldid=2667985 this], may I return, and if so, could I get a mentor? [[User:Username142857|Username142857]] ([[User talk:Username142857|discuss]] • [[Special:Contributions/Username142857|contribs]]) 17:15, 20 January 2025 (UTC)

:Hi @[[User:Username142857|Username142857]]: I am not familiar with the term &quot;mentors&quot; on WV. What did you have in mind? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 20:22, 22 January 2025 (UTC)
::@[[User:Ottawahitech|Ottawahitech]], I believe he means getting a mentor to help him with his 'return' on Wikiversity. Please correct me if I'm wrong however @[[User:Username142857|Username142857]]. [[User:RailwayEnthusiast2025|''RailwayEnthusiast2025'']] 😊 ([[User_talk:RailwayEnthusiast2025|Talk page]])  18:57, 23 January 2025 (UTC)
::'Mentors' are usually used to describe people on Wikiversity who mentor people for curatorship, custodianship etc. I think in this context, he might be trying to get a mentor to help him on Wikiversity. [[User:RailwayEnthusiast2025|&lt;span style=&quot;color:green;&quot;&gt;'''''RailwayEnthusiast2025'''''&lt;/span&gt;]] ([[User talk:RailwayEnthusiast2025|talk page]] - [[Special:Contributions/RailwayEnthusiast2025|contribs]]) 20:46, 24 January 2025 (UTC)
:::To clarify, other people have stated that I should probably leave for a while, and I'm wondering if it's safe for me to return [[User:Username142857|Username142857]] ([[User talk:Username142857|discuss]] • [[Special:Contributions/Username142857|contribs]]) 05:51, 9 February 2025 (UTC)
::::@[[User:Username142857|Username142857]]: I think you should return whenever you feel like it, honestly. [[User:Contributor 118,784|&lt;b style=&quot;color:#070&quot;&gt;Contributor&lt;/b&gt;&lt;sup style=&quot;color:#707&quot;&gt;118,784&lt;/sup&gt;]] [[User talk:Contributor 118,784|&lt;span style=&quot;color:#00F&quot;&gt;''Let's talk''&lt;/span&gt;]] 12:19, 10 February 2025 (UTC)

== Universal Code of Conduct annual review: provide your comments on the UCoC and Enforcement Guidelines ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;

{{Int:Please-translate}}.

I am writing to you to let you know the annual review period for the Universal Code of Conduct and Enforcement Guidelines is open now. You can make suggestions for changes through 3 February 2025. This is the first step of several to be taken for the annual review.
[[m:Special:MyLanguage/Universal_Code_of_Conduct/Annual_review|Read more information and find a conversation to join on the UCoC page on Meta]].

The [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee|Universal Code of Conduct Coordinating Committee]] (U4C) is a global group dedicated to providing an equitable and consistent implementation of the UCoC. This annual review was planned and implemented by the U4C. For more information and the responsibilities of the U4C, [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Charter|you may review the U4C Charter]].

Please share this information with other members in your community wherever else might be appropriate.

-- In cooperation with the U4C, [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 01:12, 24 January 2025 (UTC)
&lt;/div&gt;
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:Thanks for the link. I will have a look at it later. [[User:RailwayEnthusiast2025|&lt;span style=&quot;color:green;&quot;&gt;'''RailwayEnthusiast2025'''&lt;/span&gt;]] ([[User talk:RailwayEnthusiast2025|talk page]]|[[Special:Contributions/RailwayEnthusiast2025|contribs]]) 08:49, 24 January 2025 (UTC)

== Subscribing to this talk-page ==

Is anyone here curious to find out what is the best method of subscribing to discussions here? Until today I did not even know one could subscribe to all new topics by clicking on  ''Subscribe'' (the second ''Action'' right after ''Move''). I will have to see if indeed I am automatically subscribed to this new thread that I am hoping  to start as soon as I hit the ''Add topic'' blue button at the bottom right hand corner.

So far I have had to resort to  clicking ''Subscribe'' individually for each topic when  I wanted to receive a notification for any new replies, but unfortunately after some items I was subscribed to have been archived on January 30, I received a message telling me I  am no longer subscribed. I guess I would have to look for any updates that took place before the archive in the archive itself?

Am I making sense at all? I have managed to confuse myself, LOL. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:11, 30 January 2025 (UTC)

:You are not subscribed to threads once they are removed from a page (e.g. by archiving). The easiest way to subscribe is by clicking on the &quot;Subscribe&quot; button with the bell next to it that renders near the thread's title. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 19:44, 30 January 2025 (UTC)

== A club for Wikiversity ==

Hello there,
I would like to start a club for Wikiversity, which would be a part of outreach. Wikiversity is one of the smallest Wikimedia projects and I enjoy contributing here. How could you help me in creating a club for this?
Yours sincerely,
[[User:RailwayEnthusiast2025|RailwayEnthusiast2025]] ([[User talk:RailwayEnthusiast2025|Talk page]] - [[Special:Contributions|Contributions]]) 17:51, 31 January 2025 (UTC)

:There is a formal process for this at [[:m:Wikimedia user groups]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:18, 31 January 2025 (UTC)
::I meant like a club at an organization, school etc. Not a user group in a town or a city. —[[User:RailwayEnthusiast2025|RailwayEnthusiast2025]] ([[User talk:RailwayEnthusiast2025|Talk page]] - [[Special:Contributions|Contributions]]) 18:31, 31 January 2025 (UTC)
:::I wanted to do this, because I'm active here, but I don't know. —[[User:RailwayEnthusiast2025|RailwayEnthusiast2025]] ([[User talk:RailwayEnthusiast2025|Talk page]] - [[Special:Contributions|Contributions]]) 19:59, 12 February 2025 (UTC)
::::Dear @[[User:RailwayEnthusiast2025|RailwayEnthusiast2025]], If you could contact any established user group in your locality. They could provide support to start a wiki club. [[User:511KeV|511KeV]] ([[User talk:511KeV|discuss]] • [[Special:Contributions/511KeV|contribs]]) 04:41, 28 March 2025 (UTC)
:::::Dear @[[User:511KeV|511KeV]], As said in my previous message, I wish to start a club at an organization, school etc. I wish to start a small club like this, not a user group in a town/city. I don't think you understand what I'm trying to say. —[[User:RailwayEnthusiast2025|RailwayEnthusiast2025]] ([[User talk:RailwayEnthusiast2025|Talk page]] - [[Special:Contributions|Contributions]]) 16:23, 28 March 2025 (UTC)
::::::@@[[User:RailwayEnthusiast2025|RailwayEnthusiast2025]] Forming a non-affiliated club is a straightforward process. Gather a group of interested individuals and create a simple page on Meta-Wiki outlining the club’s purpose and how others can join and start editing. If your club focuses on a specific theme, such as medicine or the arts, you can mention it on the page.
::::::However, if you intend to establish a university- or school-affiliated club, you should seek permission from the institution. Start by submitting a formal application to the relevant authority at your college or university. [[User:511KeV|511KeV]] ([[User talk:511KeV|discuss]] • [[Special:Contributions/511KeV|contribs]]) 13:26, 29 March 2025 (UTC)
:::::::The latter is what I intend to do, and thanks for the help. I will start working on it soon. —[[User:RailwayEnthusiast2025|RailwayEnthusiast2025]] ([[User talk:RailwayEnthusiast2025|Talk page]] - [[Special:Contributions|Contributions]]) 14:23, 29 March 2025 (UTC)

== Global ban proposal for Shāntián Tàiláng ==

Hello. This is to notify the community that there is an ongoing global ban proposal for [[species:User:Shāntián_Tàiláng|User:Shāntián Tàiláng]] who has been active on this wiki. You are invited to participate at [[metawiki:Requests_for_comment/Global_ban_for_Shāntián_Tàiláng|m:Requests for comment/Global ban for Shāntián Tàiláng]]. [[User:Wüstenspringmaus|Wüstenspringmaus]] ([[User talk:Wüstenspringmaus|discuss]] • [[Special:Contributions/Wüstenspringmaus|contribs]]) 12:50, 2 February 2025 (UTC)

:Hi @[[User:Wüstenspringmaus|Wüstenspringmaus]], Looks like the RFC you started in an effort to  globally ban [[User:Shāntián Tàiláng]] has still not concluded. Forgive me, but I am indef-blocked on META so cannot ask there:
:* Is there no time limit on such nominations?
:* I am not familiar with the subject of this ban nomination, but I think there might be some unsupported allegations against them, such as harassment which is a serious issue. If I'm wrong please forgive me, I did spend a lot of time plowing through this lengthy page.
:* Many of us prefer to spend more of our time adding information to the wiki-projects that we are involved in and less  to endless discussions. The Nomination page on META is now '''43,962 bytes long''' and growing, and will require any new participant spend a great deal of unproductive time to come up to speed.
:Is it expectedad that the only people who Support or Oppose your nomination be personally familiar with the User in question? Cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 23:43, 16 February 2025 (UTC)

== Reminder: first part of the annual UCoC review closes soon ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;

{{Int:Please-translate}}.

This is a reminder that the first phase of the annual review period for the Universal Code of Conduct and Enforcement Guidelines will be closing soon. You can make suggestions for changes through [[d:Q614092|the end of day]], 3 February 2025. This is the first step of several to be taken for the annual review.
[[m:Special:MyLanguage/Universal_Code_of_Conduct/Annual_review|Read more information and find a conversation to join on the UCoC page on Meta]]. After review of the feedback, proposals for updated text will be published on Meta in March for another round of community review. 

Please share this information with other members in your community wherever else might be appropriate.

-- In cooperation with the U4C, [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 00:49, 3 February 2025 (UTC)
&lt;/div&gt;
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== Self-deleting pages that I nominated for deletion myself ==
In 2024, I nominated multiple pages for deletion via [[:Template:Proposed deletion]] (see also [[Special:WhatLinksHere/Template:Proposed deletion]]). The three-month protective period for most of them now expired.

Example pages: [[Astronomy outline]], [[VELS mathematics]], [[Particle mechanics]].

It would be ideal if the deleting person would be different from the nominating person. However, no one seems to be interested in deleting these pages.

Should I feel free to delete the pages I nominated myself? I think it could be okay, but I can also imagine someone being stringent about these matters and requiring the four-eye principle. One rationale for allowing deleting myself is that the English Wikiversity has only few active administrators and therefore, the four-eye principle would create too much of delay and overhead; on a more admin-populated project, the four-eye principle is more workable. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:08, 16 February 2025 (UTC)

:OK I'll bite :-)
:Looks like enwv has a different ''Proposed deletion'' notice than other wiki-projects. One thing I noticed immediately is that there is no reason or explanation required for the deletion proposal. 
:I understand that all a deletion will accomplish is to remove those articles from public view. They will still continue to exist, but only admins will see them. May I ask @[[User:Dan Polansky|Dan Polansky]], why do you believe these 3 articles should be deleted? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 23:08, 16 February 2025 (UTC)
:: I always provide a reason for deletion. And  thus, e.g. [[Astronomy outline]] states: &quot;The Nominator gave the following reason for their nomination:&quot;, &quot;too low quality to serve as a learning resource; most links are redlinks; no further reading&quot;. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:18, 17 February 2025 (UTC)
: I went ahead and deleted the three listed pages. I will wait a little longer before I proceed further. Most of the usual admins do not seem to be around, though, so the absence of opposition does not tell us much. And thus, I am proceeding at risk, and undo is possible by an admin or quasi-admin. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:41, 24 February 2025 (UTC)
:@[[User:Dan Polansky|Dan Polansky]] You proposed deletion back in October. Yes, it's fine if you are now the one to delete it. Often there is only one user at a time interested in cleaning up Wikiversity. That person does it until they choose not to. Then after a while, someone else steps up. I cleaned up my own proposed deletions for years with very few complaints. If someone wants to object, they need to be willing to speak up and review your proposed deletions. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:51, 26 February 2025 (UTC)
:: Thank you. I went ahead and quasi-deleted 3 more pages, this time by moving them to user space (since I could find the main creator). I will make more deletions or quasi-deletions later. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:47, 26 February 2025 (UTC)

==  Upcoming Language Community Meeting (Feb 28th, 14:00 UTC) and Newsletter ==

&lt;section begin=&quot;message&quot;/&gt;
Hello everyone!
[[File:WP20Symbols WIKI INCUBATOR.svg|right|frameless|150x150px|alt=An image symbolising multiple languages]]
We’re excited to announce that the next '''Language Community Meeting''' is happening soon, '''February 28th at 14:00 UTC'''! If you’d like to join, simply sign up on the '''[[mw:Wikimedia_Language_and_Product_Localization/Community_meetings#28_February_2025|wiki page]]'''.

This is a participant-driven meeting where we share updates on language-related projects, discuss technical challenges in language wikis, and collaborate on solutions. In our last meeting, we covered topics like developing language keyboards, creating the Moore Wikipedia, and updates from the language support track at Wiki Indaba.

'''Got a topic to share?''' Whether it’s a technical update from your project, a challenge you need help with, or a request for interpretation support, we’d love to hear from you! Feel free to '''reply to this message''' or add agenda items to the document '''[[etherpad:p/language-community-meeting-feb-2025|here]]'''.

Also, we wanted to highlight that the sixth edition of the Language &amp; Internationalization newsletter (January 2025) is available here: [[:mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2025/January|Wikimedia Language and Product Localization/Newsletter/2025/January]]. This newsletter provides updates from the October–December 2024 quarter on new feature development, improvements in various language-related technical projects and support efforts, details about community meetings, and ideas for contributing to projects. To stay updated, you can subscribe to the newsletter on its wiki page: [[:mw:Wikimedia Language and Product Localization/Newsletter|Wikimedia Language and Product Localization/Newsletter]].

We look forward to your ideas and participation at the language community meeting, see you there!
&lt;section end=&quot;message&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 08:29, 22 February 2025 (UTC)
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== Replicate [[c:Template:Imagestack]] ==

I find this feature on Commons quite practical, and would like to use it on Wikiversity. But just copying the content to {{tl|Imagestack}} is not enough. The example on {{tl|Imagestack/sandbox}} remains static. Does someone know how to implement the JavaScript? [[User:Watchduck|Watchduck]] &lt;small&gt;([[User talk:Watchduck|quack]])&lt;/small&gt; 18:31, 26 February 2025 (UTC)

:I don't know how to implement the JavaScript here. I haven't used the Imagestack feature before. —[[User:RailwayEnthusiast2025|RailwayEnthusiast2025]] ([[User talk:RailwayEnthusiast2025|Talk page]] - [[Special:Contributions|Contributions]]) 21:11, 20 March 2025 (UTC)

== Universal Code of Conduct annual review: proposed changes are available for comment ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;

{{Int:Please-translate}}.

I am writing to you to let you know that [[m:Special:MyLanguage/Universal_Code_of_Conduct/Annual_review/Proposed_Changes|proposed changes]] to the [[foundation:Special:MyLanguage/Policy:Universal_Code_of_Conduct/Enforcement_guidelines|Universal Code of Conduct (UCoC) Enforcement Guidelines]] and [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Charter|Universal Code of Conduct Coordinating Committee (U4C) Charter]] are open for review. '''[[m:Special:MyLanguage/Universal_Code_of_Conduct/Annual_review/Proposed_Changes|You can provide feedback on suggested changes]]''' through the [[d:Q614092|end of day]] on Tuesday, 18 March 2025. This is the second step in the annual review process, the final step will be community voting on the proposed changes.
[[m:Special:MyLanguage/Universal_Code_of_Conduct/Annual_review|Read more information and find relevant links about the process on the UCoC annual review page on Meta]].

The [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee|Universal Code of Conduct Coordinating Committee]] (U4C) is a global group dedicated to providing an equitable and consistent implementation of the UCoC. This annual review was planned and implemented by the U4C. For more information and the responsibilities of the U4C, [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Charter|you may review the U4C Charter]].

Please share this information with other members in your community wherever else might be appropriate.

-- In cooperation with the U4C, [[m:User:Keegan (WMF)|Keegan (WMF)]] 18:52, 7 March 2025 (UTC)

&lt;/div&gt;
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== Your wiki will be in read-only soon ==

&lt;section begin=&quot;server-switch&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;

[[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-Tech%2FServer+switch&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]

The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster.

All traffic will switch on '''{{#time:j xg|2025-03-19|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2025-03-19T14:00|en}} {{#time:H:i e|2025-03-19T14:00}}]'''.

Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. 

A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. 

'''You will be able to read, but not edit, all wikis for a short period of time.'''

*You will not be able to edit for up to an hour on {{#time:l j xg Y|2025-03-19|en}}.
*If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case.

''Other effects'':

*Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped.
* We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards.
* [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes.

This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. 

'''Please share this information with your community.'''&lt;/div&gt;&lt;section end=&quot;server-switch&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:14, 14 March 2025 (UTC)
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== Wikidata and Sister Projects: an online event ==

Hello everyone, I’m writing to announce an upcoming event called [[wikidata:Event:Wikidata and Sister Projects|'''Wikidata and Sister Projects''']] that will be a mini online conference to highlight the different ways Wikidata can be connected and integrated with the other WM projects.

We are currently looking for session ideas and speakers for our program and wanted to reach out in case there were any editors here that might have a cool idea for a session proposal. Sessions can be found on the [[wikidata:Event talk:Wikidata and Sister Projects|'''event discussion page''']].

As previously mentioned, we would like to showcase the relationship between Wikibooks and Wikidata, such as the storing of metadata and sitelinking between books and their respective Wikidata items. Do you have an idea for a session? We'd love to hear about it!

The event is scheduled between '''May 29 - June 1st, 2025'''. If you have any questions about the event, would like more information or have a session idea to propose, please feel free to get in touch by replying to this post or writing on the event page or on my [[v:User_talk:Danny_Benjafield_(WMDE)|talk page]]. Thanks for reading, - [[wikidata:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[wikidata:User talk:Danny Benjafield (WMDE)|&lt;span class=&quot;signature-talk&quot;&gt;{{int:Talkpagelinktext}}&lt;/span&gt;]]) 07:48, 1 April 2025 (UTC)

== Final proposed modifications to the Universal Code of Conduct Enforcement Guidelines and U4C Charter now posted ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;
The proposed modifications to the [[foundation:Special:MyLanguage/Policy:Universal_Code_of_Conduct/Enforcement_guidelines|Universal Code of Conduct Enforcement Guidelines]] and the U4C Charter [[m:Universal_Code_of_Conduct/Annual_review/2025/Proposed_Changes|are now on Meta-wiki for community notice]] in advance of the voting period. This final draft was developed from the previous two rounds of community review. Community members will be able to vote on these modifications starting on 17 April 2025. The vote will close on 1 May 2025, and results will be announced no later than 12 May 2025. The U4C election period, starting with a call for candidates, will open immediately following the announcement of the review results. More information will be posted on [[m:Special:MyLanguage//Universal_Code_of_Conduct/Coordinating_Committee/Election|the wiki page for the election]] soon.

Please be advised that this process will require more messages to be sent here over the next two months. 

The [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee|Universal Code of Conduct Coordinating Committee (U4C)]] is a global group dedicated to providing an equitable and consistent implementation of the UCoC. This annual review was planned and implemented by the U4C. For more information and the responsibilities of the U4C, you may [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Charter|review the U4C Charter]].

Please share this message with members of your community so they can participate as well.

-- In cooperation with the U4C, [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User_talk:Keegan (WMF)|talk]]) 02:05, 4 April 2025 (UTC)
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== Wikidata and Sister Projects: An online community event ==

''(Apologies for posting in English)''

Hello everyone, I am excited to share news of an upcoming online event called '''[[d:Event:Wikidata_and_Sister_Projects|Wikidata and Sister Projects]]''' celebrating the different ways Wikidata can be used to support or enhance with another Wikimedia project. The event takes place over 4 days between '''May 29 - June 1st, 2025'''.

We would like to invite speakers to present at this community event, to hear success stories, challenges, showcase tools or projects you may be working on, where Wikidata has been involved in Wikipedia, Commons, WikiSource and all other WM projects.

If you are interested in attending, please [[d:Special:RegisterForEvent/1291|register here]].
If you would like to speak at the event, please fill out this Session Proposal template on the [[d:Event_talk:Wikidata_and_Sister_Projects|event talk page]], where you can also ask any questions you may have. 

I hope to see you at the event, in the audience or as a speaker, - [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 09:18, 11 April 2025 (UTC)
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== Vote now on the revised UCoC Enforcement Guidelines and U4C Charter ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;

The voting period for the revisions to the Universal Code of Conduct Enforcement Guidelines (&quot;UCoC EG&quot;) and the UCoC's Coordinating Committee Charter is open now through the end of 1 May (UTC) ([https://zonestamp.toolforge.org/1746162000 find in your time zone]). [[m:Special:MyLanguage/Universal_Code_of_Conduct/Annual_review/2025/Voter_information|Read the information on how to participate and read over the proposal before voting]] on the UCoC page on Meta-wiki.

The [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee|Universal Code of Conduct Coordinating Committee (U4C)]] is a global group dedicated to providing an equitable and consistent implementation of the UCoC. This annual review of the EG and Charter was planned and implemented by the U4C. Further information will be provided in the coming months about the review of the UCoC itself. For more information and the responsibilities of the U4C, you may [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Charter|review the U4C Charter]].

Please share this message with members of your community so they can participate as well.

In cooperation with the U4C -- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User_talk:Keegan (WMF)|talk]]) 00:35, 17 April 2025 (UTC)
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== FYI: Can Citizen Science Be Trusted? New Study of Birds Shows It Can ==

https://www.ucdavis.edu/news/can-citizen-science-be-trusted-new-study-birds-shows-it-can —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:08, 23 April 2025 (UTC)

== Vote on proposed modifications to the UCoC Enforcement Guidelines and U4C Charter ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
The voting period for the revisions to the Universal Code of Conduct Enforcement Guidelines and U4C Charter closes on 1 May 2025 at 23:59 UTC ([https://zonestamp.toolforge.org/1746162000 find in your time zone]). [[m:Special:MyLanguage/Universal Code of Conduct/Annual review/2025/Voter information|Read the information on how to participate and read over the proposal before voting]] on the UCoC page on Meta-wiki.

The [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Universal Code of Conduct Coordinating Committee (U4C)]] is a global group dedicated to providing an equitable and consistent implementation of the UCoC. This annual review was planned and implemented by the U4C. For more information and the responsibilities of the U4C, you may [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Charter|review the U4C Charter]].

Please share this message with members of your community in your language, as appropriate, so they can participate as well.

In cooperation with the U4C -- &lt;section end=&quot;announcement-content&quot; /&gt;

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;
[[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 03:41, 29 April 2025 (UTC)&lt;/div&gt;
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== Question Centre ==

I have a question: 

'''1.''''Is it possible to change your username? Or is it permament? 

''Antworte zu meinem Kommentar, und Ich werde zu dir abonnieren. ''

[[User:Kumpa-pasión|Kumpa-pasión]] ([[User talk:Kumpa-pasión|discuss]] • [[Special:Contributions/Kumpa-pasión|contribs]]) 15:18, 30 April 2025 (UTC)

:Hello {{ping|Kumpa-pasión}} To change your username, you can go to [https://meta.wikimedia.org/wiki/Special:GlobalRenameRequest Special:GlobalRenameRequest]. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:42, 2 May 2025 (UTC)

== Names of pages I am creating, one man's look at X ==
I am creating pages like [[One man's look at LibreOffice]], but I am increasingly dissatisfied with this naming scheme. It just means that &quot;One man's look at X&quot; is nothing but &quot;Dan Polansky's look at X&quot;; what is so special about Dan Polansky that he is the &quot;one man&quot;, which other people are not? I prefer &quot;X (Dan Polansky)&quot;, but that was previously rejected (I should find the discussion, but I am too lazy now). What was not rejected is &quot;X/Dan Polansky&quot; (as in [[COVID-19/Dan Polansky]]), but I find it greatly suboptimal: there is nothing in that syntax that suggests that &quot;Dan Polansky&quot; is an author name; compare a possible &quot;Philosophy/Aristotle&quot;, which would be ''about'' Aristotle and not ''by'' Aristotle.

Perhaps we can have a discussion/conversation about alternative proposals and what makes them preferable and dispreferable, desirable and undesirable? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:07, 1 May 2025 (UTC)
: If a main space page is meant only for one user's view, then perhaps that page should instead be located in that user's space. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:12, 17 May 2025 (UTC)
:: That would not work: pages in user space are not Google search indexed, from what I understand. One's spending effort to write and publish an article and then having it ignored by readers since not found via Google Search is not rewarding; I do not see why people would like to do it, and they apparently don't. Moreover, since other editors can comment on the article on the talk page, it is vital that the author does not have the right to have the article deleted on a whim; an article should be deleted only in well justified rare cases (ethical breach, etc.).
:: I think that a page being author-specific should be the usual case, not the rare case, in Wikiversity. It is the case with Wikijournal articles. It also seems to be the case with the Motivation and Emotion pages, e.g. as listed in [[Motivation and emotion/Book/2024]]; and thus, e.g. [[Motivation and emotion/Book/2024/Abusive supervision]] has TJDuus as the main author as per the assignment and revision history (there are auxiliary editors, but the author seems to maintain editorial control?)
:: Since Wikiversity pages are not organized by the principle of being encyclopedic and by avoidance of original research, I do not see how the free-for-all editing of Wikipedia could possibly work here.
:: Some of the best materials I have seen in the English Wikiversity either have a single author or single main author. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:10, 17 May 2025 (UTC)

== We will be enabling the new Charts extension on your wiki soon! ==

''(Apologies for posting in English)''

Hi all! We have good news to share regarding the ongoing problem with graphs and charts affecting all wikis that use them.

As you probably know, the [[:mw:Special:MyLanguage/Extension:Graph|old Graph extension]] was disabled in 2023 [[listarchive:list/wikitech-l@lists.wikimedia.org/thread/EWL4AGBEZEDMNNFTM4FRD4MHOU3CVESO/|due to security reasons]]. We’ve worked in these two years to find a solution that could replace the old extension, and provide a safer and better solution to users who wanted to showcase graphs and charts in their articles. We therefore developed the [[:mw:Special:MyLanguage/Extension:Chart|Charts extension]], which will be replacing the old Graph extension and potentially also the [[:mw:Extension:EasyTimeline|EasyTimeline extension]].

After successfully deploying the extension on Italian, Swedish, and Hebrew Wikipedia, as well as on MediaWiki.org, as part of a pilot phase, we are now happy to announce that we are moving forward with the next phase of deployment, which will also include your wiki.

The deployment will happen in batches, and will start from '''May 6'''. Please, consult [[:mw:Special:MyLanguage/Extension:Chart/Project#Deployment Timeline|our page on MediaWiki.org]] to discover when the new Charts extension will be deployed on your wiki. You can also [[:mw:Special:MyLanguage/Extension:Chart|consult the documentation]] about the extension on MediaWiki.org.

If you have questions, need clarifications, or just want to express your opinion about it, please refer to the [[:mw:Special:MyLanguage/Extension_talk:Chart/Project|project’s talk page on Mediawiki.org]], or ping me directly under this thread. If you encounter issues using Charts once it gets enabled on your wiki, please report it on the [[:mw:Extension_talk:Chart/Project|talk page]] or at [[phab:tag/charts|Phabricator]].

Thank you in advance! -- [[User:Sannita (WMF)|User:Sannita (WMF)]] ([[User talk:Sannita (WMF)|talk]]) 15:07, 6 May 2025 (UTC)
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== Progressive translations ==

If you gradually translate more and more words in a text it's called &quot;progressive translation&quot; apparently. If we were doing, say, English to Hungarian it would look like &quot;I took the ''vonat'' (train) to Budapest&quot; and later on &quot;I saw the river from the ''vonat''&quot;. I want to be able to read novels and pick up vocabulary in this way, as well as make them (or rather get an AI to make them) and share them with other language learners. 

It's education so I thought you might be interested in hosting them, and maybe some people here would be interested in helping out. Thanks for any feedback [[User:Progressive translator|Progressive translator]] ([[User talk:Progressive translator|discuss]] • [[Special:Contributions/Progressive translator|contribs]]) 16:54, 6 May 2025 (UTC)

== Call for Candidates for the Universal Code of Conduct Coordinating Committee (U4C) ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
The results of voting on the Universal Code of Conduct Enforcement Guidelines and Universal Code of Conduct Coordinating Committee (U4C) Charter is [[m:Special:MyLanguage/Universal Code of Conduct/Annual review/2025#Results|available on Meta-wiki]].

You may now [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2025/Candidates|submit your candidacy to serve on the U4C]] through 29 May 2025 at 12:00 UTC. Information about [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2025|eligibility, process, and the timeline are on Meta-wiki]]. Voting on candidates will open on 1 June 2025 and run for two weeks, closing on 15 June 2025 at 12:00 UTC.

If you have any questions, you can ask on [[m:Talk:Universal Code of Conduct/Coordinating Committee/Election/2025|the discussion page for the election]]. -- in cooperation with the U4C, &lt;section end=&quot;announcement-content&quot; /&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User_talk:Keegan (WMF)|discuss]])&lt;/bdi&gt; 22:08, 15 May 2025 (UTC)
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== RfC ongoing regarding Abstract Wikipedia (and your project) ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;
''(Apologies for posting in English, if this is not your first language)''

Hello all! We opened a discussion on Meta about a very delicate issue for the development of [[:m:Special:MyLanguage/Abstract Wikipedia|Abstract Wikipedia]]: where to store the abstract content that will be developed through functions from Wikifunctions and data from Wikidata. Since some of the hypothesis involve your project, we wanted to hear your thoughts too. 

We want to make the decision process clear: we do not yet know which option we want to use, which is why we are consulting here. We will take the arguments from the Wikimedia communities into account, and we want to consult with the different communities and hear arguments that will help us with the decision. The decision will be made and communicated after the consultation period by the Foundation.

You can read the various hypothesis and have your say at [[:m:Abstract Wikipedia/Location of Abstract Content|Abstract Wikipedia/Location of Abstract Content]]. Thank you in advance! -- [[User:Sannita (WMF)|Sannita (WMF)]] ([[User talk:Sannita (WMF)|&lt;span class=&quot;signature-talk&quot;&gt;{{int:Talkpagelinktext}}&lt;/span&gt;]]) 15:27, 22 May 2025 (UTC)
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== Wikimedia Foundation Board of Trustees 2025 Selection &amp; Call for Questions ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[[m:Special:MyLanguage/Wikimedia Foundation elections/2025/Announcement/Selection announcement|{{int:interlanguage-link-mul}}]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Wikimedia Foundation elections/2025/Announcement/Selection announcement}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Dear all,

This year, the term of 2 (two) Community- and Affiliate-selected Trustees on the Wikimedia Foundation Board of Trustees will come to an end [1]. The Board invites the whole movement to participate in this year’s selection process and vote to fill those seats.

The Elections Committee will oversee this process with support from Foundation staff [2]. The Governance Committee, composed of trustees who are not candidates in the 2025 community-and-affiliate-selected trustee selection process (Raju Narisetti, Shani Evenstein Sigalov, Lorenzo Losa, Kathy Collins, Victoria Doronina and Esra’a Al Shafei) [3], is tasked with providing Board oversight for the 2025 trustee selection process and for keeping the Board informed. More details on the roles of the Elections Committee, Board, and staff are here [4].

Here are the key planned dates:

* May 22 – June 5: Announcement (this communication) and call for questions period [6]
* June 17 – July 1, 2025: Call for candidates
* July 2025: If needed, affiliates vote to shortlist candidates if more than 10 apply [5]
* August 2025: Campaign period
* August – September 2025: Two-week community voting period
* October – November 2025: Background check of selected candidates
* Board’s Meeting in December 2025: New trustees seated

Learn more about the 2025 selection process - including the detailed timeline, the candidacy process, the campaign rules, and the voter eligibility criteria - on this Meta-wiki page [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2025|[link]]].

'''Call for Questions'''

In each selection process, the community has the opportunity to submit questions for the Board of Trustees candidates to answer. The Election Committee selects questions from the list developed by the community for the candidates to answer. Candidates must answer all the required questions in the application in order to be eligible; otherwise their application will be disqualified. This year, the Election Committee will select 5 questions for the candidates to answer. The selected questions may be a combination of what’s been submitted from the community, if they’re alike or related. [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2025/Questions_for_candidates|[link]]]

'''Election Volunteers'''

Another way to be involved with the 2025 selection process is to be an Election Volunteer. Election Volunteers are a bridge between the Elections Committee and their respective community. They help ensure their community is represented and mobilize them to vote. Learn more about the program and how to join on this Meta-wiki page [[m:Wikimedia_Foundation_elections/2025/Election_volunteers|[link].]]

Thank you!

[1] https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections/2022/Results

[2] https://foundation.wikimedia.org/wiki/Committee:Elections_Committee_Charter

[3] https://foundation.wikimedia.org/wiki/Resolution:Committee_Membership,_December_2024

[4] https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections_committee/Roles

[5] https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections/2025/FAQ

[6] https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections/2025/Questions_for_candidates

Best regards,

Victoria Doronina

Board Liaison to the Elections Committee

Governance Committee&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 03:08, 28 May 2025 (UTC)
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== Vote now in the 2025 U4C Election ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;

{{Int:Please-translate}}

Eligible voters are asked to participate in the 2025 [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee|Universal Code of Conduct Coordinating Committee]] election. More information–including an eligibility check, voting process information, candidate information, and a link to the vote–are available on Meta at the [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Election/2025|2025 Election information page]]. The vote closes on 17 June 2025 at [https://zonestamp.toolforge.org/1750161600 12:00 UTC].

Please vote if your account is eligible. Results will be available by 1 July 2025. -- In cooperation with the U4C, [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 23:01, 13 June 2025 (UTC) &lt;/div&gt;
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== Geometric growth in views ==

Wikiversity seems to be experiencing an [https://stats.wikimedia.org/#/en.wikiversity.org/reading/total-page-views/normal|bar|all|~total|monthly unprecedented amount of traffic], literally doubling in May '25 with almost 60 million monthly views. (Note practically no growth from 2016-24. From a [[Wikiversity:Colloquium/archives/December_2024#An_unexplained_spurt_of_Wikiversity_page_views|previous thread's link]], this is only partially reflected on the [https://pageviews.wmcloud.org/siteviews/?platform=all-access&amp;source=pageviews&amp;agent=user&amp;range=this-year&amp;sites=en.wikiversity.org|en.wikibooks.org|en.wikiquote.org|en.wikisource.org Pageviews widget], except for Wikisource somewhat.)

I haven't seen any corresponding unprecedented [https://stats.wikimedia.org/#/en.wikiversity.org/contributing/active-editors/normal%7Cline%7Call%7C(page_type)~content*non-content%7Cmonthly activity] however. Anyone know what's up? LLM crawling maybe? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 21:56, 15 June 2025 (UTC)

:I can only assume that it's AI, yes. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:17, 18 June 2025 (UTC)

== Wikimedia Foundation Board of Trustees 2025 - Call for Candidates ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:&lt;div class=&quot;plainlinks&quot;&gt;''[[m:Special:MyLanguage/Wikimedia Foundation elections/2025/Announcement/Call for candidates|{{int:interlanguage-link-mul}}]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Wikimedia Foundation elections/2025/Announcement/Call for candidates}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''&lt;/div&gt;
Hello all,

The [[m:Special:MyLanguage/Wikimedia Foundation elections/2025|call for candidates for the 2025 Wikimedia Foundation Board of Trustees selection is now open]] from June 17, 2025 – July 2, 2025 at 11:59 UTC [1]. The Board of Trustees oversees the Wikimedia Foundation's work, and each Trustee serves a three-year term [2]. This is a volunteer position.

This year, the Wikimedia community will vote in late August through September 2025 to fill two (2) seats on the Foundation Board. Could you – or someone you know – be a good fit to join the Wikimedia Foundation's Board of Trustees? [3]

Learn more about what it takes to stand for these leadership positions and how to submit your candidacy on [[m:Special:MyLanguage/Wikimedia Foundation elections/2025/Candidate application|this Meta-wiki page]] or encourage someone else to run in this year's election.

Best regards,

Abhishek Suryawanshi&lt;br /&gt;
Chair of the Elections Committee

On behalf of the Elections Committee and Governance Committee

[1] https://meta.wikimedia.org/wiki/Special:MyLanguage/Wikimedia_Foundation_elections/2025/Call_for_candidates

[2] https://foundation.wikimedia.org/wiki/Legal:Bylaws#(B)_Term.

[3] https://meta.wikimedia.org/wiki/Special:MyLanguage/Wikimedia_Foundation_elections/2025/Resources_for_candidates&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:44, 17 June 2025 (UTC)
&lt;!-- Message sent by User:RamzyM (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=28866958 --&gt;

== Sister Projects Task Force reviews Wikispore and Wikinews ==

&lt;section begin=&quot;message&quot;/&gt;
Dear Wikimedia Community,

The [[m:Wikimedia Foundation Community Affairs Committee|Community Affairs Committee (CAC)]]  of the Wikimedia Foundation Board of Trustees assigned [[m:Wikimedia Foundation Community Affairs Committee/Sister Projects Task Force|the Sister Projects Task Force (SPTF)]] to update and implement a procedure for assessing the lifecycle of Sister Projects – wiki [[m:Wikimedia projects|projects supported by Wikimedia Foundation (WMF)]].

A vision of relevant, accessible, and impactful free knowledge has always guided the Wikimedia Movement. As the ecosystem of Wikimedia projects continues to evolve, it is crucial that we periodically review existing projects to ensure they still align with our goals and community capacity.

Despite their noble intent, some projects may no longer effectively serve their original purpose. '''Reviewing such projects is not about giving up – it's about responsible stewardship of shared resources'''. Volunteer time, staff support, infrastructure, and community attention are finite, and the non-technical costs tend to grow significantly as our ecosystem has entered a different age of the internet than the one we were founded in. Supporting inactive projects or projects that didn't meet our ambitions can unintentionally divert these resources from areas with more potential impact.

Moreover, maintaining projects that no longer reflect the quality and reliability of the Wikimedia name stands for, involves a reputational risk. An abandoned or less reliable project affects trust in the Wikimedia movement.

Lastly, '''failing to sunset or reimagine projects that are no longer working can make it much harder to start new ones'''. When the community feels bound to every past decision – no matter how outdated – we risk stagnation. A healthy ecosystem must allow for evolution, adaptation, and, when necessary, letting go. If we create the expectation that every project must exist indefinitely, we limit our ability to experiment and innovate.

Because of this, SPTF reviewed two requests concerning the lifecycle of the Sister Projects to work through and demonstrate the review process. We chose Wikispore as a case study for a possible new Sister Project opening and Wikinews as a case study for a review of an existing project. Preliminary findings were discussed with the CAC, and a community consultation on both proposals was recommended.

=== Wikispore ===

The [[m:Wikispore|application to consider Wikispore]] was submitted in 2019. SPTF decided to review this request in more depth because rather than being concentrated on a specific topic, as most of the proposals for the new Sister Projects are, Wikispore has the potential to nurture multiple start-up Sister Projects.

After careful consideration, the SPTF has decided '''not to recommend''' Wikispore as a Wikimedia Sister Project. Considering the current activity level, the current arrangement allows '''better flexibility''' and experimentation while WMF provides core infrastructural support. 

We acknowledge the initiative's potential and seek community input on what would constitute a sufficient level of activity and engagement to reconsider its status in the future.

As part of the process, we shared the decision with the Wikispore community and invited one of its leaders, Pharos, to an SPTF meeting.

Currently, we especially invite feedback on measurable criteria indicating the project's readiness, such as contributor numbers, content volume, and sustained community support. This would clarify the criteria sufficient for opening a new Sister Project, including possible future Wikispore re-application. However, the numbers will always be a guide because any number can be gamed.

=== Wikinews ===

We chose to review Wikinews among existing Sister Projects because it is the one for which we have observed the highest level of concern in multiple ways.

Since the SPTF was convened in 2023, its members have asked for the community's opinions during conferences and community calls about Sister Projects that did not fulfil their promise in the Wikimedia movement.[https://commons.wikimedia.org/wiki/File:WCNA_2024._Sister_Projects_-_opening%3F_closing%3F_merging%3F_splitting%3F.pdf &lt;nowiki&gt;[1]&lt;/nowiki&gt;][https://meta.wikimedia.org/wiki/Wikimedia_Foundation_Community_Affairs_Committee/Sister_Projects_Task_Force#Wikimania_2023_session_%22Sister_Projects:_past,_present_and_the_glorious_future%22 &lt;nowiki&gt;[2]&lt;/nowiki&gt;][https://meta.wikimedia.org/wiki/WikiConvention_francophone/2024/Programme/Quelle_proc%C3%A9dure_pour_ouvrir_ou_fermer_un_projet_%3F &lt;nowiki&gt;[3]&lt;/nowiki&gt;] Wikinews was the leading candidate for an evaluation because people from multiple language communities proposed it. Additionally, by most measures, it is the least active Sister Project, with the greatest drop in activity over the years.

While the Language Committee routinely opens and closes language versions of the Sister Projects in small languages, there has never been a valid proposal to close Wikipedia in major languages or any project in English. This is not true for Wikinews, where there was a proposal to close English Wikinews, which gained some traction but did not result in any action[https://meta.wikimedia.org/wiki/Proposals_for_closing_projects/Closure_of_English_Wikinews &lt;nowiki&gt;[4]&lt;/nowiki&gt;][https://meta.wikimedia.org/wiki/WikiConvention_francophone/2024/Programme/Quelle_proc%C3%A9dure_pour_ouvrir_ou_fermer_un_projet_%3F &lt;nowiki&gt;[5]&lt;/nowiki&gt;, see section 5] as well as a draft proposal to close all languages of Wikinews[https://meta.wikimedia.org/wiki/Talk:Proposals_for_closing_projects/Archive_2#Close_Wikinews_completely,_all_languages? &lt;nowiki&gt;[6]&lt;/nowiki&gt;].

[[:c:File:Sister Projects Taskforce Wikinews review 2024.pdf|Initial metrics]] compiled by WMF staff also support the community's concerns about Wikinews.

Based on this report, SPTF recommends a community reevaluation of Wikinews. We conclude that its current structure and activity levels are the lowest among the existing sister projects. SPTF also recommends pausing the opening of new language editions while the consultation runs.

SPTF brings this analysis to a discussion and welcomes discussions of alternative outcomes, including potential restructuring efforts or integration with other Wikimedia initiatives.

'''Options''' mentioned so far (which might be applied to just low-activity languages or all languages) include but are not limited to:
*Restructure how Wikinews works and is linked to other current events efforts on the projects,
*Merge the content of Wikinews into the relevant language Wikipedias, possibly in a new namespace,
*Merge content into compatibly licensed external projects,
*Archive Wikinews projects.
Your insights and perspectives are invaluable in shaping the future of these projects. We encourage all interested community members to share their thoughts on the relevant discussion pages or through other designated feedback channels.

=== Feedback and next steps ===

We'd be grateful if you want to take part in a conversation on the future of these projects and the review process. We are setting up two different project pages: [[m:Public consultation about Wikispore|Public consultation about Wikispore]] and [[m:Public consultation about Wikinews|Public consultation about Wikinews]]. Please participate between 27 June 2025 and 27 July 2025, after which we will summarize the discussion to move forward. You can write in your own language.

I will also host a community conversation 16th July Wednesday 11.00 UTC and 17th July Thursday 17.00 UTC (call links to follow shortly) and will be around at Wikimania for more discussions. 
&lt;section end=&quot;message&quot;/&gt;

-- [[User:Victoria|Victoria]] on behalf of the Sister Project Task Force, 20:57, 27 June 2025 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=User:Johan_(WMF)/Sister_project_MassMassage_on_behalf_of_Victoria/Target_list&amp;oldid=28911188 --&gt;</text>
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  <page>
    <title>Wikiversity:Sandbox</title>
    <ns>4</ns>
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    <revision>
      <id>2720869</id>
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      <contributor>
        <username>Ruud Loeffen</username>
        <id>2998353</id>
      </contributor>
      <comment>add evaluation 8.8.11 Topological Field Framework – AI Rating Summary</comment>
      <origin>2720869</origin>
      <model>wikitext</model>
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      <text bytes="2199" sha1="ib5cwwk1jmshihwn7sluyy3u5uzd6k1" xml:space="preserve">{{Please leave this line alone (sandbox heading)}}

=== '''8.8.11 Topological Field Framework – AI Rating Summary''' ===

''Related link:'' [https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework on ResearchGate]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Proposes a geometric origin of particle properties and fundamental constants, but lacks direct comparison with observational or experimental datasets. Empirical testing is suggested but not yet demonstrated. || ★★☆☆☆
|-
| '''Internal Consistency''' || Builds a coherent and logically structured model grounded in topology and pressure gradients. Concepts are well integrated, with minimal contradictions. || ★★★★☆
|-
| '''Predictive Power''' || Offers a pathway to derive constants such as G, c, and Λ from topology and boundary conditions. However, quantitative predictions are still under development or pending validation. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges gravitational theory, particle physics, and topology. Aligns with ideas in quantum geometry, though not yet embedded in mainstream formulations. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Dense but conceptually focused. Uses field and pressure analogies to unify gravity and gauge interactions, though the abstract nature may limit accessibility. || ★★★☆☆
|-
| '''Heuristic Value''' || Provides an original and stimulating approach to unify physical constants via geometry. Encourages rethinking of foundational assumptions in physics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Revives geometrical unification ideals from early 20th-century physics and connects them to modern field-based ontology. Philosophically grounded. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs differential geometry, topological mapping, and field pressure modeling. Mathematical structure is present, but derivations are at a conceptual stage. || ★★★☆☆
|}

'''Total: 27/40'''</text>
      <sha1>ib5cwwk1jmshihwn7sluyy3u5uzd6k1</sha1>
    </revision>
  </page>
  <page>
    <title>Wikiversity:Blocking policy</title>
    <ns>4</ns>
    <id>2074</id>
    <revision>
      <id>2720888</id>
      <parentid>2648843</parentid>
      <timestamp>2025-07-06T08:49:24Z</timestamp>
      <contributor>
        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <minor />
      <comment>/* Common rationales for blocks */</comment>
      <origin>2720888</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5388" sha1="7hgtc0q9x9o6ftaz83ml1v9qsoywtea" xml:space="preserve">{{proposal|WV:BLOCK|WV:BP}}

The '''blocking policy''' explains when and why [[WV:A|custodians]] may block or unblock [[Wikiversity:Types of user accounts|user accounts]], IP addresses, and ranges of IP addresses. The [[Special:Log/block|block log]] allows anyone to track blocks and unblocks at [[Wikiversity]]. A '''block''' revokes editing privileges at Wikiversity to stop behavior inconsistent with the Wikiversity [[Wikiversity:Mission|mission]] and [[Wikiversity:What is Wikiversity|scope]] for either a definite or indefinite time. An '''unblock''' restores editing privileges at Wikiversity after accepted practices and [[Wikiversity:Civility|appropriate behaviors]] are likely to be understood. A block does not otherwise restrict access to Wikiversity, and usually people can continue to edit their own user discussion page to encourage dialog about [[Wikiversity:Who are Wikiversity participants?| participation at Wikiversity]].

Anyone may [[Wikiversity:RCA|ask custodians]] to consider reviewing a person's recent behavior. If you are blocked and feel that you understand how to behave in a way consistent with the mission and scope, you can ask for the decision to be reviewed on your discussion page, or by e-mail if you cannot edit your discussion page.

== When are blocks appropriate? ==
Firstly, [[WV:AGF|assume good faith]] and ask questions and discuss concerns on a user's [[Help:Talk page|user discussion page]]. Be concise and specific when suggesting solutions, explain and encourage behaviors consistent with the [[Wikiversity:Mission|Wikiversity mission]] and scope to [[Wikiversity:Be bold|resolve conflicts yourself]], and try [[Wikiversity:Civility|alternatives]] when appropriate.

On occasion, a block may be appropriate after a good faith discussion, other reasonable solutions have been exhausted, and the person continues behaviors not consistent with participation at Wikiversity. People who [[Wikiversity:Vandalism|vandalize]] and [[Wikiversity:External links|spam]] may be blocked immediately before considering anything else.

The following caveats apply to blocks:

# Blocks for behavior that has ceased or may happen in the future are inappropriate. Blocks are to deter continuing recent behavior.
# Participants with a history of good faith edits are to be informed about their block on their user discussion page.
# A custodian capable of impartial treatment is recommended when possible. Other custodians should [[WV:RCA|ask for a second opinion]].
# Blocks for IP addresses and IP address ranges should be kept short because often other people are affected too.

== Common rationales for blocks ==
{{shortcut|WV:EVASION}}
Custodians are encouraged to first discuss when in doubt, or when a block is unusual. The following are common rationales for blocks:

{{MultiCol}}
* '''Threats''' to take legal action (&quot;[[w:legal threat|legal threat]]&quot;) or to cause harm (&quot;[[w:Wikipedia:Threats of violence|malice]]&quot;).
* '''[[Wikiversity:Privacy policy|Disclosure of personal information]]''' without consent.
* '''Libelous material''' about living people.
* Persistent '''harassment''' or '''[[w:Wikipedia:No personal attacks|personal attacks]]'''.
* Persistent use of '''copyright works without permission'''.
* '''Use of [[Wikiversity:Username|inappropriate usernames]]'''. If unintentional, the user will be allowed a [[Wikiversity:Changing username|name change]].
{{ColBreak}}
* Persistent '''promotions''' with no clear benefit to education or learners.
* Use of multiple accounts to '''affect community consensus'''.
* '''[[WV:Bots|Bots]] without approval to operate or malfunctioning''' will be immediately blocked.
* Compromised accounts
* '''Behaviors that have a net negative effect''' per community consensus.
* Circumventing revocation of privileges.
{{EndMultiCol}}

== When should unblocks be considered? ==
People whose behavior was consistent with the Wikiversity [[Wikiversity:Mission|mission]] and [[Wikiversity:What is Wikiversity|scope]] may be unblocked immediately. People who understand and agree to participate appropriately at Wikiversity may be unblocked. You are encouraged to discuss why a person was blocked, explain and encourage behaviors consistent with the Wikiversity mission and scope, and suggest solutions that may help encourage appropriate participation before you [[Wikiversity:Request custodian action|ask custodians]] to unblock. If you were blocked, you may ask custodians to review your block by adding {{tl|unblock}} to your [[Special:MyTalk|user discussion page]].

An impartial custodian may review the circumstances of a block and determine an appropriate response or action. A custodian may set conditions to ensure [[Wikiversity:Civility|civility]] and behaviors remain appropriate. Custodians may decline to act on a request to unblock, and are encouraged to [[Wikiversity:Request custodian action|ask for a second opinion]] when in doubt, or when an unblock is controversial or unusual.

Custodians may refer people to [[Wikiversity:Community Review]] when a block is based on community consensus, and link to prior community consensus for review.

==See also==
* [[Wikiversity:Blocking]]
* [[Wikiversity:Custodianship#User blocks]]
* [[Meta:No open proxies]]
* [[Meta:Global bans]]
* [[Template:Block]]
* [[Template:Blocked]]
* [[Template:Blocked user]]

{{official policies}}
{{proposed policies}}</text>
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  </page>
  <page>
    <title>Wikiversity:Bots/Status</title>
    <ns>4</ns>
    <id>2413</id>
    <revision>
      <id>2720837</id>
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      <contributor>
        <username>ShakespeareFan00</username>
        <id>6645</id>
      </contributor>
      <minor />
      <origin>2720837</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="9782" sha1="lvd0nqnfo033pr10vlu1dq2nwb3d5g6" xml:space="preserve">[[cs:Wikiverzita:Bot/Žádosti]]
[[fr:Wikiversité:Bot/Statut]]
[[it:Wikiversità:Bot/Autorizzazioni]]
[[pt:Wikiversidade:Robôs/Pedidos de aprovação]]
''This page allows bot operators to ask for approval to use a bot on the English-language Wikiversity.''

'''Please read [[Wikiversity:Bots|Wikiversity policy about bots]] first.'''

Bureaucrats are able to give and remove bot status using the [[Special:UserRights]] feature.  Request are usually handled after about 7-10 days, to allow time for comments and questions from the community.  If you do not receive a timely response to your request, feel free to leave a message on the talk page of a [http://en.wikiversity.org/w/index.php?title=Special%3AListUsers&amp;username=&amp;group=bureaucrat&amp;limit=50 Bureaucrat].

Older status requests are [[/Archive/]]d.

The wikicode below is a suggestion for formating a bot request:

&lt;pre&gt;
== BotName ==
* '''Bot name''': {{User|BotName}}
* '''Bot operator''': {{User|Name}}
* '''Automatic or manually assisted''': 
* '''Purpose of the bot''': 
* '''Edit period(s)''': 
* '''Programming language(s) (and API) used''': 
* '''Other projects that are already using this bot''': 
* '''Additional information''': 
&lt;/pre&gt;

'''Requests for bot status'''

''Add new bot requests at the bottom''

== Leaderbot ==
* '''Bot name''': {{User|Leaderbot}}
* '''Bot operator''': {{User|Leaderboard}}
* '''Automatic or manually assisted''': Automatic
* '''Purpose of the bot''': [[meta:Global_reminder_bot]]
* '''Edit period(s)''': Daily (see below though)
* '''Programming language(s) (and API) used''': Python
* '''Other projects that are already using this bot''': Wikifunctions and some projects that do not require approval for bots that do not require a bot flag. See [[meta:Global reminder bot/global]] for the full list.
* '''Additional information''': I don't expect this to be used all that much, but the bots page requires approval regardless. This will ''not'' edit in a way requiring a bot flag. [[User:Leaderboard|Leaderboard]] ([[User talk:Leaderboard|discuss]] • [[Special:Contributions/Leaderboard|contribs]]) 18:55, 22 August 2024 (UTC)

:: {{ping|Leaderboard}} Thanks for the ping on my talk page. [https://en.wikiversity.org/wiki/Special:Log?type=rights&amp;user=&amp;page=Leaderbot Leaderbot user rights activated]. Could you perhaps update here: [[Wikiversity:Bots#Currently flagged bots]]? Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:20, 19 September 2024 (UTC)
:::@[[User:Jtneill|Jtneill]] {{done}} [[User:Leaderboard|Leaderboard]] ([[User talk:Leaderboard|discuss]] • [[Special:Contributions/Leaderboard|contribs]]) 04:55, 19 September 2024 (UTC)

== Tule-bot ==
* '''Bot name''': {{User|Tule-bot}}
* '''Bot operator''': {{User|Tule-hog}}
* '''Automatic or manually assisted''': Automatic
* '''Purpose of the bot''': lua-formatted lists of highly transcluded templates
* '''Edit period(s)''': Weekly (could be made less frequent for WV)
* '''Programming language(s) (and API) used''': Python
* '''Other projects that are already using this bot''': Modeled on [[:w:User:Ahechtbot#Task 6|Ahechtbot's Task 6]]
* '''Additional information''': Currently [[Module:Transclusion count]] uses irrelevant data periodically copied from Wikipedia to this site's [[Special:PrefixIndex/Module:Transclusion_count/data/|data pages]]. A bot is required to keep the information up to date and site-specific. Somewhat confusingly, there is already a semi-active, unregistered, Wikiversity-based [[User:Ahechtbot|Ahechtbot]] but it doesn't have a Wikiversity version of &lt;code&gt;[[:w:User:Ahechtbot/transclusioncount.py|transclusioncount.py]]&lt;/code&gt;, and appears to use the transclusion count for Wikipedia-based templates, as is seen by [[Template:Edit fully-protected]] which I have just created, but claims to be used on 7,400 pages (the Wikipedia version's count), instead of the correct [https://linkcount.toolforge.org/index.php?project=en.wikiversity.org&amp;page=Template%3AEdit+fully-protected 0 pages]. (Another example is Wikiversity's [[Module:Babel]] which is actually only used on [https://linkcount.toolforge.org/index.php?project=en.wikiversity.org&amp;page=Module%3ABabel 118 pages], not 39,000.) My Lua capabilities are minimal-to-nonexistent, but I can scrounge by some Python and SQL, so I can take a crack at the task - if someone more qualified would prefer to do it, feel free! [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:36, 1 October 2024 (UTC)

== calris25bot ==
* '''Bot name''': [[User:CalRis25/calris25bot|calris25bot]]
* '''Bot operator''': [[User:CalRis25|CalRis25]]
* '''Automatic or manually assisted''': Automatic, although I do not understand the ''exact'' meaning of &quot;manually assisted&quot;. 
* '''Purpose of the bot''': The purpose is twofold: 1. Initial upload of the pages (2200 of 3200 articles pages plus about 300 REDIRECT-pages) for the project ''[[Illustrated Companion to the Latin Dictionary]]'' (see also the [[Illustrated Companion to the Latin Dictionary/RICH-2K/Project description|project's description]]). 2. Switching the article-pages from the initial version to the production version by removing a heading. For more see ''Additional information'' and the bot's description page.
* '''Edit period(s)''': The bot will be used twice: 1. Initial upload. 2. Switching the article-pages from the initial version to the production version.
* '''Programming language(s) (and API) used''': Pywikibot
* '''Other projects that are already using this bot''': None
* '''Additional information''': For more, see the bot's description page. 1. The initial upload will be done calling Pywikiboot's ''pagefromfile''-script (one call per page-creation) using the ''-minor''-parameter (= mark the edit as &quot;minor&quot;). 2. The switch from initial version of the article pages to production-version will use a single call of Pywikibot's ''replace''-script for ''all'' article pages (= 3200) pages. Note: I can change this to smaller chunks for each call of ''replace''. Please inform me, if that is wanted. '''{{Color|Red|NOTE: The project is ready to be launched and is only awaiting the upload of the rest of the articles, for which this bot-permit is necessary.}}''' [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 15:45, 29 October 2024 (UTC)

@[[User:CalRis25|CalRis25]]: Please see [[meta:Bot policy]]. &quot;A bot must be run using a separate account from the operator, as no human editor should be granted a bot flag.&quot; It does not appear as though you have created a separate account for your bot.

I'm also inclined to suggest that, perhaps, having a separate bot account shouldn't be necessary in this case. As I understand it, this will be a short-term deployment only used to upload and quickly modify pages. There is no current planned ongoing usage.

In my experience, if you limit your bot to one update every 10 seconds (or longer) and no more than 500 edits per day, you won't cause any issues and also won't get flagged for excessive edits. More than 500 per day will trigger an internal block of some type. I don't recall whether it's 60 minutes or 24 hours. I just know I hit it a couple of times myself.

If you want to work around the limitations and use your own account, please proceed. If you want to use true bot status, please create an account for your bot and let me know on my talk page. [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:11, 4 November 2024 (UTC)

:Hello Dave, thank your for the quick answer. Actually I ''did'' create an account (''calris25bot''), and Pywikibot uses it in the user-password-file. However, if I can go on without the permit, that is fine for me. These edits-by-script are indeed only for the beginning of the project. I will take care to a) mark the edits as &quot;minor&quot;, b) put a delay of at least 10 seconds between edits, and c) limit the edits to 500 per day. Bye. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 15:46, 4 November 2024 (UTC)
:Sorry, I just checked doing a test-run with 50 page-creation-edits. The &quot;minor&quot;-option doesn't seem to work for creation of pages (which ''does'' make sense). Is it okay, if I continue as detailed (minus the minor-flag for the page-creation edits)? I'm going to wait for your replay. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 16:13, 4 November 2024 (UTC)
::@[[User:CalRis25|CalRis25]]: Something didn't work as you expected. When I go to [[User:Calris25bot]], there is no account by that name. I can't say why. I only know it's not there. And there's no way to approve bot status on a non-account.
::To confirm, look at the edit history on the pages your bot is editing. If they show your account, the bot is operating as you. If they show something else, please provide a page link so I can check the history and see what account it is using.
::I don't think you'll run into any problems as long as you limit your efforts to 10 seconds and 500 per day. At least, when I did such things a couple of years ago, those were the limits I experienced. Good luck!
::[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 16:24, 4 November 2024 (UTC)
:::Thank you, Dave. I'll continue with the edits as described without bot-status. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 16:35, 4 November 2024 (UTC).</text>
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  <page>
    <title>School:Medicine</title>
    <ns>100</ns>
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      <timestamp>2025-07-05T15:50:05Z</timestamp>
      <contributor>
        <ip>200.36.178.33</ip>
      </contributor>
      <comment>I changed the bad word</comment>
      <origin>2720829</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="14838" sha1="syenqoylgq1lm9jmjmp4mdyka9928jn" xml:space="preserve">&lt;div style=&quot;padding:10px 2em;line-height:1em;font-size:2em;color:#6155ff;text-align:center;&quot;&gt;
'''Welcome to the [[WV:IS|&lt;span style=&quot;color:#6155ff;&quot;&gt;Wikiversity&lt;/span&gt;]] School of {{{school name|Medicine}}}!'''
&lt;/div&gt;
&lt;HR noshade style=&quot;background-color:{{{Colour-dark|#6155ff}}};height:5px;margin:6px;margin-bottom:6px;&quot;&gt;
&lt;div style=&quot;background-color:#fff; min-width: 236px;margin-left:6px;overflow:auto;&quot;&gt;&lt;gallery mode=&quot;packed-hover&quot; widths=&quot;180&quot; heights=&quot;200&quot;&gt;
File:US Navy 040331-N-5821W-004 Hospitalman Richard Joy shows eighth-grade students from Naval Air Station Sigonella's Stephen Decatur School different medical instruments used in surgery in the United States Naval Hospital Sigonell.jpg
File:FEMA - 45183 - FEMA Administrator talks about Katrina recovery respo.jpg
File:Apar festa 0001.jpg|'''FOAM''' is for [http://lifeinthefastlane.com/foam/ '''Free Online Access to Meducation!''']
File:WikiJournal of Medicine logo.svg|link=Wikiournal of Medicine|&lt;span style=&quot;font-family:Monotype Corsiva; font-size: 15pt&quot;&gt;[[WikiJournal of Medicine|WikiJournal&lt;br&gt; of Medicine]]&lt;/span&gt;
&lt;/gallery&gt;&lt;/div&gt;
&lt;HR noshade style=&quot;background-color:#b0b0b0;margin:24px&quot;&gt;

&lt;!-- Header --&gt;
{{center top}}
{|style=&quot;width:100%;margin-top:+.7em;background-color:#fcfcfc;border:1px solid #ccc&quot;
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{|style=&quot;width:280px;border:solid 0px;background:none&quot;
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&lt;div style=&quot;font-size:133%;border:none;margin: 0;padding:.1em;color:#000&quot;&gt;
&lt;big&gt;'''W&lt;small&gt;ELCOME TO THE&lt;/small&gt; S&lt;small&gt;CHOOL OF&lt;/small&gt; M&lt;small&gt;EDICINE&lt;/small&gt; !'''&lt;/big&gt;&lt;br&gt;
&lt;small&gt; ''Part of [[Portal:Medicine|Medicine]]''&lt;/small&gt;&lt;/div&gt;
&lt;div style=&quot;top:+0.2em;font-size: 95%&quot;&gt;&lt;/div&gt;
&lt;div style=&quot;width:100%;text-align:center;font-size:80%;&quot;&gt;&lt;/div&gt;
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|style=&quot;width:18%;font-size:95%;color:#000&quot;|
|style=&quot;width:10%;font-size:95%&quot;;color:#000&quot;|
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{{center bottom}}

&lt;!-- Introduction --&gt;
&lt;div style=&quot;float:right; width:100%&quot;&gt;
{{Portal:Engineering/box-header|&lt;big&gt;School of {{PAGENAME}} &lt;/big&gt;|{{FULLPAGENAME}}/Intro|}}
[[File:WikiJournal of Medicine logo.svg|right|120x120px]]

Medicine is the science and practice of the diagnosis, treatment, and prevention of disease. Medicine encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness. Contemporary medicine applies biomedical sciences, biomedical research, pathology, microbiology, genetics, and medical technology to diagnose, treat, and prevent injury and disease, typically through pharmaceuticals or surgery, but also through therapies as diverse as psychotherapy, external splints and traction, medical devices, biologics, and ionizing radiation, amongst others.&lt;ref&gt;[[Wikipedia: Medicine]]&lt;/ref&gt;

{{clear}}

{{Portal:Engineering/box-footer|}}
&lt;/div&gt;
&lt;!-- End intro --&gt;

&lt;!-- Departments --&gt;
&lt;div style=&quot;float:right; width:100%&quot;&gt;
{{Portal:Engineering/box-header|Divisions and Departments|{{FULLPAGENAME}}/Departments|}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;

{|style=&quot;background: transparent;&quot;
|width=50px| ||width=350px| '''Department of Anatomy''' ||width=325px| '''Department of Biochemistry''' ||width=325px| '''Department of Physiology'''
|-
| || '''Department of Forensic Medicine &amp; Toxicology''' || '''Department of Microbiology''' || '''Department of Pathology'''
|-
| || '''Department of Pharmacology'''  || '''Department of Anesthesiology''' || '''Department of Community Medicine''' 
|-
| || '''Department of Dermatology &amp; Venereology''' || '''Department of Medicine''' || '''Department of Obstetrics &amp; Gynecology'''
|-
| || '''Department of Ophthalmology''' || '''Department of Orthopedics''' || '''Department of Otorhinolaryngology'''
|-
| || '''Department of Pediatrics''' || '''Department of Psychiatry''' || '''Department of Surgery'''
|}

&lt;/div&gt;
{{Portal:Engineering/box-footer|}}
&lt;/div&gt;
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&lt;div style=&quot;float:left; width:53%;&quot;&gt; &lt;!-- This width added to the the margin below to equal 99%--&gt;

{{Portal:Engineering/box-header|''School news and current events''|{{FULLPAGENAME}}/News and events|}}
{{{{FULLPAGENAME}}/News and events}}
{{Portal:Engineering/box-footer|}}

{{Portal:Engineering/box-header|''Learning Resources''|{{FULLPAGENAME}}/Learning Resources|}}
{{{{FULLPAGENAME}}/Learning Resources}}
{{Portal:Engineering/box-footer|}}

{{Portal:Engineering/box-header|''Active participants''|{{FULLPAGENAME}}/Active participants|}}
{{{{FULLPAGENAME}}/Active participants}}
{{Portal:Engineering/box-footer|}}

&lt;/div&gt;
&lt;!-- End Left column --&gt;

&lt;!-- Right column --&gt;
&lt;div style=&quot;float:right; width:46%&quot;&gt; &lt;!-- This margin should be right of the above --&gt;

{{Portal:Engineering/box-header|''Research projects/Questions''|{{FULLPAGENAME}}/Research projects|}}
{{{{FULLPAGENAME}}/Research projects}}
{{Portal:Engineering/box-footer|}}

{{Portal:Engineering/box-header|''Wikipedia articles''|{{FULLPAGENAME}}/Wikipedia articles|}}
{{{{FULLPAGENAME}}/Wikipedia articles}}
{{Portal:Engineering/box-footer|}}

{{Portal:Engineering/box-header|''Open source software''|{{FULLPAGENAME}}/Open source software|}}
{{{{FULLPAGENAME}}/Open source software}}
{{Portal:Engineering/box-footer|}}

{{Portal:Engineering/box-header|''External links''|{{FULLPAGENAME}}/External links|}}
{{{{FULLPAGENAME}}/External links}}
{{Portal:Engineering/box-footer|}}

&lt;/div&gt;
&lt;!-- End right column --&gt;

&lt;div style=&quot;float:right; width:100%&quot;&gt;

{{Portal:Engineering/box-header|''Textbooks''|{{FULLPAGENAME}}/Textbooks|}}
{{{{FULLPAGENAME}}/Textbooks}}
{{Portal:Engineering/box-footer|}}

&lt;/div&gt;


__NOTOC__

[[Category:Engineering]]
[[Category:Engineering and Technology]]

[[Category:Wikiversity schools]]


[[ar:كلية علوم الهندسة]]
[[el:Σχολή:Πολυτεχνική]]
[[es:Facultad de Ingeniería]]
[[fr:Faculté:Sciences de l'ingénieur]]
[[it:Facoltà:Ingegneria]]

&lt;blockquote&gt;
===== &lt;small&gt;Divisions and Departments&lt;/small&gt; =====
&lt;/blockquote&gt;Anatomy

Physiology

Biochemistry&lt;div style=&quot;font-size:1.4em;padding:18px;text-align:left;&quot;&gt;&lt;/div&gt;
==School Noticeboard==
'''November 2013'''
* Wikiversity medicine needs a unique identity, distinct from the role of [[w:Main Page|Wikipedia]] and [[b:Main page|Wikibooks]]. What might that role be? What progress are we making? Share your ideas on the [[School talk:Medicine|Talk page]].

==Educational [[Help:Resources by type|Resources]] tools to make them== 
Learning medicine requires more than passive reading for understanding. Here is a growing list of resource types that can be useful in various contexts, as well as some especially good links to essential things you really should try (if you haven't already) either to find your own resources, or, hopefully to contribute here!

* [[File:Crystal128-kanagram.svg|24px]] Introductions / Explanations / Topic summaries / Blogs (non-technical language)
* [[File:Report-edit.svg|24px]] Research studies / published reviews / theories / summaries / clinical scenarios and case reports (including simulation scenarios)
* [[File:Plan.png|24px]] Curriculum documents, lesson plans, articles
* [[File:Farm-Fresh slideshow.png|x24px]] Linear (normal) slideshow presentations, e.g. PowerPoint or the free [http://www.openoffice.org/product/windows.html Open Office Impress]
* [[File:Maket icon.svg|24px]] Comparison or summary tables
* [[File:Applications-internet.svg|24px]] WebQuests, which guide the student through sequences of resources, preferably including a variety of other resource formats
* [[File:Nuvola apps korganizer.svg|24px]] Assessment outlines / marking guides / [[Help:Quiz-Simple|quizzes]] / checklists (need to know about [http://gawande.com/the-checklist-manifesto Atul Gawande and the Checklist Manifesto])
* [[File:Nuvola apps kolourpaint.png|24px]] Pictures / Photos (search [[Commons:|Wikimedia Commons]] and  [http://www.flickr.com/search/?q=&amp;l=cc&amp;ss=0&amp;ct=0&amp;mt=all&amp;w=all&amp;adv=1 CC-BY-SA Images at Flickr], or [[w:Comparison of raster graphics editors|use a graphic editor]])
* [[File:Nuvola apps kcoloredit.svg|24px]] Vector illustrations (try [http://inkscape.org/ Inkscape] - free software)
* [[File:Nuvola apps tree.svg|24px]] Mindmaps (need to try [http://freeplane.sourceforge.net/wiki/index.php/Main_Page Freeplane] - free software)
* [[File:My personal black cat.gif|24px]] Animations (try [http://www.pencil-animation.org/ Pencil] for 2D, or [http://www.blender.org/ Blender] for 3D if you are ambitious!)
* [[File:AdiumSoundset.png|24px]] Podcasts / Vodcasts / Screencasts / Videos ([http://www.youtube.com/ Youtube], [https://www.khanacademy.org/ Khan Academy], [http://www.ted.com/talks TED Talks], and short-format presentation styles like [[w:PechaKucha|Pecha Kucha]])
*[[File:Nuvola apps flashkard.png|24px]] Flashcards (try [http://ankisrs.net/ Anki] - free software, with spaced repetition for optimised revision and retention of information, or [https://evernote.com/ Evernote] used with the [http://www.revunote.com/ Revunote app for android]). These may vary the order and timing of repetitions, but the feedback response (the second side of the flashcard) is the same.
*[[File:Nuvola apps kpresenter.png|24px]] [http://pegasus.cc.ucf.edu/~ytao/module1.htm# Non-linear Powerpoint presentations] and medical information apps. The only interactivity is in the order or choice of available information topics presented.
*[[File:Presa de decissions.png|24px]] Games, Virtual patient apps and online flash/html interactive modules (try [https://play.google.com/store/apps/details?id=com.medicaljoyworks.prognosis&amp;hl=en Prognosis- Your Diagnosis] for Android). These can vary in quality. Low level interactions may have a series of trivial roadblocks ('click on the nose to continue') or disconnected stimulus-response feedback (see quizzes above). Variations include different visual ways of triggering the response, e.g. click or touch, drag/drop or mouse-over. Better examples may use more complex branching scenarios where each decision affects the next problem, and a range of responses is possible rather than just good or bad responses.

== Educational approaches ==
* Lectures / Tutorials / Clinical skills demonstrations / Labs
* Bedside teaching
* Ward rounds / Grand rounds
*[[Image:Nuvola apps kopete.png|24px]] Join in the conversation on Twitter (try following #meded or #foamed) and [http://www.tweetdeck.com/ TweetDeck]
*[[Image:Nuvola apps chat.png|24px]] Create and contribute to blogs and their comments / polls / discussion forum (need to know about [http://lifeinthefastlane.com/ Life in the Fast Lane])
*[[Image:Nuvola apps kdmconfig.png|24px]] Collaboration through Wikiversity, Wikieducator etc.
*[[Image:Multilingual Wikipedia logo.gif|24px]] [[Outreach:Education Portal/Newsletter/May 2013/First ever medical school education program pilot begins at UCSF|Medical School Wikipedia Editathons]]
*[[Image:Small cup gold.png|32px]] [http://smacc.net.au/category/pk-talk/ Pecha Kucha competitions]
*[[Image:Crystal Clear app Community Help.png|24px]] Simulation in teams (which benefits from high quality simulation scenarios and trained teachers to deliver them), including support with [http://virtualheroes.com/projects/3diteams video games] or [http://www.isimulatetechnologies.com/ ipad simulators]. Importantly, the simulation scenario can be changed by the teacher to respond in realtime to individual student skill levels/deficits/areas of interest/teaching points, making it much more powerful. Some also [http://www.clinispace.com/videos.html include videos for 'just-in-time' learning].
*[[Image:Crystal Clear app package games.svg|32px]] [http://www.abc.net.au/tv/seriousgames/ Serious games]{{dead link}} (e.g. Simulation with [http://smacc.net.au/sonowars/ SonoWars] and [http://smacc.net.au/category/simwars/ SimWars])


&lt;div style=&quot;background-color:#9088ff; padding:12px; text-align:center; color:white;&quot;&gt;

===&lt;span style=&quot;color:white;&quot;&gt;Other Links&lt;/span&gt;===
&lt;/div&gt;
&lt;div style=&quot;padding:12px;border:3px solid #9088ff&quot;&gt;
* [[Wikipedia:Book:Health care|The Wikipedia Open Textbook of Medicine]] - a book made up of a selection of very high quality wikipedia articles covering core concepts in medicine.
* [http://www.wikidoc.org/index.php/Main_Page WikiDoc The Living Textbook of Medicine] - another medical textbook / encyclopaedia, linking to google searches for further resources.
* Content creation platforms (e.g. [http://pinterest.com/‎ Pinterest] or [http://learni.st/ Learnist])
* [https://www.meducation.net/ Meducation] - Thousands of free resources for medical students. Meducation supports a community of 50,000 medics and has over 40,000 resources.
* [[b:Subject:Medicine|Medical books]] at Wikibooks
* ''[[WikiJournal of Medicine]]'' - an academic medical journal that is integrated with Wikipedia
&lt;/div&gt;

===&lt;span style=&quot;color:#6155ff;&quot;&gt;Current Learning Projects&lt;/span&gt;===

* [[Dominant group/Medicine]]
* [[Gene project]]
* [[Draft:Medicine|Medicine]]
* [[Strategies for Engineered Negligible Senescence]]
* [[Life extension]]
* [[Cryonics]]
* [[Biotechnology]] 

&lt;div style=&quot;font-size:1.4em;padding:18px;text-align:left;&quot;&gt;There are three active medical learning projects here. Why not start another one?&lt;/div&gt;
&lt;HR noshade style=&quot;background-color:{{{Colour-dark|#6155ff}}};height:3px;margin:6px;margin-bottom:6px;&quot;&gt;


{{Medical disclaimer}}

&lt;big&gt;FAQ: What do you want to know?&lt;/big&gt;
{{collapse top|[[Image:Nuvola apps bookcase.png|32px]] How can I create medical education resources? ''&lt;small&gt;- (click here)&lt;/small&gt;''|width=100%|border=0px|bg=#a8a1ff|border2=0px}}
{{{education resources}}}

{{collapse bottom}}
{{collapse top|[[Image:Nuvola apps kdmconfig.png|32px]] I'd like to help, where do I sign up? ''&lt;small&gt;- (click here)&lt;/small&gt;''|width=100%|border=0px|bg=#a8a1ff|border2=0px}}

&lt;big&gt;&lt;div style=&quot;text-align: center;&quot;&gt;You can get started curating medical resources on Wikiversity [[Wikiversity:Getting_involved|right now]].&lt;/div&gt;&lt;/big&gt;

If you'd like, you can also [[Wikiversity:Getting involved|register with Wikiversity]]. Please read the [[Wikiversity:Medical disclaimer|Wikiversity medical disclaimer]] before starting. Most importantly, completion of learning materials in this site [[Wikiversity:What Wikiversity is not|'''does not confer any academically accredited degree''']] or bestow any medicolegal professional status to practice medicine. 
{{collapse bottom}}
{{Basic sciences}}
{{Sisterlinks|Medicine}}
&lt;!-- categories --&gt;
[[Category:Medical Terminology]]
[[Category:Medicine| ]]
[[Category:Wikiversity schools]]

&lt;!-- interlanguage links --&gt;
[[ar:كلية علوم الطب]]
[[de:Fachbereich Humanmedizin]]
[[es:Departamento de Medicina]]
[[fr:Faculté:Médecine]]
[[it:Facoltà:Medicina e chirurgia]]
[[pt:Portal:Ciências Médicas]]
[[ru:Факультет медицины]]</text>
      <sha1>syenqoylgq1lm9jmjmp4mdyka9928jn</sha1>
    </revision>
    <revision>
      <id>2720830</id>
      <parentid>2720829</parentid>
      <timestamp>2025-07-05T15:51:44Z</timestamp>
      <contributor>
        <ip>200.36.178.33</ip>
      </contributor>
      <comment>Change some columns</comment>
      <origin>2720830</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="14832" sha1="4dtrbs1rapynccb7av750zntagkfay6" xml:space="preserve">&lt;div style=&quot;padding:10px 2em;line-height:1em;font-size:2em;color:#6155ff;text-align:center;&quot;&gt;
'''Welcome to the [[WV:IS|&lt;span style=&quot;color:#6155ff;&quot;&gt;Wikiversity&lt;/span&gt;]] School of {{{school name|Medicine}}}!'''
&lt;/div&gt;
&lt;HR noshade style=&quot;background-color:{{{Colour-dark|#6155ff}}};height:5px;margin:6px;margin-bottom:6px;&quot;&gt;
&lt;div style=&quot;background-color:#fff; min-width: 236px;margin-left:6px;overflow:auto;&quot;&gt;&lt;gallery mode=&quot;packed-hover&quot; widths=&quot;180&quot; heights=&quot;200&quot;&gt;
File:US Navy 040331-N-5821W-004 Hospitalman Richard Joy shows eighth-grade students from Naval Air Station Sigonella's Stephen Decatur School different medical instruments used in surgery in the United States Naval Hospital Sigonell.jpg
File:FEMA - 45183 - FEMA Administrator talks about Katrina recovery respo.jpg
File:Apar festa 0001.jpg|'''FOAM''' is for [http://lifeinthefastlane.com/foam/ '''Free Online Access to Meducation!''']
File:WikiJournal of Medicine logo.svg|link=Wikiournal of Medicine|&lt;span style=&quot;font-family:Monotype Corsiva; font-size: 15pt&quot;&gt;[[WikiJournal of Medicine|WikiJournal&lt;br&gt; of Medicine]]&lt;/span&gt;
&lt;/gallery&gt;&lt;/div&gt;
&lt;HR noshade style=&quot;background-color:#b0b0b0;margin:24px&quot;&gt;

&lt;!-- Header --&gt;
{{center top}}
{|style=&quot;width:100%;margin-top:+.7em;background-color:#fcfcfc;border:1px solid #ccc&quot;
|style=&quot;width:50%;color:#000&quot;|
{|style=&quot;width:280px;border:solid 0px;background:none&quot;
|-
|style=&quot;width:280px;text-align:center;white-space:nowrap;color:#000&quot; |
&lt;div style=&quot;font-size:133%;border:none;margin: 0;padding:.1em;color:#000&quot;&gt;
&lt;big&gt;'''W&lt;small&gt;ELCOME TO THE&lt;/small&gt; S&lt;small&gt;CHOOL OF&lt;/small&gt; M&lt;small&gt;EDICINE&lt;/small&gt; !'''&lt;/big&gt;&lt;br&gt;
&lt;small&gt; ''Part of [[Portal:Medicine|Medicine]]''&lt;/small&gt;&lt;/div&gt;
&lt;div style=&quot;top:+0.2em;font-size: 95%&quot;&gt;&lt;/div&gt;
&lt;div style=&quot;width:100%;text-align:center;font-size:80%;&quot;&gt;&lt;/div&gt;
|}
|style=&quot;width:18%;font-size:95%;color:#000&quot;|
|style=&quot;width:10%;font-size:95%&quot;;color:#000&quot;|
|}
{{center bottom}}

&lt;!-- Introduction --&gt;
&lt;div style=&quot;float:right; width:100%&quot;&gt;
{{Portal:Engineering/box-header|&lt;big&gt;School of {{PAGENAME}} &lt;/big&gt;|{{FULLPAGENAME}}/Intro|}}
[[File:WikiJournal of Medicine logo.svg|right|120x120px]]

Medicine is the science and practice of the diagnosis, treatment, and prevention of disease. Medicine encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness. Contemporary medicine applies biomedical sciences, biomedical research, pathology, microbiology, genetics, and medical technology to diagnose, treat, and prevent injury and disease, typically through pharmaceuticals or surgery, but also through therapies as diverse as psychotherapy, external splints and traction, medical devices, biologics, and ionizing radiation, amongst others.&lt;ref&gt;[[Wikipedia: Medicine]]&lt;/ref&gt;

{{clear}}

{{Portal:Engineering/box-footer|}}
&lt;/div&gt;
&lt;!-- End intro --&gt;

&lt;!-- Departments --&gt;
&lt;div style=&quot;float:right; width:100%&quot;&gt;
{{Portal:Engineering/box-header|Divisions and Departments|{{FULLPAGENAME}}/Departments|}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;

{|style=&quot;background: transparent;&quot;
|width=50px| ||width=350px| '''Department of Anatomy''' ||width=325px| '''Department of Biochemistry''' ||width=325px| '''Department of Physiology'''
|-
| || '''Department of Forensic Medicine &amp; Toxicology''' || '''Department of Microbiology''' || '''Department of Pathology'''
|-
| || '''Department of Pharmacology'''  || '''Department of Anesthesiology''' || '''Department of Community Medicine''' 
|-
| || '''Department of Dermatology &amp; Venereology''' || '''Department of Medicine''' || '''Department of Obstetrics &amp; Gynecology'''
|-
| || '''Department of Ophthalmology''' || '''Department of Orthopedics''' || '''Department of Otorhinolaryngology'''
|-
| || '''Department of Pediatrics''' || '''Department of Psychiatry''' || '''Department of Surgery'''
|}

&lt;/div&gt;
{{Portal:Engineering/box-footer|}}
&lt;/div&gt;
&lt;!-- End departments --&gt;

&lt;!-- Start of two column format --&gt;
&lt;!-- Left column --&gt;
&lt;div style=&quot;float:left; width:53%;&quot;&gt; &lt;!-- This width added to the the margin below to equal 99%--&gt;

{{Portal:Engineering/box-header|''School news and current events''|{{FULLPAGENAME}}/News and events|}}
{{{{FULLPAGENAME}}/News and events}}
{{Portal:Engineering/box-footer|}}

{{Portal:Engineering/box-header|''Learning Resources''|{{FULLPAGENAME}}/Learning Resources|}}
{{{{FULLPAGENAME}}/Learning Resources}}
{{Portal:Engineering/box-footer|}}

{{Portal:Engineering/box-header|''Active participants''|{{FULLPAGENAME}}/Active participants|}}
{{{{FULLPAGENAME}}/Active participants}}
{{Portal:Engineering/box-footer|}}

&lt;/div&gt;
&lt;!-- End Left column --&gt;

&lt;!-- Right column --&gt;
&lt;div style=&quot;float:right; width:46%&quot;&gt; &lt;!-- This margin should be right of the above --&gt;

{{Portal:Engineering/box-header|''Research projects/Questions''|{{FULLPAGENAME}}/Research projects|}}
{{{{FULLPAGENAME}}/Research projects}}
{{Portal:Engineering/box-footer|}}

{{Portal:Engineering/box-header|''Wikipedia articles''|{{FULLPAGENAME}}/Wikipedia articles|}}
{{{{FULLPAGENAME}}/Wikipedia articles}}
{{Portal:Engineering/box-footer|}}

{{Portal:Engineering/box-header|''Open source software''|{{FULLPAGENAME}}/Open source software|}}
{{{{FULLPAGENAME}}/Open source software}}
{{Portal:Engineering/box-footer|}}

{{Portal:Engineering/box-header|''External links''|{{FULLPAGENAME}}/External links|}}
{{{{FULLPAGENAME}}/External links}}
{{Portal:Engineering/box-footer|}}

&lt;/div&gt;
&lt;div style=&quot;float:right; width:100%&quot;&gt;&lt;/div&gt;


{{Portal:Engineering/box-header|''Textbooks''|{{FULLPAGENAME}}/Textbooks|}}
{{{{FULLPAGENAME}}/Textbooks}}
{{Portal:Engineering/box-footer|}}&lt;!-- End right column --&gt;__NOTOC__

[[Category:Engineering]]
[[Category:Engineering and Technology]]

[[Category:Wikiversity schools]]


[[ar:كلية علوم الهندسة]]
[[el:Σχολή:Πολυτεχνική]]
[[es:Facultad de Ingeniería]]
[[fr:Faculté:Sciences de l'ingénieur]]
[[it:Facoltà:Ingegneria]]

&lt;blockquote&gt;
===== &lt;small&gt;Divisions and Departments&lt;/small&gt; =====
&lt;/blockquote&gt;Anatomy

Physiology

Biochemistry&lt;div style=&quot;font-size:1.4em;padding:18px;text-align:left;&quot;&gt;&lt;/div&gt;
==School Noticeboard==
'''November 2013'''
* Wikiversity medicine needs a unique identity, distinct from the role of [[w:Main Page|Wikipedia]] and [[b:Main page|Wikibooks]]. What might that role be? What progress are we making? Share your ideas on the [[School talk:Medicine|Talk page]].

==Educational [[Help:Resources by type|Resources]] tools to make them== 
Learning medicine requires more than passive reading for understanding. Here is a growing list of resource types that can be useful in various contexts, as well as some especially good links to essential things you really should try (if you haven't already) either to find your own resources, or, hopefully to contribute here!

* [[File:Crystal128-kanagram.svg|24px]] Introductions / Explanations / Topic summaries / Blogs (non-technical language)
* [[File:Report-edit.svg|24px]] Research studies / published reviews / theories / summaries / clinical scenarios and case reports (including simulation scenarios)
* [[File:Plan.png|24px]] Curriculum documents, lesson plans, articles
* [[File:Farm-Fresh slideshow.png|x24px]] Linear (normal) slideshow presentations, e.g. PowerPoint or the free [http://www.openoffice.org/product/windows.html Open Office Impress]
* [[File:Maket icon.svg|24px]] Comparison or summary tables
* [[File:Applications-internet.svg|24px]] WebQuests, which guide the student through sequences of resources, preferably including a variety of other resource formats
* [[File:Nuvola apps korganizer.svg|24px]] Assessment outlines / marking guides / [[Help:Quiz-Simple|quizzes]] / checklists (need to know about [http://gawande.com/the-checklist-manifesto Atul Gawande and the Checklist Manifesto])
* [[File:Nuvola apps kolourpaint.png|24px]] Pictures / Photos (search [[Commons:|Wikimedia Commons]] and  [http://www.flickr.com/search/?q=&amp;l=cc&amp;ss=0&amp;ct=0&amp;mt=all&amp;w=all&amp;adv=1 CC-BY-SA Images at Flickr], or [[w:Comparison of raster graphics editors|use a graphic editor]])
* [[File:Nuvola apps kcoloredit.svg|24px]] Vector illustrations (try [http://inkscape.org/ Inkscape] - free software)
* [[File:Nuvola apps tree.svg|24px]] Mindmaps (need to try [http://freeplane.sourceforge.net/wiki/index.php/Main_Page Freeplane] - free software)
* [[File:My personal black cat.gif|24px]] Animations (try [http://www.pencil-animation.org/ Pencil] for 2D, or [http://www.blender.org/ Blender] for 3D if you are ambitious!)
* [[File:AdiumSoundset.png|24px]] Podcasts / Vodcasts / Screencasts / Videos ([http://www.youtube.com/ Youtube], [https://www.khanacademy.org/ Khan Academy], [http://www.ted.com/talks TED Talks], and short-format presentation styles like [[w:PechaKucha|Pecha Kucha]])
*[[File:Nuvola apps flashkard.png|24px]] Flashcards (try [http://ankisrs.net/ Anki] - free software, with spaced repetition for optimised revision and retention of information, or [https://evernote.com/ Evernote] used with the [http://www.revunote.com/ Revunote app for android]). These may vary the order and timing of repetitions, but the feedback response (the second side of the flashcard) is the same.
*[[File:Nuvola apps kpresenter.png|24px]] [http://pegasus.cc.ucf.edu/~ytao/module1.htm# Non-linear Powerpoint presentations] and medical information apps. The only interactivity is in the order or choice of available information topics presented.
*[[File:Presa de decissions.png|24px]] Games, Virtual patient apps and online flash/html interactive modules (try [https://play.google.com/store/apps/details?id=com.medicaljoyworks.prognosis&amp;hl=en Prognosis- Your Diagnosis] for Android). These can vary in quality. Low level interactions may have a series of trivial roadblocks ('click on the nose to continue') or disconnected stimulus-response feedback (see quizzes above). Variations include different visual ways of triggering the response, e.g. click or touch, drag/drop or mouse-over. Better examples may use more complex branching scenarios where each decision affects the next problem, and a range of responses is possible rather than just good or bad responses.

== Educational approaches ==
* Lectures / Tutorials / Clinical skills demonstrations / Labs
* Bedside teaching
* Ward rounds / Grand rounds
*[[Image:Nuvola apps kopete.png|24px]] Join in the conversation on Twitter (try following #meded or #foamed) and [http://www.tweetdeck.com/ TweetDeck]
*[[Image:Nuvola apps chat.png|24px]] Create and contribute to blogs and their comments / polls / discussion forum (need to know about [http://lifeinthefastlane.com/ Life in the Fast Lane])
*[[Image:Nuvola apps kdmconfig.png|24px]] Collaboration through Wikiversity, Wikieducator etc.
*[[Image:Multilingual Wikipedia logo.gif|24px]] [[Outreach:Education Portal/Newsletter/May 2013/First ever medical school education program pilot begins at UCSF|Medical School Wikipedia Editathons]]
*[[Image:Small cup gold.png|32px]] [http://smacc.net.au/category/pk-talk/ Pecha Kucha competitions]
*[[Image:Crystal Clear app Community Help.png|24px]] Simulation in teams (which benefits from high quality simulation scenarios and trained teachers to deliver them), including support with [http://virtualheroes.com/projects/3diteams video games] or [http://www.isimulatetechnologies.com/ ipad simulators]. Importantly, the simulation scenario can be changed by the teacher to respond in realtime to individual student skill levels/deficits/areas of interest/teaching points, making it much more powerful. Some also [http://www.clinispace.com/videos.html include videos for 'just-in-time' learning].
*[[Image:Crystal Clear app package games.svg|32px]] [http://www.abc.net.au/tv/seriousgames/ Serious games]{{dead link}} (e.g. Simulation with [http://smacc.net.au/sonowars/ SonoWars] and [http://smacc.net.au/category/simwars/ SimWars])


&lt;div style=&quot;background-color:#9088ff; padding:12px; text-align:center; color:white;&quot;&gt;

===&lt;span style=&quot;color:white;&quot;&gt;Other Links&lt;/span&gt;===
&lt;/div&gt;
&lt;div style=&quot;padding:12px;border:3px solid #9088ff&quot;&gt;
* [[Wikipedia:Book:Health care|The Wikipedia Open Textbook of Medicine]] - a book made up of a selection of very high quality wikipedia articles covering core concepts in medicine.
* [http://www.wikidoc.org/index.php/Main_Page WikiDoc The Living Textbook of Medicine] - another medical textbook / encyclopaedia, linking to google searches for further resources.
* Content creation platforms (e.g. [http://pinterest.com/‎ Pinterest] or [http://learni.st/ Learnist])
* [https://www.meducation.net/ Meducation] - Thousands of free resources for medical students. Meducation supports a community of 50,000 medics and has over 40,000 resources.
* [[b:Subject:Medicine|Medical books]] at Wikibooks
* ''[[WikiJournal of Medicine]]'' - an academic medical journal that is integrated with Wikipedia
&lt;/div&gt;

===&lt;span style=&quot;color:#6155ff;&quot;&gt;Current Learning Projects&lt;/span&gt;===

* [[Dominant group/Medicine]]
* [[Gene project]]
* [[Draft:Medicine|Medicine]]
* [[Strategies for Engineered Negligible Senescence]]
* [[Life extension]]
* [[Cryonics]]
* [[Biotechnology]] 

&lt;div style=&quot;font-size:1.4em;padding:18px;text-align:left;&quot;&gt;There are three active medical learning projects here. Why not start another one?&lt;/div&gt;
&lt;HR noshade style=&quot;background-color:{{{Colour-dark|#6155ff}}};height:3px;margin:6px;margin-bottom:6px;&quot;&gt;


{{Medical disclaimer}}

&lt;big&gt;FAQ: What do you want to know?&lt;/big&gt;
{{collapse top|[[Image:Nuvola apps bookcase.png|32px]] How can I create medical education resources? ''&lt;small&gt;- (click here)&lt;/small&gt;''|width=100%|border=0px|bg=#a8a1ff|border2=0px}}
{{{education resources}}}

{{collapse bottom}}
{{collapse top|[[Image:Nuvola apps kdmconfig.png|32px]] I'd like to help, where do I sign up? ''&lt;small&gt;- (click here)&lt;/small&gt;''|width=100%|border=0px|bg=#a8a1ff|border2=0px}}

&lt;big&gt;&lt;div style=&quot;text-align: center;&quot;&gt;You can get started curating medical resources on Wikiversity [[Wikiversity:Getting_involved|right now]].&lt;/div&gt;&lt;/big&gt;

If you'd like, you can also [[Wikiversity:Getting involved|register with Wikiversity]]. Please read the [[Wikiversity:Medical disclaimer|Wikiversity medical disclaimer]] before starting. Most importantly, completion of learning materials in this site [[Wikiversity:What Wikiversity is not|'''does not confer any academically accredited degree''']] or bestow any medicolegal professional status to practice medicine. 
{{collapse bottom}}
{{Basic sciences}}
{{Sisterlinks|Medicine}}
&lt;!-- categories --&gt;
[[Category:Medical Terminology]]
[[Category:Medicine| ]]
[[Category:Wikiversity schools]]

&lt;!-- interlanguage links --&gt;
[[ar:كلية علوم الطب]]
[[de:Fachbereich Humanmedizin]]
[[es:Departamento de Medicina]]
[[fr:Faculté:Médecine]]
[[it:Facoltà:Medicina e chirurgia]]
[[pt:Portal:Ciências Médicas]]
[[ru:Факультет медицины]]</text>
      <sha1>4dtrbs1rapynccb7av750zntagkfay6</sha1>
    </revision>
  </page>
  <page>
    <title>Wikibooks</title>
    <ns>0</ns>
    <id>15151</id>
    <revision>
      <id>2720820</id>
      <parentid>2720818</parentid>
      <timestamp>2025-07-05T13:07:06Z</timestamp>
      <contributor>
        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <minor />
      <comment>Reverted edits by [[Special:Contributions/118.172.39.10|118.172.39.10]] ([[User_talk:118.172.39.10|talk]]) to last version by [[User:MathXplore|MathXplore]] using [[Wikiversity:Rollback|rollback]]</comment>
      <origin>2612541</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4739" sha1="1xl2o2oteaorllsj6c1trrag350los9" xml:space="preserve">{{daughters}}
[[b:Main Page|Wikibooks]], previously called Wikimedia Free Textbook Project and Wikimedia-Textbooks, is a wiki for the creation of free content books. Wikibooks is a [[Wikimedia]] project that was started on July 10, 2003 with the mission to create a free collection of open-content textbooks that anyone can edit. Since its founding, volunteers have written over 35,000 modules in a multitude of textbooks.

== What is the difference between Wikibooks and Wikiversity? ==
Wikibooks hosts textbooks. Wikiversity does not host textbooks. [[Wikiversity:History of Wikiversity|Wikiversity started at Wikibooks, but later evolved into a separate project]]. Wikiversity is for types of learning resources that are not hosted by other Wikimedia projects. Wikiversity is exploring ways to use [[wiki]] technology to support learning communities.

:&quot;...the idea here is to also host learning communities, so people who are actually trying to learn, actually have a place to come and interact and help each other figure out how to learn things. We're also going to be hosting and fostering research into how these kinds of things can be used more effectively.&quot; ([http://wikimania2006.wikimedia.org/wiki/Opening_Plenary_%28transcript%29#Wikiversity_.2826:35.29 source])

==How can Wikiversity and Wikibooks complement each other?==
Wikiversity participants can learn about a topic and then use what they have learned to improve textbooks at Wikibooks or encyclopedia articles at [[Wikipedia]]. Helping make textbooks and encyclopedia articles are just two types of learning activities. Many other types of learning activities are being explored at Wikiversity. Take a look at [[:Category:Learning activities]].

Many Wikiversity schools, divisions, departments and [[learning resources]] have a ''&quot;Wikibooks&quot;'' section that links directly to [[b:WB:SUBJECT|relevant subjects]] at Wikibooks. See ''[[Wikiversity and Wikibooks services]]'' for more ways to help Wikiversity and Wikibooks complement each other.

==Ideas for classroom use==
Several classes at brick-and-mortar University have utilized Wikibooks for a &quot;real world&quot; class. For example [[b:Ethnomedicine|Ethnomedicine]] was created in a vigorous and rather astonishing fashion. It facilitated both the learning of the individuals of the class, and also made valuable information available for others to use. 

You could create a syllabus for your class here at Wikiversity, and then have students create a book as a study or homework tool over at Wikibooks. All of this content would be available for the free use by others at a later date. You can use the [[Template:Protected course|protected course template]] to ensure pages for your students remain consistent with your intentions for the duration of the course.

Wikiversity is still rather new, and you are encouraged to be creative in the ways that you utilize Wikibooks and Wikiversity for your learning goals.

== Organization of Wikibooks ==
Textbooks at Wikibooks are broken into 8 major subjects, which are then further subdivided into more specific subjects in a hierarchical manner. Each subject page corresponds to a different subject area such as mathematics, computer science, or history. Books on Wikibooks are also organized into alphabetical, Dewey-Decimal, and Library of Congress classification categories, which may be browsed independently from the subjects.

Books for children from birth until age 12 are located in [[b:Wikijunior|Wikijunior]], a sub-project of Wikibooks. Wikijunior books encompass material from all subjects, and are specifically written for children. Some Wikijunior books are intended to accompany a classroom learning atmosphere, but many books are useful for at-home learning between parent and child.

==See also==
* [[Wikiversity:Service community]]
* [[Wikiversity and Wikibooks services]]
* [[Wikibooks research]]
* [[Risk Management/Tailored Wikibooks]]

== WikiMediaFoundation Labs ==
* '''[http://mediawiki2latex.wmflabs.org/ MediaWiki to Latex converter for Wikibooks]'''&lt;ref&gt;Dirk Hünniger (2012-2020) MediaWiki to LaTeX Converter - URL: http://mediawiki2latex.wmflabs.org (accessed 2020/04/25)&lt;/ref&gt; - by Dirk Hünniger ([[b:de:Benutzer:Dirk_Huenniger/wb2pdf/manual|Wikibook-Manual]])
** '''Input:''' Wikibook URL
** '''Output:''' PDF-Document of the Wikibook
: Please create PDF books with less than 500 pages only and consider to install the tool on your own Linux computer (if possible) to leave the server capacity on wmflabs-Server for people that do not have ability to install the MediaWiki converter on their own computer.

== See also ==
* [[w:Wikibooks|Wikibooks]] (Wikipedia)

== References ==

[[Category:Wikibooks| ]]
[[Category:Document Management]]</text>
      <sha1>1xl2o2oteaorllsj6c1trrag350los9</sha1>
    </revision>
  </page>
  <page>
    <title>Talk:Learning the Basics of French/Lesson:Introducing Yourself/3</title>
    <ns>1</ns>
    <id>17509</id>
    <revision>
      <id>2720845</id>
      <parentid>79205</parentid>
      <timestamp>2025-07-05T19:48:34Z</timestamp>
      <contributor>
        <username>ShakespeareFan00</username>
        <id>6645</id>
      </contributor>
      <minor />
      <origin>2720845</origin>
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      <format>text/x-wiki</format>
      <text bytes="1857" sha1="awp2y6prksmtg0bjqs0p2wxh23sh9va" xml:space="preserve">I thought this one would be about age so that they could learn avoir?--[[User:66.238.170.34|66.238.170.34]] 17:47, 8 January 2007 (UTC)

I concur, this material can be used for a later lesson.--[[User:Elatanatari|Elatanatari]] 00:06, 19 January 2007 (UTC)


=== Make it so? ===
----
*Yes

__NOTOC__ __NOEDITSECTION__
{| cellpadding=&quot;10&quot; cellspacing=&quot;5&quot; style=&quot;width: 99%; background-color: inherit; margin-left: auto; margin-right: auto&quot;
| style=&quot;background-color: Cornsilk; border: 1px solid #777777; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;&quot; colspan=&quot;2&quot; |
{{Courses in French - Table - Float Right v2}}
&lt;br&gt;
== Proposition ==

== Simple Conversation ==

Here is a sample conversation:

Marc and Jeanette have just met.

Marc: Bonjour. Je m'appelle Marc. Et toi?

Jeanette: Bonjour, Marc! Moi, je m'appelle Jeanette. Quel âge as-tu?

Marc: J'ai seize ans, et toi? 

Jeanette: J'ai dix-sept ans.

Marc: Oh lala, J'ai un rendez-vous, à demain!

Jeanette: À demain.

==G: The verb avoir==

&quot;Avoir&quot; can be translated as &quot;to have&quot;.

===Expressing Age===
''Avoir'' is used to express age.
*Tu as quel âge? - How old are you? [lit: You have what age?]
*J'ai trente ans. - I'm thirty (years old). [lit: I have thirty years]

===Formation===

{{French Present Verb|avoir|to have|100|v|have|has
|ai|
|as|
|a|
|avons|
|avez|
|ont|
|audio=[[b:Media:French Verb - avoir.ogg|audio]]
}}

===Examples===

{| class=&quot;wikitable&quot; border=&quot;1&quot; width=&quot;50%&quot;
|J'ai deux stylos.
|I have two pens.
|-
|Tu as trois frères.
|You have three brothers.
|-
|Il a une idée.
|He has an idea.
|}

===Expressing Age===
''Avoir'' is used to express age.
*Tu as quel âge? - How old are you? [lit: You have what age?]
*J'ai trente ans. - I'm thirty (years old). [lit: I have thirty years]
|}</text>
      <sha1>awp2y6prksmtg0bjqs0p2wxh23sh9va</sha1>
    </revision>
  </page>
  <page>
    <title>User talk:ShakespeareFan00</title>
    <ns>3</ns>
    <id>27178</id>
    <revision>
      <id>2720862</id>
      <parentid>2660803</parentid>
      <timestamp>2025-07-06T04:18:04Z</timestamp>
      <contributor>
        <username>Ruud Loeffen</username>
        <id>2998353</id>
      </contributor>
      <comment>/* == Thanks for your careful formatting corrections == */ new section</comment>
      <origin>2720862</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="13579" sha1="m5sp0ee9yy5nthv927eqn5z2b3e03wm" xml:space="preserve">&lt;!--&lt;div style=&quot;text-align: center; width: 60%; margin: auto; padding: 1em; border: solid 2px gold; background-color: royalblue; color: white; font-weight: bold;&quot;&gt;&lt;span style=&quot;letter-spacing: 14px;&quot;&gt;NOT ACTIVELY EDITING&lt;/span&gt;{{#if:|&lt;br /&gt;&lt;br /&gt;{{{1}}}}}&lt;/div&gt;
&lt;div style=&quot;text-align: center; font-weight: bold;&quot;&gt; Because of what I feel may have been a monumental expression and demonstration of &quot;technical incompetence&quot; in an off-wiki situation which had consequences.
&lt;/div&gt;
--&gt;
[[User talk:ShakespeareFan00/Sfan00 IMG|Archiv of message sent to alternate account]] 

== Welcome ==

While you've been on IRC for a bit, I'm glad to see you finally doing some learning projects. :) We should do a bit of scoping on the software that both wikio and wikicast will need, whether it be just docs/notes on existing stuff or actual new development.

I hope you enjoy your time here! [[User:Historybuff|Historybuff]] 20:47, 16 February 2007 (UTC)

== technical question ==

&quot;do we currently have the option with the current setup of transmission break in?&quot; &lt;-- I have that option in in the OSX version of version of MuSE (muse.dyne.org). I tried it on the old (slow processor) machine I am using and it was really horrible...either because I did not know what I was doing or it was beyond the capacity of my processor. For quality and reliability, I think it would be best to stream playlists directly from the icecast server. Under those conditions it might be possible do &quot;transmission break in&quot;, but I'm not sure about that. Alternatively, someone could produce the audio stream from a more powerful PC or a different OS. The Macintosh version of MuSE is not really supported and seems to lack some of the documented features of the software. Also, as I recall, there was another type of software for making streams, but no Mac version. [[User:Moulton]] and [[User:Historybuff]] know much more about this stuff than I do. --[[User:JWSchmidt|JWSchmidt]] 22:30, 1 November 2008 (UTC)

:&quot;'break into' the transmission to make a suitable announcment, I will come up with some wording&quot; &lt;-- almost any content is welcome and I can add it to the [[Wiki Campus Radio/Active audio stream|audio stream]] on short notice. --[[User:JWSchmidt|JWSchmidt]] 18:45, 3 November 2008 (UTC)

===Audio barnstar===
[[Image:AudioBarnstar.png|thumb|right|Audio barnstar]] Thanks for your contributions to Wikiversity. --[[User:JWSchmidt|JWSchmidt]] 05:29, 5 November 2008 (UTC)

== Possibility ==

Have you considered this?:  [[n:Wikinews:Story_preparation/John_Mcain_wins_U.S._Presidency]]  [[user:Jade Knight|The Jade Knight]] &lt;sup&gt;[[User talk:Jade Knight|(d'viser)]]&lt;/sup&gt; 08:41, 4 November 2008 (UTC)

== cells ==

Sure, a [http://en.wikiversity.org/w/index.php?title=User_talk:JWSchmidt&amp;diff=0&amp;oldid=571452 podcast] would be fun. I assume you mean the recent work from Venter's group. What aspect of the story are you interested in? --[[User:JWSchmidt|JWSchmidt]] 04:32, 23 May 2010 (UTC)

===virus===
It might be useful to add a section on microbial disease to [[RNA interference/Medical]]. --[[User:JWSchmidt|JWSchmidt]] 17:56, 31 May 2010 (UTC)

== Your messages ==

Thank you for your message. I do not own a copy of the Chronological Table of the Statutes. I had access to it through a library which I now unfortunately have to pay to visit. I am unable to give any commitment that I will be able to upload it. Regards. [[User:James500|James500]] ([[User talk:James500|discuss]] • [[Special:Contributions/James500|contribs]]) 13:16, 5 August 2013 (UTC)

I think that criminal trespass (ie to land) is probably a suitable topic for Wikipedia, and that a list could go there. This subject is discussed in the thirteenth edition of Smith and Hogan's Criminal Law at p 974 (at the end of a chapter on burglary and related offences under the heading of &quot;other trespass offences&quot;). That book suggests, as further reading on this subject, chapter 5 of The Law of Public Order and Protest, 2010, by P Thornton et al. The twelfth edition of Card, Cross and Jones: Criminal Law has sections on offences of &quot;entering and remaining on property&quot; and aggravated trespass from pages 349 to 356. So it is probably a notable topic. [[User:James500|James500]] ([[User talk:James500|discuss]] • [[Special:Contributions/James500|contribs]]) 21:01, 8 September 2013 (UTC)

== Double Redirects ==

Thanks for your help on the double redirects. We do have a bot that cleans those up. But if you'd like to help with some of the other [[:Category:Wikiversity maintenance]] items, it would be most appreciated! -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 12:52, 5 April 2016 (UTC)

== Instructional Design ==

Instructional Design is a graduate course sequence at Indiana University. Students were required to use Wikiversity for their content development. They haven't participated here for several years now. You're not likely to get a response regarding [[Instructional design/Discussion Roles]]. At this point we can correct it however makes the most sense to us. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 13:24, 19 August 2020 (UTC)

== Curatorship ==

I'd like to nominate you for [[Wikiversity:Curators|curatorship]] if you are interested. It gives you more content management tools. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:33, 28 August 2020 (UTC)

:{{ping|Dave Braunschweig}} Thank you for the offer, but at present I will have to decline, as I don't have enough experience or policy knowledge, in addition I don't technically &quot;need&quot; the tools to continue with the Lint fixes.. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 22:18, 28 August 2020 (UTC)

==Edit query==
[https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2020%2FCompassion_focused_therapy&amp;type=revision&amp;diff=2201199&amp;oldid=2201197] - just checking re the intention of this edit? The student working on the page didn't understand why the hanging indent template was hidden? Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:00, 9 September 2020 (UTC)

:: Good catch... I'd commented it to find the LintError, and forget to de-comment it after the repair was completed... HTH.  Repaired.[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 13:02, 9 September 2020 (UTC)

== Again: Please look at your edits, before saving them! ==

In [https://en.wikiversity.org/w/index.php?title=Zhegalkin_twins&amp;diff=prev&amp;oldid=2570225 this edit] you have replaced &lt;code&gt;small&lt;/code&gt; tags by {{tl|smaller block}}, which does not exist. (What you meant was {{tl|small block}}.) If you had bothered to look at your edit before saving it, you would have seen, that the whole paragraph was replaced by a red link. You have done this before, when you replaced working &lt;code&gt;font&lt;/code&gt; tags by broken &lt;code&gt;span&lt;/code&gt; tags. (See [[User_talk:Watchduck#I_don't_understand_your_reinsertion_of_obselete_syntax..|here]].) Plase stop assuming that your edits should work, and instead use the ''show preview'' button. [[User:Watchduck|Watchduck]] &lt;small&gt;([[User talk:Watchduck|quack]])&lt;/small&gt; 09:32, 17 October 2023 (UTC)

When you replaced &lt;code&gt;&amp;lt;small&amp;gt;&lt;/code&gt; by {{tl|Small block}}, have you made sure that the content did not contain equals signs or tags with attributes? See [[Template talk:Small block]]. --[[User:Watchduck|Watchduck]] &lt;small&gt;([[User talk:Watchduck|quack]])&lt;/small&gt; 11:26, 22 April 2024 (UTC)

:Please provide SPECFIC examples, I was not finding many pages with {{tl|small block}} and an equals sign still present. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:30, 22 April 2024 (UTC)

::Well, this template is almost unused. It's more complicated for {{tl|X-smaller block}}. I would say that in {{tl|Chapter navigation top}} you have a lot of trust, that all this stuff will never contain a forbidden character. &lt;small&gt;(Equals signs are [[User:Watchduck/sandbox/A=B|not forbidden]] in page names.)&lt;/small&gt; So especially there, I would rather have a styled div tag. But generally, I would not put pass large amounts of stuff as parameter into a template. Where templates really improve usability, it might be better to replace start and end tags separately &lt;small&gt;(as I did with {{tl|Collapsible START}})&lt;/small&gt;. --[[User:Watchduck|Watchduck]] &lt;small&gt;([[User talk:Watchduck|quack]])&lt;/small&gt; 12:35, 22 April 2024 (UTC)

::&lt;small&gt;Ah, I realize you actually did that using &lt;code&gt;&lt;nowiki&gt;{{X-smaller block/s}}&lt;/nowiki&gt;&lt;/code&gt; and &lt;code&gt;&lt;nowiki&gt;{{X-smaller block/e}}&lt;/nowiki&gt;&lt;/code&gt;. --[[User:Watchduck|Watchduck]] &lt;small&gt;([[User talk:Watchduck|quack]])&lt;/small&gt; 14:01, 22 April 2024 (UTC)&lt;/small&gt;
:::Query does Wikiversity implement Template Data? There's a tool I use over on Wikisource to look for 'mangled' parameters included unescaped = signs? [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 14:04, 22 April 2024 (UTC)

I assume he has a pattern-matching script that traverses the site and makes these minor adjustments. Kind of neat. Care to share the code? [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 12:06, 22 April 2024 (UTC)

Please take a look at [https://en.wikiversity.org/w/index.php?title=Template:Seal_pyramids_Liana_and_Ivy&amp;diff=prev&amp;oldid=2659322 your edit] of my template, open the second box &lt;small&gt;(''pyramid Ivy'')&lt;/small&gt;, and within that the first box &lt;small&gt;(''overview'')&lt;/small&gt;. {{tl|Small block}} produces &lt;code&gt;{{{1}}}&lt;/code&gt; instead of small text, because the text contains an equals sign. What is wrong with the ''show preview'' button? Are you too cool for using it? --[[User:Watchduck|Watchduck]] &lt;small&gt;([[User talk:Watchduck|quack]])&lt;/small&gt; 00:10, 3 October 2024 (UTC)
: Odd.. I was sure I had used preview on that..&lt;br&gt;BTW: Please add - &lt;syntaxhighlight lang=&quot;wikitext&quot;&gt;
// create a user defined object
var myLintHints = { };
// specify some object component
myLintHints.rooms = &quot;*&quot;;
// communicate user defined object
mw.hook( &quot;lintHint.config&quot; ).fire( myLintHints );
// finally, load gadget
mw.loader.load( &quot;https://en.wikipedia.org/w/index.php?title=User:PerfektesChaos/js/lintHint/r.js&amp;action=raw&amp;bcache=1&amp;maxage=86400&amp;ctype=text/javascript&quot; );
&lt;/syntaxhighlight&gt;to your Common.js, and recheck the templates you've made. The issue that was I attempting to resolve was that block level elements like p breaks can't appear inside &lt;nowikI&gt;&lt;small&gt;&lt;/nowikI&gt;.  You probably should be using {{tl|small block}} as you suggested previously. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 00:20, 3 October 2024 (UTC)

::I would find these templates more readable as {{tl|Small START}} and {{tl|Small END}}. And I would add the parameters ''size'' &lt;small&gt;(default 85)&lt;/small&gt; and ''opacity'' &lt;small&gt;(default 1)&lt;/small&gt;. Then {{tl|X-smaller block}} could be replaced by &lt;code&gt;&lt;nowiki&gt;{{Small START|72}}&lt;/nowiki&gt;&lt;/code&gt;. What do you think? --[[User:Watchduck|Watchduck]] &lt;small&gt;([[User talk:Watchduck|quack]])&lt;/small&gt; 09:08, 3 October 2024 (UTC)
::: Elsewhere Wikiversity has used /top /end. But if you want to rename and add the additional functions I have no objections. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:18, 3 October 2024 (UTC)
::::The opposite of ''top'' is ''bottom'' – not ''end''. &lt;small&gt;*shaking my head*&lt;/small&gt; Technically the slash is understandable, but I would avoid it for the sake of visual clarity.
::::Do you have access to a bot, that can make all the replacements? --[[User:Watchduck|Watchduck]] &lt;small&gt;([[User talk:Watchduck|quack]])&lt;/small&gt; 09:43, 3 October 2024 (UTC)
::::: I don't have a bot, but would suggest using something like AWB. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:46, 3 October 2024 (UTC)
::::::Actually, no automation was needed. I don't get, where all the transclusions of {{tl|X-smaller block}} come from. --[[User:Watchduck|Watchduck]] &lt;small&gt;([[User talk:Watchduck|quack]])&lt;/small&gt; 12:18, 3 October 2024 (UTC)

== Thanks for your careful formatting corrections ==


Dear ShakespeareFan00,

Thanks for your recent markup corrections on the [[Cosmic Influx Theory]] and [[AI-Assisted Evaluation of Cosmological Theories]] pages. I noticed the small fixes with italic tags — these things are easy to miss, so I appreciate the cleanup.

If you ever plan to make more changes beyond formatting (especially in scientific content), feel free to leave a short note here or on the article talk pages. I’m actively working on these pages and would gladly coordinate.

Kind regards,  
[[User:Ruud Loeffen|Ruud Loeffen]] ([[User talk:Ruud Loeffen|discuss]] • [[Special:Contributions/Ruud Loeffen|contribs]]) 04:18, 6 July 2025 (UTC)</text>
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    <title>Teletraffic engineering/What is tariffing?</title>
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      <text bytes="6577" sha1="sz71eqwq7yh50eumqpa5rkjbx96jkro" xml:space="preserve">Author: Moses Chisala

== What is Tariffing? ==
=== Summary ===
This document is about [[w:Tariffing|'''tariffing''']] as applied in the Telecommunications industrial. Several factors have been looked at; tariffing policy entities looking at the customer and what should be priced. Also components of tariffing or tariffs such as; Why are tariffs charged?, Components of tariffs, Special tariffs and Impact of tariffs on traffic.

=== Definition ===
The word '''tariffing''' comes from the word [http://www.answers.com/topic/tariff ''tariff''] which means; tax, duty, due, fee, excise, levy or toll paid towards the use of a specific service. In the telecommunication environment it applies to the charging of telecommunication services that have been already used or prior to. Therefore, '''tariffing''' can be defined as the process of fixing a duty, fee or a price on the telecommunication services provided by the service provider and utilized by the end user (consumer) and the '''public policy regulating body''' acting as an overseer.
The regulating body provides standards and guidelines to both the service provider and the end user. The standards and regulations imposed differ from one country to another.

Some of the elements affecting tariffing are:- Monopoly or competition; Pricing and Tariffs; Universal Service; Network interconnections and Abuse of Dominance.

'''Tariffing policy entities:'''

'''''Customer'''''

An end user customer uses one telecommunications network to initiate a communication to another customer of the same network or another. An ''''''interconnector'''''' is a network operator that terminates a communication from a customer of another network operator to a customer of its network.

'''''What Should Be Priced?'''''

a. Rate Elements and Rate Structure

&quot;Price elements and the structure of prices are intended to address two related issues:
on the supply side, to ration scarce resources, and on the demand side, to change
consumption behavior of end users.

The decision to make the next telephone call depends on the price of that incremental call, not the average price of all calls. The decision to talk for the next minute, once a call is placed, is based on the perceived price of that incremental minute. The decision to subscribe to a service is based on
the perceived price of that incremental service. Each of these marginal decisions is performed by comparing the perceived price to the perceived benefit to be obtained. Customers often undertake these decisions with poor information, incomplete understanding, and only a vague notion of the actual price that will be charged. Time-of-day pricing is a crude form of peak load pricing, intended to cause users to change their behavior by shifting some of their calling to off-peak periods. Multi-part tariffs (fixed charge + usage-sensitive charge) can be used to segment the market according to user characteristics.&quot; [http://www.pegasus.or.id/Reports/89)%20Telecom%20Pricing.pdf [2]]

The figure below shows a simple telecommunication network indicating the routing of the local call and long-distance call.

                         Simple Telecommunication Network

b. “Product” Definitions

&quot;Fundamentally, the circuit switched telephone network is a time-sharing network. Telephone companies set different prices for different minutes of use, depending on the identity of the user, the distance of the call, and the time of day.&quot; [http://www.pegasus.or.id/Reports/89)%20Telecom%20Pricing.pdf [2]]

The following componets also should be considered when looking at tariffing;

[[w:Tariffing#Why_are_tariffs_charged.3F|Why are tariffs charged?]]

[[w:Tariffing#Components_of_tariffs|Components of tariffs]]

[[w:Tariffing#Special_tariffs|Special tariffs]]

[[w:Tariffing#Impact_of_tariffs_on_traffic|Impact of tariffs on traffic]]

'''Price-elasticity of demand'''

Elasticity of demand for new installations may be estimated taking into account the subjective price perception of potential customers. Price elasticity expresses the sensitivity of customers to the cost of the service. The elasticity parameter is calculated as the ratio of percentage change in demand (quantity sold per period) caused by a percentage change in price.

==== Example ====
'''Example 1'''

If the average price for the new service that has been introduced in the network is R15 and the elasticity of revenue is 0.7. Asuming 4% drop in quantity demand.

Calculate

I. elasticity of quantity demand

II. the new price

'''Solutions'''

'''I.'''

&lt;math&gt;E_{RP} = 1 + E_{qp}&lt;/math&gt;

0.7 = 1 + Eqp

Eqp = '''- 0.3'''

'''II.'''

Eqp = [(Q1/Qo) - 1]/[(P1/Po-1]

- 0.3 = [-0.04]/[15/Po-1]

Po = '''R13.24'''

====Exercises ====

'''Question 1'''

A mobile network provider charging R2 per 1Mb data download has a subscriber base of 1.2 million for a  period of six months. The subscriber base increases in five months to 1.6 million after the 64% reduction per download.

Calculate

I. the initial quantity demand

II. the relative Change in quantity demand

III. the relative change in price

IV. elasticity of quantity demand

V. elasticity of revenues

VI. comment on the answer in v.
{{collapse top|Solutions to Module 16}}
{{collapse top|I}}  '''Qo = 200,000'''{{collapse bottom}}
{{collapse top|II}} '''(Q1-Qo)/Qo = 0.6'''{{collapse bottom}}
{{collapse top|III}}'''(P1-Po)/Po = -0.64'''{{collapse bottom}}
{{collapse top|IV}} '''Eqp = -0.9375'''{{collapse bottom}}
{{collapse top|V}}  ''' ERP = 0.0625'''{{collapse bottom}}
{{collapse top|VI}} Demand is [http://www.ingrimayne.com/econ/elasticity/Elastic1.html '''inelastic'''] whenever the elasticity coefficient is less than modulars one. When it is greater than then the demand  is called [http://www.ingrimayne.com/econ/elasticity/Elastic1.html elastic].{{collapse bottom}}
{{collapse bottom}}

=== References ===

[1] INTERNATIONAL TELECOMMUNICATION UNION SERIES D SUPPLEMENT 3 (03/93)

[2] http://www.ingrimayne.com/econ/elasticity/Elastic1.html

[3] Steensrtup M., Routing in Communication Networks. Prentice Hall Inc, New Jersey, 1995

[4] Hanharan H., Integrated Digital Communications. School of Electrical and Information Engineering,  University of the Witwatersrand, Johannesburg, 2006.

[5] [[[w:Tariffing|http://en.wikipedia.org/wiki/Tariffing]]]

[6] Kennedy I.G., Why is Network Planning Important?, Lecture Notes, ELEN5007 - Teletraffic              Engineering, School of Electrical and Information Engineering, University of the Witwatersrand, 2005.

[[Category:Teletraffic engineering]]
[[Category:Tariffing]]</text>
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      <text bytes="131" sha1="qt2w4t84h5ic27y561b6lrmkshf3qsy" xml:space="preserve">__NOTOC__ __NOEDITSECTION__
{| width=&quot;100%&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; valign=&quot;top&quot; border=&quot;0&quot; |&lt;noinclude&gt;&lt;br clear=&quot;all&quot;&gt;
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      <comment>Your test edits worked :).. but were out of cope</comment>
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      <text bytes="176" sha1="0y78orjscu2kjefbh8sxa3hndfny7il" xml:space="preserve">{{welcome}}
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 19:25, 5 July 2025 (UTC)</text>
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      <text bytes="3799" sha1="4fz21zvf2u5i4d3lzxc77eszwnb9f6u" xml:space="preserve">&lt;big&gt; &lt;b&gt; REMARK: We did the solution on our own &lt;/b&gt;&lt;/big&gt;

|}
== Problem ==


Do the integration by parts to reveal three more terms   :  &lt;math&gt; {f(x)=f(x_0)+\frac {x-x_0}{1!} f(x_0)+\int\limits_{x}^{x_0}(x-t)f''(t)dt } &lt;/math&gt;

== Problem 2.1.2 ==
&lt;big&gt;use IMVT theorem to express the remainder &lt;math&gt; f^5(\S)for (x,x_0) &lt;/math&gt;&lt;/big&gt;

== Problem ==
&lt;big&gt;use IMVT theorem to express the remainder &lt;math&gt; f^5(\S)for (x,x_0) &lt;/math&gt;&lt;/big&gt;
== Solution ==


Given That
&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |
 &lt;math&gt; {f(x)=f(x_0)+\frac {x-x_0}{1!} f(x_0)+\int\limits_{x}^{x_0}(x-t)f''(t)dt } 
&lt;/math&gt;||&lt;p style=&quot;text-align:right&quot;&gt; &lt;math&gt; \displaystyle 
&lt;/math&gt; &lt;/p&gt;
|}

&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |
&lt;math&gt; \int\limits_{x}^{x_0}(x-t)f''(t)dt = -\frac {(x-t)^2}{2} f''(t)-\int\limits_{x}^{x_0}\frac{-(x-t)^2}{2}f'''(t)dt
&lt;/math&gt;|&lt;p style=&quot;text-align:right&quot;&gt; &lt;math&gt; \displaystyle 
&lt;/math&gt; &lt;/p&gt;
|}

&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |
&lt;math&gt; \int\limits_{x}^{x_0}(x-t)f''(t)dt = \frac {(x-x_0)^2}{2} f''(x_0)+\int\limits_{x}^{x_0}\frac {(x-t)^2}{2}f'''(t)dt
&lt;/math&gt;|&lt;p style=&quot;text-align:right&quot;&gt; &lt;math&gt; \displaystyle 
&lt;/math&gt; &lt;/p&gt;
|}

&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |
&lt;math&gt;
\int\limits_{x}^{x_0}\frac {(x-t)^2}{2}f'''(t)dt = -\frac {(x-t)^3}{2*3} f'''(t)-\int\limits_{x}^{x_0}\frac {-(x-t)^3}{2*3}f''''(t)dt
&lt;/math&gt;|&lt;p style=&quot;text-align:right&quot;&gt; &lt;math&gt; \displaystyle 
&lt;/math&gt; &lt;/p&gt;
|}

&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |
&lt;math&gt;
\int\limits_{x}^{x_0}\frac {(x-t)^2}{2}f'''(t)dt = \frac {(x-x_0)^3}{3!} f'''(t)+\int\limits_{x}^{x_0}\frac {(x-t)^3}{3!}f''''(t)dt
&lt;/math&gt;|&lt;p style=&quot;text-align:right&quot;&gt; &lt;math&gt; \displaystyle 
&lt;/math&gt; &lt;/p&gt;
|}

&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |
&lt;math&gt;
\int\limits_{x}^{x_0}\frac {(x-t)^3}{3}f''''(t)dt = -\frac {(x-t)^4}{4*3!} f''''(t)-\int\limits_{x}^{x_0}-\frac {(x-t)^4}{4!}f'''''(t)dt
&lt;/math&gt;|&lt;p style=&quot;text-align:right&quot;&gt; &lt;math&gt; \displaystyle 
&lt;/math&gt; &lt;/p&gt;
|}

&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |
&lt;math&gt;
\int\limits_{x}^{x_0}\frac {(x-t)^3}{3}f''''(t)dt = \frac {(x-x_0)^4}{4!} f''''(t)+\int\limits_{x}^{x_0}\frac {(x-t)^4}{4!}f''''(t)dt
&lt;/math&gt;|&lt;p style=&quot;text-align:right&quot;&gt; &lt;math&gt; \displaystyle 
&lt;/math&gt; &lt;/p&gt;
|}

&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |
&lt;math&gt;
\int\limits_{x}^{x_0}\frac {(x-t)^4}{4}f''''(t)dt
&lt;/math&gt;|&lt;p style=&quot;text-align:right&quot;&gt; &lt;math&gt; \displaystyle 
&lt;/math&gt; &lt;/p&gt;
|}

&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |
 &lt;math&gt; {f(x)=f(x_0)+\frac {x-x_0}{1!} f(x_0)+\frac {(x-x_0)^2}{2} f''(x_0)+ \frac {(x-x_0)^3}{3!} f'''(t)+\frac {(x-x_0)^4}{4!} f''''(t)+\int\limits_{x}^{x_0}\frac {(x-t)^4}{4!}f''''(t)dt} 
&lt;/math&gt;||&lt;p style=&quot;text-align:right&quot;&gt; &lt;math&gt; \displaystyle 
&lt;/math&gt; &lt;/p&gt;
|}


APPLYING IMVT THEOREM TO ABOVE EQUATION
&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |
&lt;math&gt;
\int\limits_{x}^{x_0}\frac {(x-t)^4}{4}f^(4)(t)dt  =  f^5(\xi)\frac {(x-x_0)^5}{5!} &lt;/math&gt;, &lt;math&gt;   \xi  \in (x,x_0) &lt;/math&gt;
|}

APPLYING IMVT TO EQUATION 

&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |
&lt;math&gt;\int\limits_{x}^{x_0}\frac{(x-t)^n}{n!}f^{n+1}(t)dt&lt;/math&gt;
|&lt;p style=&quot;text-align:right&quot;&gt; &lt;math&gt; \displaystyle 
&lt;/math&gt; &lt;/p&gt;
|}

&lt;span id=&quot;(1)&quot;&gt;&lt;/span&gt;
:{| style=&quot;width:100%&quot; border=&quot;0&quot;
|-
| style=&quot;width:95%&quot;  |

&lt;math&gt;f^{n+1}(\xi)\int\limits_{x}^{x_0}\frac {(x-t)^n}{n!}dt &lt;/math&gt;
&lt;math&gt; \xi \in (x,x_0)&lt;/math&gt;
|&lt;p style=&quot;text-align:right&quot;&gt; &lt;math&gt; \displaystyle 
&lt;/math&gt; &lt;/p&gt;
|}</text>
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    <title>Genes linked to psychopathy</title>
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      <comment>Revised definition</comment>
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      <text bytes="43251" sha1="1zzjttb7mx710n3l30qaiw4bclpjxmr" xml:space="preserve">Psychopathy has a polygenic basis, with six [[genes]] having been shown particular significance regarding the risk: ANKK1, [[DRD2]], DRD4, [[COMT]], MAOA, and SLC6A4 (particularly the 5-HTTLPR variant). Other notable genetic risk factors for becoming a psychopath include [[alleles]] of OXTR, AVPR1A, CADM2, PRKG1, and NR3C1. Several of these genes, like COMT, MAOA, 5-HTTLPR, OXTR, and NR3C1, undergo direct epigenetic modification following trauma. Psychopathy is principally a personality construct used by psychologists to explain and predict behavior, but may also be described as an epigenetic condition that affects neurotransmitter levels and trajectory of neurodevelopment.

The expression of psychopathy-related phenotypes depends on the combination of inherited alleles, in addition to environmental factors. Individuals are at an elevated risk of psychopathic traits if they inherit multiple core alleles located at different [[loci]], likely at least four core alleles at a minimum of three different loci. This is similar to many other spectrum disorders, such as schizotypy, which typically involve a complex interaction between genes and environmental factors. 

&lt;div align=&quot;center&quot;&gt;
 
&lt;table class=&quot;MsoTableGrid&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; style=&quot;border-collapse:collapse;border:none&quot;&gt;
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  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:14.0pt&quot;&gt;Genes
  linked to psychopathy&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
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  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Characteristics&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;ANKK1&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;DRD2&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;MAOA&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;COMT&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;5-HTTLPR&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;[[Basal endophenotype]]&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;Also associated with&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A2 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957T allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;calm&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A1 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C allele]]&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;posttraumatic stress disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C/C genotype]]&lt;span class=&quot;MsoEndnoteReference&quot;&gt; &lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;impulsive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;schizophrenia&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;antisocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;borderline personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;narcissistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;sadistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;histrionic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen by proxy &lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen syndrome&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;

== DRD2 ==
In addition to the DRD2 957C/C genotype, the DRD2 Taq1 B allele and polymorphisms in the promoter region of the DRD4 gene have also have been linked to psychopathy.  This suggests that the dissocial and impulsive basal endophenotypes can be subdivided into at least seven subtypes:  1a, 1b, 1c, 2, 3a, 3b, and 3c.
&lt;div align=center&gt;&lt;table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
 style='border-collapse:collapse;border:none'&gt;
 &lt;tr&gt;
  &lt;td width=851 colspan=4 valign=top style='width:638.4pt;border:none;
  border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:16.0pt'&gt;Impulsive/dissocial
  subtypes&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=426 colspan=2 valign=top style='width:319.2pt;border:solid windowtext 1.0pt;
  border-top:none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD2&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD4&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 rowspan=2 style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;Subtype&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;957 [[locus]]&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;Taq1
  B locus&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;-616 locus&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;2&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;                               3c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;
==Further reading==
  [http://www.ncbi.nlm.nih.gov/pubmed/16632165]
  [http://www.ncbi.nlm.nih.gov/pubmed/18833581]
  [http://www.ncbi.nlm.nih.gov/pubmed/17087792]
  [http://bjp.rcpsych.org/cgi/content/full/193/2/121]
  [http://www.genepassport.ru/publications/public/DRD2%20and%20ANKK1%20genotype%20in%20alcohol-dependent.pdf]
  [http://www.ncbi.nlm.nih.gov/pubmed/14643564]
  [http://onlinelibrary.wiley.com/doi/10.1111/j.1601-183X.2009.00543.x/full]
  [http://www.biomedcentral.com/content/pdf/1744-9081-6-4.pdf]</text>
      <sha1>1zzjttb7mx710n3l30qaiw4bclpjxmr</sha1>
    </revision>
    <revision>
      <id>2720872</id>
      <parentid>2720871</parentid>
      <timestamp>2025-07-06T05:38:35Z</timestamp>
      <contributor>
        <ip>2600:6C54:4E00:669:C4EF:D9A3:4384:EDD2</ip>
      </contributor>
      <origin>2720872</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="43255" sha1="l64x4lsawy3lbj8cv52cpbt78wr0yev" xml:space="preserve">Psychopathy has a polygenic basis, with six [[genes]] having been shown particular significance regarding the risk: ANKK1, [[DRD2]], DRD4, [[COMT]], MAOA, and SLC6A4 (particularly the 5-HTTLPR variant). Other notable genetic risk factors for becoming a psychopath include [[alleles]] of OXTR, AVPR1A, CADM2, PRKG1, and NR3C1. Several of these genes, like COMT, MAOA, 5-HTTLPR, OXTR, and NR3C1, undergo direct epigenetic modification following trauma. Psychopathy is principally a personality construct used by psychologists to explain and predict behavior, but may also be described as an epigenetic condition that affects neurotransmitter levels and the trajectory of neurodevelopment.

The expression of psychopathy-related phenotypes depends on the combination of inherited alleles, in addition to environmental factors. Individuals are at an elevated risk of psychopathic traits if they inherit multiple core alleles located at different [[loci]], likely at least four core alleles at a minimum of three different loci. This is similar to many other spectrum disorders, such as schizotypy, which typically involve a complex interaction between genes and environmental factors. 

&lt;div align=&quot;center&quot;&gt;
 
&lt;table class=&quot;MsoTableGrid&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; style=&quot;border-collapse:collapse;border:none&quot;&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;7&quot; valign=&quot;top&quot; style=&quot;border:none;border-bottom:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:14.0pt&quot;&gt;Genes
  linked to psychopathy&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;5&quot; valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Loci&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td colspan=&quot;2&quot; valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Characteristics&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;ANKK1&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;DRD2&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;MAOA&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;COMT&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;5-HTTLPR&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;[[Basal endophenotype]]&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;Also associated with&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A2 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957T allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;calm&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A1 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C allele]]&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;posttraumatic stress disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C/C genotype]]&lt;span class=&quot;MsoEndnoteReference&quot;&gt; &lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;impulsive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;schizophrenia&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;antisocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;borderline personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;narcissistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;sadistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;histrionic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen by proxy &lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen syndrome&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;

== DRD2 ==
In addition to the DRD2 957C/C genotype, the DRD2 Taq1 B allele and polymorphisms in the promoter region of the DRD4 gene have also have been linked to psychopathy.  This suggests that the dissocial and impulsive basal endophenotypes can be subdivided into at least seven subtypes:  1a, 1b, 1c, 2, 3a, 3b, and 3c.
&lt;div align=center&gt;&lt;table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
 style='border-collapse:collapse;border:none'&gt;
 &lt;tr&gt;
  &lt;td width=851 colspan=4 valign=top style='width:638.4pt;border:none;
  border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:16.0pt'&gt;Impulsive/dissocial
  subtypes&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=426 colspan=2 valign=top style='width:319.2pt;border:solid windowtext 1.0pt;
  border-top:none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD2&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD4&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 rowspan=2 style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;Subtype&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;957 [[locus]]&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;Taq1
  B locus&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;-616 locus&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;2&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;                               3c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;
==Further reading==
  [http://www.ncbi.nlm.nih.gov/pubmed/16632165]
  [http://www.ncbi.nlm.nih.gov/pubmed/18833581]
  [http://www.ncbi.nlm.nih.gov/pubmed/17087792]
  [http://bjp.rcpsych.org/cgi/content/full/193/2/121]
  [http://www.genepassport.ru/publications/public/DRD2%20and%20ANKK1%20genotype%20in%20alcohol-dependent.pdf]
  [http://www.ncbi.nlm.nih.gov/pubmed/14643564]
  [http://onlinelibrary.wiley.com/doi/10.1111/j.1601-183X.2009.00543.x/full]
  [http://www.biomedcentral.com/content/pdf/1744-9081-6-4.pdf]</text>
      <sha1>l64x4lsawy3lbj8cv52cpbt78wr0yev</sha1>
    </revision>
    <revision>
      <id>2720877</id>
      <parentid>2720872</parentid>
      <timestamp>2025-07-06T05:52:58Z</timestamp>
      <contributor>
        <ip>2600:6C54:4E00:669:C4EF:D9A3:4384:EDD2</ip>
      </contributor>
      <origin>2720877</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="43558" sha1="f9re9te9fbj1t87qtltg3jo2wsvt673" xml:space="preserve">Psychopathy has a polygenic basis, with six [[genes]] having been shown particular significance regarding the risk: ANKK1, [[DRD2]], DRD4, [[COMT]], MAOA, and SLC6A4 (particularly the 5-HTTLPR variant). Other notable genetic risk factors for becoming a psychopath include [[alleles]] of OXTR, AVPR1A, CADM2, PRKG1, and NR3C1. Several of these genes, like COMT, MAOA, 5-HTTLPR, OXTR, and NR3C1, undergo direct epigenetic modification following trauma. Psychopathy is principally a personality construct used by psychologists to explain and predict behavior, but may also be described as varying degrees of epigenetic modifications that affect neurotransmitter levels and the trajectory of neurodevelopment.

The expression of psychopathy-related phenotypes depends on the combination of inherited alleles, in addition to environmental factors. Individuals are at an elevated risk of psychopathic traits if they inherit multiple core alleles located at different [[loci]], likely at least four core alleles at a minimum of three different loci. This is similar to many other spectrum disorders, such as schizotypy, which typically involve a complex interaction between genes and environmental factors. 

No gene is sufficient or necessary for psychopathy, and psychopathy has likely existed for hundreds of thousands to millions of years, but the condition may have only reached it's modern form with the splitting of MAOA into various VNTR polymorphisms within the last 100,000 years. 

&lt;div align=&quot;center&quot;&gt;
 
&lt;table class=&quot;MsoTableGrid&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; style=&quot;border-collapse:collapse;border:none&quot;&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;7&quot; valign=&quot;top&quot; style=&quot;border:none;border-bottom:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:14.0pt&quot;&gt;Genes
  linked to psychopathy&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;5&quot; valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Loci&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td colspan=&quot;2&quot; valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Characteristics&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;ANKK1&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;DRD2&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;MAOA&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;COMT&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;5-HTTLPR&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;[[Basal endophenotype]]&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;Also associated with&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A2 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957T allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;calm&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A1 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C allele]]&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;posttraumatic stress disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C/C genotype]]&lt;span class=&quot;MsoEndnoteReference&quot;&gt; &lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;impulsive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;schizophrenia&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;antisocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;borderline personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;narcissistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;sadistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;histrionic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen by proxy &lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen syndrome&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;

== DRD2 ==
In addition to the DRD2 957C/C genotype, the DRD2 Taq1 B allele and polymorphisms in the promoter region of the DRD4 gene have also have been linked to psychopathy.  This suggests that the dissocial and impulsive basal endophenotypes can be subdivided into at least seven subtypes:  1a, 1b, 1c, 2, 3a, 3b, and 3c.
&lt;div align=center&gt;&lt;table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
 style='border-collapse:collapse;border:none'&gt;
 &lt;tr&gt;
  &lt;td width=851 colspan=4 valign=top style='width:638.4pt;border:none;
  border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:16.0pt'&gt;Impulsive/dissocial
  subtypes&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=426 colspan=2 valign=top style='width:319.2pt;border:solid windowtext 1.0pt;
  border-top:none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD2&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD4&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 rowspan=2 style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;Subtype&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;957 [[locus]]&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;Taq1
  B locus&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;-616 locus&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;2&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;                               3c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;
==Further reading==
  [http://www.ncbi.nlm.nih.gov/pubmed/16632165]
  [http://www.ncbi.nlm.nih.gov/pubmed/18833581]
  [http://www.ncbi.nlm.nih.gov/pubmed/17087792]
  [http://bjp.rcpsych.org/cgi/content/full/193/2/121]
  [http://www.genepassport.ru/publications/public/DRD2%20and%20ANKK1%20genotype%20in%20alcohol-dependent.pdf]
  [http://www.ncbi.nlm.nih.gov/pubmed/14643564]
  [http://onlinelibrary.wiley.com/doi/10.1111/j.1601-183X.2009.00543.x/full]
  [http://www.biomedcentral.com/content/pdf/1744-9081-6-4.pdf]</text>
      <sha1>f9re9te9fbj1t87qtltg3jo2wsvt673</sha1>
    </revision>
    <revision>
      <id>2720878</id>
      <parentid>2720877</parentid>
      <timestamp>2025-07-06T06:02:03Z</timestamp>
      <contributor>
        <ip>2600:6C54:4E00:669:4025:2324:DB2B:95F2</ip>
      </contributor>
      <origin>2720878</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="43274" sha1="7d880ivii0ljpd8f0etrs9809v8w2y2" xml:space="preserve">Psychopathy has a polygenic basis, with six [[genes]] having been shown particular significance regarding the risk: ANKK1, [[DRD2]], DRD4, [[COMT]], MAOA, and SLC6A4 (particularly the 5-HTTLPR variant). Other notable genetic risk factors for becoming a psychopath include [[alleles]] of OXTR, AVPR1A, CADM2, PRKG1, and NR3C1. Several of these genes, like COMT, MAOA, 5-HTTLPR, OXTR, and NR3C1, undergo direct epigenetic modification following trauma. Psychopathy is principally a personality construct used by psychologists to explain and predict behavior, but may also be described as varying degrees of epigenetic modifications that affect neurotransmitter levels and the trajectory of neurodevelopment.

The expression of psychopathy-related phenotypes depends on the combination of inherited alleles, in addition to environmental factors. Individuals are at an elevated risk of psychopathic traits if they inherit multiple core alleles located at different [[loci]], likely at least four core alleles at a minimum of three different loci. This is similar to many other spectrum disorders, such as schizotypy, which typically involve a complex interaction between genes and environmental factors. 

&lt;div align=&quot;center&quot;&gt;
 
&lt;table class=&quot;MsoTableGrid&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; style=&quot;border-collapse:collapse;border:none&quot;&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;7&quot; valign=&quot;top&quot; style=&quot;border:none;border-bottom:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:14.0pt&quot;&gt;Genes
  linked to psychopathy&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;5&quot; valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Loci&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td colspan=&quot;2&quot; valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Characteristics&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;ANKK1&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;DRD2&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;MAOA&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;COMT&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;5-HTTLPR&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;[[Basal endophenotype]]&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;Also associated with&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A2 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957T allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;calm&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A1 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C allele]]&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;posttraumatic stress disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C/C genotype]]&lt;span class=&quot;MsoEndnoteReference&quot;&gt; &lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;impulsive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;schizophrenia&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;antisocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;borderline personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;narcissistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;sadistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;histrionic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen by proxy &lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen syndrome&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;

== DRD2 ==
In addition to the DRD2 957C/C genotype, the DRD2 Taq1 B allele and polymorphisms in the promoter region of the DRD4 gene have also have been linked to psychopathy.  This suggests that the dissocial and impulsive basal endophenotypes can be subdivided into at least seven subtypes:  1a, 1b, 1c, 2, 3a, 3b, and 3c.
&lt;div align=center&gt;&lt;table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
 style='border-collapse:collapse;border:none'&gt;
 &lt;tr&gt;
  &lt;td width=851 colspan=4 valign=top style='width:638.4pt;border:none;
  border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:16.0pt'&gt;Impulsive/dissocial
  subtypes&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=426 colspan=2 valign=top style='width:319.2pt;border:solid windowtext 1.0pt;
  border-top:none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD2&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD4&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 rowspan=2 style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;Subtype&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;957 [[locus]]&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;Taq1
  B locus&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;-616 locus&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;2&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;                               3c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;
==Further reading==
  [http://www.ncbi.nlm.nih.gov/pubmed/16632165]
  [http://www.ncbi.nlm.nih.gov/pubmed/18833581]
  [http://www.ncbi.nlm.nih.gov/pubmed/17087792]
  [http://bjp.rcpsych.org/cgi/content/full/193/2/121]
  [http://www.genepassport.ru/publications/public/DRD2%20and%20ANKK1%20genotype%20in%20alcohol-dependent.pdf]
  [http://www.ncbi.nlm.nih.gov/pubmed/14643564]
  [http://onlinelibrary.wiley.com/doi/10.1111/j.1601-183X.2009.00543.x/full]
  [http://www.biomedcentral.com/content/pdf/1744-9081-6-4.pdf]</text>
      <sha1>7d880ivii0ljpd8f0etrs9809v8w2y2</sha1>
    </revision>
    <revision>
      <id>2720879</id>
      <parentid>2720878</parentid>
      <timestamp>2025-07-06T06:06:59Z</timestamp>
      <contributor>
        <ip>2600:6C54:4E00:669:4025:2324:DB2B:95F2</ip>
      </contributor>
      <origin>2720879</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="43243" sha1="6pcjq0be5r8xibc8ciow0sr3k6py4oa" xml:space="preserve">Psychopathy has a polygenic basis, with six [[genes]] having been shown particular significance regarding the risk: ANKK1, [[DRD2]], DRD4, [[COMT]], MAOA, and SLC6A4 (particularly the 5-HTTLPR variant). Other notable genetic risk factors for becoming a psychopath include [[alleles]] of OXTR, AVPR1A, CADM2, PRKG1, and NR3C1. Several of these genes, like COMT, MAOA, 5-HTTLPR, OXTR, and NR3C1, undergo direct epigenetic modification following trauma. Psychopathy is principally a personality construct used by psychologists to explain and predict behavior, but may also be described as differing neurotransmitter levels, which also affect the trajectory of neurodevelopment.

The expression of psychopathy-related phenotypes depends on the combination of inherited alleles, in addition to environmental factors. Individuals are at an elevated risk of psychopathic traits if they inherit multiple core alleles located at different [[loci]], likely at least four core alleles at a minimum of three different loci. This is similar to many other spectrum disorders, such as schizotypy, which typically involve a complex interaction between genes and environmental factors. 

&lt;div align=&quot;center&quot;&gt;
 
&lt;table class=&quot;MsoTableGrid&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; style=&quot;border-collapse:collapse;border:none&quot;&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;7&quot; valign=&quot;top&quot; style=&quot;border:none;border-bottom:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:14.0pt&quot;&gt;Genes
  linked to psychopathy&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;5&quot; valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Loci&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td colspan=&quot;2&quot; valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Characteristics&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;ANKK1&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;DRD2&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;MAOA&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;COMT&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;5-HTTLPR&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;[[Basal endophenotype]]&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;Also associated with&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A2 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957T allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;calm&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A1 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C allele]]&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;posttraumatic stress disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C/C genotype]]&lt;span class=&quot;MsoEndnoteReference&quot;&gt; &lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;impulsive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;schizophrenia&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;antisocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;borderline personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;narcissistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;sadistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;histrionic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen by proxy &lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen syndrome&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;

== DRD2 ==
In addition to the DRD2 957C/C genotype, the DRD2 Taq1 B allele and polymorphisms in the promoter region of the DRD4 gene have also have been linked to psychopathy.  This suggests that the dissocial and impulsive basal endophenotypes can be subdivided into at least seven subtypes:  1a, 1b, 1c, 2, 3a, 3b, and 3c.
&lt;div align=center&gt;&lt;table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
 style='border-collapse:collapse;border:none'&gt;
 &lt;tr&gt;
  &lt;td width=851 colspan=4 valign=top style='width:638.4pt;border:none;
  border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:16.0pt'&gt;Impulsive/dissocial
  subtypes&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=426 colspan=2 valign=top style='width:319.2pt;border:solid windowtext 1.0pt;
  border-top:none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD2&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD4&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 rowspan=2 style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;Subtype&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;957 [[locus]]&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;Taq1
  B locus&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;-616 locus&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;2&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;                               3c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;
==Further reading==
  [http://www.ncbi.nlm.nih.gov/pubmed/16632165]
  [http://www.ncbi.nlm.nih.gov/pubmed/18833581]
  [http://www.ncbi.nlm.nih.gov/pubmed/17087792]
  [http://bjp.rcpsych.org/cgi/content/full/193/2/121]
  [http://www.genepassport.ru/publications/public/DRD2%20and%20ANKK1%20genotype%20in%20alcohol-dependent.pdf]
  [http://www.ncbi.nlm.nih.gov/pubmed/14643564]
  [http://onlinelibrary.wiley.com/doi/10.1111/j.1601-183X.2009.00543.x/full]
  [http://www.biomedcentral.com/content/pdf/1744-9081-6-4.pdf]</text>
      <sha1>6pcjq0be5r8xibc8ciow0sr3k6py4oa</sha1>
    </revision>
    <revision>
      <id>2720880</id>
      <parentid>2720879</parentid>
      <timestamp>2025-07-06T06:13:08Z</timestamp>
      <contributor>
        <ip>2600:6C54:4E00:669:4025:2324:DB2B:95F2</ip>
      </contributor>
      <origin>2720880</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="43257" sha1="d2py6y4mcwgh989e66vf6z4wgr8vt8c" xml:space="preserve">Psychopathy has a polygenic basis, with six [[genes]] having been shown particular significance regarding the risk: ANKK1, [[DRD2]], DRD4, [[COMT]], MAOA, and SLC6A4 (particularly the 5-HTTLPR variant). Other notable genetic risk factors for becoming a psychopath include [[alleles]] of OXTR, AVPR1A, CADM2, PRKG1, and NR3C1. Several of these genes, like COMT, MAOA, 5-HTTLPR, OXTR, and NR3C1, undergo direct epigenetic modification following trauma. Psychopathy is principally a personality construct used by psychologists to explain and predict behavior, but may also be described as a spectrum of differing neurotransmitter levels, which also affect the trajectory of neurodevelopment.

The expression of psychopathy-related phenotypes depends on the combination of inherited alleles, in addition to environmental factors. Individuals are at an elevated risk of psychopathic traits if they inherit multiple core alleles located at different [[loci]], likely at least four core alleles at a minimum of three different loci. This is similar to many other spectrum disorders, such as schizotypy, which typically involve a complex interaction between genes and environmental factors. 

&lt;div align=&quot;center&quot;&gt;
 
&lt;table class=&quot;MsoTableGrid&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; style=&quot;border-collapse:collapse;border:none&quot;&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;7&quot; valign=&quot;top&quot; style=&quot;border:none;border-bottom:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:14.0pt&quot;&gt;Genes
  linked to psychopathy&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;5&quot; valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Loci&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td colspan=&quot;2&quot; valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Characteristics&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;ANKK1&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;DRD2&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;MAOA&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;COMT&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;5-HTTLPR&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;[[Basal endophenotype]]&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;Also associated with&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A2 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957T allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;calm&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A1 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C allele]]&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;posttraumatic stress disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C/C genotype]]&lt;span class=&quot;MsoEndnoteReference&quot;&gt; &lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;impulsive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;schizophrenia&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;antisocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;borderline personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;narcissistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;sadistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;histrionic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen by proxy &lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen syndrome&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;

== DRD2 ==
In addition to the DRD2 957C/C genotype, the DRD2 Taq1 B allele and polymorphisms in the promoter region of the DRD4 gene have also have been linked to psychopathy.  This suggests that the dissocial and impulsive basal endophenotypes can be subdivided into at least seven subtypes:  1a, 1b, 1c, 2, 3a, 3b, and 3c.
&lt;div align=center&gt;&lt;table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
 style='border-collapse:collapse;border:none'&gt;
 &lt;tr&gt;
  &lt;td width=851 colspan=4 valign=top style='width:638.4pt;border:none;
  border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:16.0pt'&gt;Impulsive/dissocial
  subtypes&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=426 colspan=2 valign=top style='width:319.2pt;border:solid windowtext 1.0pt;
  border-top:none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD2&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD4&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 rowspan=2 style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;Subtype&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;957 [[locus]]&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;Taq1
  B locus&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;-616 locus&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;2&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;                               3c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;
==Further reading==
  [http://www.ncbi.nlm.nih.gov/pubmed/16632165]
  [http://www.ncbi.nlm.nih.gov/pubmed/18833581]
  [http://www.ncbi.nlm.nih.gov/pubmed/17087792]
  [http://bjp.rcpsych.org/cgi/content/full/193/2/121]
  [http://www.genepassport.ru/publications/public/DRD2%20and%20ANKK1%20genotype%20in%20alcohol-dependent.pdf]
  [http://www.ncbi.nlm.nih.gov/pubmed/14643564]
  [http://onlinelibrary.wiley.com/doi/10.1111/j.1601-183X.2009.00543.x/full]
  [http://www.biomedcentral.com/content/pdf/1744-9081-6-4.pdf]</text>
      <sha1>d2py6y4mcwgh989e66vf6z4wgr8vt8c</sha1>
    </revision>
    <revision>
      <id>2720881</id>
      <parentid>2720880</parentid>
      <timestamp>2025-07-06T06:21:00Z</timestamp>
      <contributor>
        <ip>2600:6C54:4E00:669:4025:2324:DB2B:95F2</ip>
      </contributor>
      <comment>Revert</comment>
      <origin>2720881</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="43216" sha1="ihbeuaateke5gjusvo5of8eiqsvn5bl" xml:space="preserve">Psychopathy has a polygenic basis, with six [[genes]] having been shown particular significance regarding the risk: ANKK1, [[DRD2]], DRD4, [[COMT]], MAOA, and SLC6A4 (particularly the 5-HTTLPR variant). Other notable genetic risk factors for becoming a psychopath include [[alleles]] of OXTR, AVPR1A, CADM2, PRKG1, and NR3C1. Several of these genes, like COMT, MAOA, 5-HTTLPR, OXTR, and NR3C1, undergo direct epigenetic modification following trauma. Psychopathy is principally a personality construct used by psychologists to explain and predict behavior, but may also be described as a condition which affects the trajectory of neurodevelopment.

The expression of psychopathy-related phenotypes depends on the combination of inherited alleles, in addition to environmental factors. Individuals are at an elevated risk of psychopathic traits if they inherit multiple core alleles located at different [[loci]], likely at least four core alleles at a minimum of three different loci. This is similar to many other spectrum disorders, such as schizotypy, which typically involve a complex interaction between genes and environmental factors. 

&lt;div align=&quot;center&quot;&gt;
 
&lt;table class=&quot;MsoTableGrid&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; style=&quot;border-collapse:collapse;border:none&quot;&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;7&quot; valign=&quot;top&quot; style=&quot;border:none;border-bottom:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:14.0pt&quot;&gt;Genes
  linked to psychopathy&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;5&quot; valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Loci&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td colspan=&quot;2&quot; valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Characteristics&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;ANKK1&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;DRD2&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;MAOA&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;COMT&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;5-HTTLPR&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;[[Basal endophenotype]]&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;Also associated with&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A2 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957T allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;calm&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A1 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C allele]]&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;posttraumatic stress disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C/C genotype]]&lt;span class=&quot;MsoEndnoteReference&quot;&gt; &lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;impulsive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;schizophrenia&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;antisocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;borderline personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;narcissistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;sadistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;histrionic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen by proxy &lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen syndrome&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;

== DRD2 ==
In addition to the DRD2 957C/C genotype, the DRD2 Taq1 B allele and polymorphisms in the promoter region of the DRD4 gene have also have been linked to psychopathy.  This suggests that the dissocial and impulsive basal endophenotypes can be subdivided into at least seven subtypes:  1a, 1b, 1c, 2, 3a, 3b, and 3c.
&lt;div align=center&gt;&lt;table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
 style='border-collapse:collapse;border:none'&gt;
 &lt;tr&gt;
  &lt;td width=851 colspan=4 valign=top style='width:638.4pt;border:none;
  border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:16.0pt'&gt;Impulsive/dissocial
  subtypes&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=426 colspan=2 valign=top style='width:319.2pt;border:solid windowtext 1.0pt;
  border-top:none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD2&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD4&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 rowspan=2 style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;Subtype&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;957 [[locus]]&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;Taq1
  B locus&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;-616 locus&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;2&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;                               3c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;
==Further reading==
  [http://www.ncbi.nlm.nih.gov/pubmed/16632165]
  [http://www.ncbi.nlm.nih.gov/pubmed/18833581]
  [http://www.ncbi.nlm.nih.gov/pubmed/17087792]
  [http://bjp.rcpsych.org/cgi/content/full/193/2/121]
  [http://www.genepassport.ru/publications/public/DRD2%20and%20ANKK1%20genotype%20in%20alcohol-dependent.pdf]
  [http://www.ncbi.nlm.nih.gov/pubmed/14643564]
  [http://onlinelibrary.wiley.com/doi/10.1111/j.1601-183X.2009.00543.x/full]
  [http://www.biomedcentral.com/content/pdf/1744-9081-6-4.pdf]</text>
      <sha1>ihbeuaateke5gjusvo5of8eiqsvn5bl</sha1>
    </revision>
    <revision>
      <id>2720882</id>
      <parentid>2720881</parentid>
      <timestamp>2025-07-06T07:44:05Z</timestamp>
      <contributor>
        <ip>92.119.36.70</ip>
      </contributor>
      <origin>2720882</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="43224" sha1="mofhjrhuwxiuqi8few56rvl6gtivers" xml:space="preserve">Psychopathy has a polygenic basis, with six [[genes]] having been shown particular significance regarding the risk: ANKK1, [[DRD2]], DRD4, [[COMT]], MAOA, and SLC6A4 (particularly the 5-HTTLPR variant). Other notable genetic risk factors for becoming a psychopath include [[alleles]] of OXTR, AVPR1A, CADM2, PRKG1, and NR3C1. Several of these genes, like COMT, MAOA, 5-HTTLPR, OXTR, and NR3C1, undergo direct epigenetic modification following trauma. Psychopathy is principally a personality construct used by psychologists to explain and predict behavior, but it may also be viewed as a spectrum of traits shaped by atypical patterns of neurodevelopment.

The expression of psychopathy-related phenotypes depends on the combination of inherited alleles, in addition to environmental factors. Individuals are at an elevated risk of psychopathic traits if they inherit multiple core alleles located at different [[loci]], likely at least four core alleles at a minimum of three different loci. This is similar to many other spectrum disorders, such as schizotypy, which typically involve a complex interaction between genes and environmental factors. 

&lt;div align=&quot;center&quot;&gt;
 
&lt;table class=&quot;MsoTableGrid&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; style=&quot;border-collapse:collapse;border:none&quot;&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;7&quot; valign=&quot;top&quot; style=&quot;border:none;border-bottom:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:14.0pt&quot;&gt;Genes
  linked to psychopathy&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;5&quot; valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Loci&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td colspan=&quot;2&quot; valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Characteristics&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;ANKK1&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;DRD2&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;MAOA&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;COMT&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;5-HTTLPR&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;[[Basal endophenotype]]&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;Also associated with&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A2 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957T allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;calm&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A1 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C allele]]&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;posttraumatic stress disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C/C genotype]]&lt;span class=&quot;MsoEndnoteReference&quot;&gt; &lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;impulsive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;schizophrenia&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;antisocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;borderline personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;narcissistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;sadistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;histrionic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen by proxy &lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen syndrome&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;

== DRD2 ==
In addition to the DRD2 957C/C genotype, the DRD2 Taq1 B allele and polymorphisms in the promoter region of the DRD4 gene have also have been linked to psychopathy.  This suggests that the dissocial and impulsive basal endophenotypes can be subdivided into at least seven subtypes:  1a, 1b, 1c, 2, 3a, 3b, and 3c.
&lt;div align=center&gt;&lt;table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
 style='border-collapse:collapse;border:none'&gt;
 &lt;tr&gt;
  &lt;td width=851 colspan=4 valign=top style='width:638.4pt;border:none;
  border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:16.0pt'&gt;Impulsive/dissocial
  subtypes&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=426 colspan=2 valign=top style='width:319.2pt;border:solid windowtext 1.0pt;
  border-top:none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD2&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD4&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 rowspan=2 style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;Subtype&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;957 [[locus]]&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;Taq1
  B locus&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;-616 locus&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;2&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;                               3c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;
==Further reading==
  [http://www.ncbi.nlm.nih.gov/pubmed/16632165]
  [http://www.ncbi.nlm.nih.gov/pubmed/18833581]
  [http://www.ncbi.nlm.nih.gov/pubmed/17087792]
  [http://bjp.rcpsych.org/cgi/content/full/193/2/121]
  [http://www.genepassport.ru/publications/public/DRD2%20and%20ANKK1%20genotype%20in%20alcohol-dependent.pdf]
  [http://www.ncbi.nlm.nih.gov/pubmed/14643564]
  [http://onlinelibrary.wiley.com/doi/10.1111/j.1601-183X.2009.00543.x/full]
  [http://www.biomedcentral.com/content/pdf/1744-9081-6-4.pdf]</text>
      <sha1>mofhjrhuwxiuqi8few56rvl6gtivers</sha1>
    </revision>
    <revision>
      <id>2720886</id>
      <parentid>2720882</parentid>
      <timestamp>2025-07-06T08:43:05Z</timestamp>
      <contributor>
        <ip>92.119.36.94</ip>
      </contributor>
      <origin>2720886</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="43227" sha1="1oz33m3z5wq9wsep03avxhi1son26lo" xml:space="preserve">Psychopathy has a polygenic basis, with six [[genes]] having been shown particular significance regarding the risk: ANKK1, [[DRD2]], DRD4, [[COMT]], MAOA, and SLC6A4 (particularly the 5-HTTLPR variant). Other notable genetic risk factors for becoming a psychopath include [[alleles]] of OXTR, AVPR1A, CADM2, PRKG1, and NR3C1. Several of these genes, like COMT, MAOA, 5-HTTLPR, OXTR, and NR3C1, undergo direct epigenetic modification following trauma. Psychopathy is principally a personality construct used by psychologists to explain and predict behavior, but it may also be viewed as a spectrum of traits connected to atypical patterns of neurodevelopment.

The expression of psychopathy-related phenotypes depends on the combination of inherited alleles, in addition to environmental factors. Individuals are at an elevated risk of psychopathic traits if they inherit multiple core alleles located at different [[loci]], likely at least four core alleles at a minimum of three different loci. This is similar to many other spectrum disorders, such as schizotypy, which typically involve a complex interaction between genes and environmental factors. 

&lt;div align=&quot;center&quot;&gt;
 
&lt;table class=&quot;MsoTableGrid&quot; border=&quot;1&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; style=&quot;border-collapse:collapse;border:none&quot;&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;7&quot; valign=&quot;top&quot; style=&quot;border:none;border-bottom:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:14.0pt&quot;&gt;Genes
  linked to psychopathy&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td colspan=&quot;5&quot; valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Loci&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td colspan=&quot;2&quot; valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;&lt;span style=&quot;font-size:12.0pt&quot;&gt;Characteristics&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;ANKK1&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;DRD2&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;MAOA&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;COMT&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;5-HTTLPR&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;[[Basal endophenotype]]&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; align=&quot;center&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal&quot;&gt;&lt;b&gt;Also associated with&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A2 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957T allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;calm&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[Taq1 A1 allele]] &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C allele]]&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;posttraumatic stress disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;[[957C/C genotype]]&lt;span class=&quot;MsoEndnoteReference&quot;&gt; &lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;impulsive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;schizophrenia&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele &lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;antisocial personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;borderline personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;narcissistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;sadistic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;histrionic personality disorder&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;dissocial&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen by proxy &lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border:solid windowtext 1.0pt;border-top:none;
  padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Taq1 A1 allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;957T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;&amp;nbsp;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;low activity&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;long&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;anxious&lt;/p&gt;
  &lt;/td&gt;
  &lt;td valign=&quot;top&quot; style=&quot;border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;
  border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt&quot;&gt;
  &lt;p class=&quot;MsoNormal&quot; style=&quot;margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal&quot;&gt;Munchausen syndrome&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;

== DRD2 ==
In addition to the DRD2 957C/C genotype, the DRD2 Taq1 B allele and polymorphisms in the promoter region of the DRD4 gene have also have been linked to psychopathy.  This suggests that the dissocial and impulsive basal endophenotypes can be subdivided into at least seven subtypes:  1a, 1b, 1c, 2, 3a, 3b, and 3c.
&lt;div align=center&gt;&lt;table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0
 style='border-collapse:collapse;border:none'&gt;
 &lt;tr&gt;
  &lt;td width=851 colspan=4 valign=top style='width:638.4pt;border:none;
  border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:16.0pt'&gt;Impulsive/dissocial
  subtypes&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=426 colspan=2 valign=top style='width:319.2pt;border:solid windowtext 1.0pt;
  border-top:none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD2&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;DRD4&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 rowspan=2 style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;span style='font-size:14.0pt'&gt;Subtype&lt;/span&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;957 [[locus]]&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;&lt;span style='font-size:12.0pt'&gt;Taq1
  B locus&lt;/span&gt;&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;&lt;b&gt;-616 locus&lt;/b&gt;&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616G allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;1c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;2&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-negative&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3a&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;T allele&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal align=center style='margin-bottom:0cm;margin-bottom:.0001pt;
  text-align:center;line-height:normal'&gt;3b&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
 &lt;tr&gt;
  &lt;td width=213 style='width:159.6pt;border:solid windowtext 1.0pt;border-top:
  none;padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;B1 allele-positive&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 style='width:159.6pt;border-top:none;border-left:none;
  border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;-616C/C genotype&lt;/p&gt;
  &lt;/td&gt;
  &lt;td width=213 valign=top style='width:159.6pt;border-top:none;border-left:
  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
  padding:0cm 5.4pt 0cm 5.4pt'&gt;
  &lt;p class=MsoNormal style='margin-bottom:0cm;margin-bottom:.0001pt;line-height:
  normal'&gt;                               3c&lt;/p&gt;
  &lt;/td&gt;
 &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/div&gt;
==Further reading==
  [http://www.ncbi.nlm.nih.gov/pubmed/16632165]
  [http://www.ncbi.nlm.nih.gov/pubmed/18833581]
  [http://www.ncbi.nlm.nih.gov/pubmed/17087792]
  [http://bjp.rcpsych.org/cgi/content/full/193/2/121]
  [http://www.genepassport.ru/publications/public/DRD2%20and%20ANKK1%20genotype%20in%20alcohol-dependent.pdf]
  [http://www.ncbi.nlm.nih.gov/pubmed/14643564]
  [http://onlinelibrary.wiley.com/doi/10.1111/j.1601-183X.2009.00543.x/full]
  [http://www.biomedcentral.com/content/pdf/1744-9081-6-4.pdf]</text>
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{{../STa|sacrum|'''bone'''}} {{../Stf|sagging|fashion|sagger|&amp;sub;pants}} {{../STy|saki|monkey}}
{{../STy|salsa|music}} {{../STj|saltant|{{../Wr|attitude (heraldry)#Salient|jumpy}}}} {{../STy|sambar|deer}} {{../STj|sanies|{{../Wp|ichor}}}} {{../STb|saola|bovine}} {{../STd|anoa|sapiutan|{{../Ty|buffalo}}}}{{../STd|manilkara zapota#Other names|sapota|fruit}}  {{../Stf|sati|practice|satī|suicide}}
{{../STc|convolvulus scammonia|scammony|bindweed}} {{../STf|scape|botany|stem}} {{../STb|scapula|'''bone'''}} {{../STd|phytolacca americana#cite note-8|scoke|pokeweed}} {{../STj|sconce|head{{../Wq|sconce}}}} {{../STb|scop|poet}} {{../STw|scot|and lot|tax}} {{../STb|scoter|seaduck}} {{../STs|scotia|moth}} {{../STd|conscience|scruple|doubt}}
{{../STd|scrying|scry|divine}} {{../STj|scut|{{../Ty|tail}}}} {{../STd|scutching|scutch|prepare}} {{../STb|scute|scale}} {{../STb|scutage|tax}}
{{../STc|sebaceous gland|sebum|secretion}} {{../STd|fresco-secco|secco|dry}} {{../STd|cyperaceae|sedge|≈grass}} {{../STd|medieval hunting#Hawk|seel|falconry}} {{../STb|seer|prophet{{../Wq|seer}}}} {{../STb|segue|flow&amp;nbsp;on}} {{../STb|seisin|~ownership}} {{../STj|selva|forest}} {{../STs|senna|plant}} {{../STb|sept|clan}} {{../STb|seraph|angel}} {{../STd|serinus|serin|finch}} {{../Stu|serous|membrane|serosa}} {{../STw|serous|fluid|watery}} {{../STb|serow|≈goat}} {{../STj|serpigo|{{../Wr|dermatophytosis|ringworm}}}} {{../STb|serval|cat}} {{../STj|sessile|{{../Wr|sessility|immobile}}}} {{../STb|sestina|poem}} {{../STb|seta|bristle}} {{../STb|sext|prayer}}
{{../STc|shamanism|shaman|medium}} {{../STs|shaw|woodland}} {{../STd|vitellaria|shea|tree}} {{../STb|shebeen|club}} {{../STj|sherpa|helper+}} {{../STb|shill|stooge}} {{../STb|shinty|≈hockey}} {{../STd|pig farming#Terminology|shoat|piglet}} {{../STb|shogun|dictator}} {{../STb|shola|forest}}
{{../STa|sibyl|seeress}} {{../STd|scribal abbreviation|sigil|abrvtn}} {{../STy|sika|deer}} {{../STb|simony|corruption}} {{../STb|sisal|{{../Wp|agave}}}} {{../STb|siskin|bird}} {{../STy|sitka|deer}} {{../STw|situs|solitus|position}} {{../STb|sizar|student}}
{{../STa|skald|poet}} {{../STb|skua|bird}}
{{../STnx}}{{../STd|prunus spinosa|sloe|blackthorn}}
{{../STnx}}{{../STb|smew|duck}} {{../STb|smegma|≈cheese}} {{../STd|juvenile fish#Juvenile salmon|smolt|{{../Ty|fish}}}}
{{../STc|centropomidae|snook|fish}} {{../STb|snot|nose⊂}}
{{../STnx}}{{../STf|soke|legal|jurisdiction}} {{../STd|aeschynomene aspera|sola|pith}} {{../Stu|commercial|sorghum|solam}} {{../STd|solfège|solfa|{{../Ty|re}}tones}} {{../STb|somite|∈embryo}} {{../STb|sone|loudness}} {{../STf|sopor|sleep|'''sleep'''}} {{../STf|sora|bird|{{../Sm|crake}}}} {{../STj|sorb|{{../Wr|sorbus|tree}}}} {{../STb|sorghum|grass}} {{../STb|sortal|criterion}} {{../STb|sorus|[spores]}} {{../STd|souq|souk|market}} {{../STb|soursop|fruit}} {{../STb|sowar|cavalier}}
{{../STa|spahi|cavalry}} {{../STd|bract#Spathe|spathe|'''bract'''}}{{../STb|specie|'''money'''}} {{../STb|spectrin|protein}} {{../STb|sphagnum|∈bog}} {{../STb|spirula|squid}} {{../STb|sprat|{{../Ty|fish}}}} {{../Stw|tropical|sprue|disease}} {{../STd|euphorbiaceae|spurge|plants}}
{{../STc|domestic pigeon#For food|squab|{{../Ty|pigeon}}}}
{{../STd|scilla|squill|herb}}
{{../STnx}}{{../STb|sternum|∈chest}} {{../STy|stifle|joint}} {{../STb|stipa|grass}} {{../STf|stipe|botany|stalk}} {{../STb|stipule|outgrowth}} {{../STd|cattle#Terminology|stirk|yearling}} {{../STd|gens|stirps|∈family}} {{../STb|stoat|ermine}} {{../STb|stoma|pore}} {{../STd|stotting|stot|'''jump'''}} {{../STd|stretch marks|stria|scar}} {{../STb|strophe|↑ode}} {{../STb|stye|{{../Ty|@}}eye}}
{{../STa|sumo|wrestling}} {{../STf|supra|grammar|⇑}} {{../STw|sural|nerve|∈calf}} {{../STb|sutra|aphorism}} {{../Stf|sati|practice|suttee|{{../Rd|'''funeral'''}}}} {{../STd|spermophilus|suslik|squirrel}}
{{../STc|swaging|swage|forge}}
{{../STnx}}{{../STp|sais|syce|{{../Wr|groom (profession)|groom}}}} {{../STj|sylva|forest{{../Wq|sylva}}}} {{../STb|syndeton|coördinator}} {{../STb|synod|council}}

{{../eB|T}}
{{../STa|tacet|music}} {{../STf|tagma|biology|group}} {{../STb|tahr|'''goat'''}} {{../STb|taiga|forest}} {{../STb|taipan|snake}} {{../STd|honey possum|tait|{{../Ty|possum}}}} {{../STb|takin|~goat}} {{../STs|tala|music}} {{../STd|eye for an eye|talion|retribution}} {{../STd|large treeshrew|tana|'''treeshrew'''{{../Wq|tana}}}} {{../STb|tango|dance}} {{../STb|tansy|aster}} {{../STj|tantara|blast{{../Wq|tantara}}}} {{../STb|tapir|ungulate}} {{../STb|taps|lights&amp;nbsp;out}} {{../STb|tarpan|horse}} {{../STf|tarsus|skeleton|&amp;isin;foot}} {{../STb|tarsier|primate}} {{../Stw|beilschmiedia|tawa|tree}} {{../STb|tayra|weasel}}
{{../STa|tegmen|wing}} {{../STb|teind|tithe}} {{../STf|tela|disambiguation|web}} {{../STd|Sunda Stink Badger|teledu|skunk}} {{../STb|teleost|fish}} {{../STd|telicity|telic|purposeful}} {{../STb|telium|spore}} {{../STd|tellina|tellin|mollusc}}
{{../STb|tempo|timing}} {{../sTw|glossary of contract bridge terms|tenace|bridge}} {{../STb|tench|fish}} {{../STh|tenet|dogma}} {{../STd|tenrecidae|tenrec|{{../Ty|mammal}}}} {{../STb|tepal|petal}} {{../STb|terce|prayer}} {{../STd|falcon#Etymology|tercel| {{../Ty|♂}}falcon}} {{../STb|tercet|poetry}} {{../STf|teredo|bivalve|shipworm}} {{../STb|terete|{{../Xr|terete|rod}}}} {{../STb|tergum|tail}} {{../STd|flight feather#Tertials|tertial|feather}} {{../STb|tertian|music}} {{../STd|seed#Seed coat|testa|[seed]}}
{{../STa|theism|{{../Ty|re}}god}} {{../STj|thetic|dogmatic{{../Wq|Thetical Grammar}}}} {{../STl|thew|Etymology 3|muscle}} {{../STb|thorp|hamlet}} {{../STb|thrall|serf}} {{../STb|thrips|bug}} {{../STj|thrutch|squeeze}}
{{../STa|tibia|bone}} {{../STs|tila|moth}} {{../STb|tilaka|3{{../Ty|rd}}&amp;nbsp;eye}} {{../STb|tilia|lime}} {{../STb|tinea|ringworm}} {{../STd|herbal and fruit teas|tisane|tea}} {{../STj|titan|giant{{../Wq|titan}}}} {{../STb|titi|monkey}} {{../STd|alectryon excelsus|tītoki|tree}}
{{../STa|tmesis|gram&amp;nbsp;mar}}
{{../STnx}}{{../Stu|school|shark|tope}} {{../STb|tophus|gout⇒}} {{../STb|topi|antelope}} {{../STb|torero|fighter}} {{../Stq|cusk|fish|torsk}} {{../STq|trunk|anatomy|torso}}
{{../STc|trepanging|trepang|{{../Ty|c}}cucumber}} {{../STb|trett|{{../Ty|4}}waste}} {{../STb|triage|priority}}
{{../STd|charonia|triton|{{../Ty|'''c'''}}snail}} {{../STb|trogon|bird}} {{../STj|tronc|{{../Wr|tip (gratuity)|&amp;lt;tips&amp;gt;}}}} {{../STb|trugo|game}}
{{../STc|eucalyptus gomphocephala|tuart|tree}} {{../STb|tuatara|reptile}} {{../STb|tucket|fanfare}} {{../STd|schoenoplectus acutus|tule|bulrush}}
{{../STd|vernicia fordii|tung|{{../Wp|spurge}}}} {{../STb|tupelo|tree}} {{../STb|tunicle|vestment}} {{../STb|turbary|{{../Ty|re}}bog}} {{../STb|turbit|pigeon}} {{../STb|turbot|flatfish}} {{../STf|turion|botany|bud}} {{../STd|operculina turpethum|turpeth|{{../Ty|laxative}}}} {{../STd|hypericum androsaemum|tutsan|shrub}} {{../STj|tweet|{{../Wr|bird vocalization|chirp}}}} {{../STb|twite|finch}} {{../STb|typha|bulrush}}

{{../eB|U}}
{{../STi|ubiety|thereness}}
{{../STnx}}{{../STw|udal|law|tenure}} {{../STb|udder|mammaries}}
{{../STnx}}{{../STb|uhlan|lancer}}
{{../STnx}}{{../STb|ukase|edict}}
{{../STa|ulna|bone}} {{../STf|ultima|linguistics|{{../Sm|sylla}}'''ble'''}}
{{../STa|umbel|flowers}}
{{../STnx}}{{../STb|uncial|{{../TY|SCRIPT}}}}
{{../STnx}}{{../STd|antiaris#Poison|upas|poison}}
{{../STnx}}{{../STb|uria|auk}} {{../STf|ursus|genus|bear}}
{{../STnx}}{{../STf|utricle|ear|pouch}} {{../Stw|palatine|uvula|∈mouth}}

{{CourseCat}}</text>
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__NOTOC__

'''Associate editors''' help in copy-editing submissions, contacting prospective peer reviewers, formatting accepted manuscripts, and integrating suitable material into Wikipedia. They can also vote in board elections. If you are interested in joining as an associate editor, you can '''[https://en.wikiversity.org/w/index.php?title=Talk:WikiJournal_of_Medicine/Associate_editors&amp;action=edit&amp;section=new&amp;preload=WikiJournal_of_Medicine%2FAssociate_editors%2FApplication&amp;preloadtitle=Associate+editor+application&amp;summary=Associate+editor+application apply here]'''. All previous applications can be [[Talk:WikiJournal_of_Medicine/Associate_editors|viewed here]].

{{wjm_h2|Associate editors}}
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{{:WikiJournal User Group/Associate editors}}

{{wjm_h2|Duties of associate editors}}
{{#section-h:WikiJournal_User_Group/Ethics_statement|Duties of the associate editors}}
*''[[WikiJournal User Group/Ethics statement|Full ethics statement]]'', by the WikiJournal User Group

{{wjm_h2|Apply}}
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      <text bytes="4312" sha1="2kx625z4tmbiihg16r8c9mw36hd6mh0" xml:space="preserve">==South America==
&amp;emsp;The overall history of South America is given {{../GHC|History of South America}}.&amp;nbsp;
The history of the Americas as a whole is given {{../GHC|History of the Americas}}, and the Wikipedia '''portal''' for Latin America is {{../GHC|Portal:Latin America}}.

&amp;emsp; Otherwise, links to the history of the individual countries and their constituents follow in alphabetical sequence of the countries.&amp;nbsp;

===Argentina===

{{../GHc1|Venezuela|Uruguay|Brazil|Bolivia}} Its {{../GHca|Argentina|'''History'''}} and of its &lt;span style=&quot;font-weight:bold&gt;{{../GHcD|Provinces|of Argentina}}&lt;/span&gt;.

Provinces within {{../GHcE|Regions|of Argentina}} (these are a bit confused, notionally W⇒E then N⇒S).

&amp;emsp; {{../GHcF|Argentine|Northwest}}:&amp;nbsp; {{../GHcD|Jujuy|Province}} {{../GHcC|Salta|Argentina}} {{../GHcD|Tucumán|Province}} {{../GHcD|Catamarca|Province}}

&amp;emsp; {{../GHc|Gran Chaco}}&amp;nbsp; {{../GHcD|Formosa|Province}} {{../GHcD|Chaco|Province}} {{../GHcD|Santiago&amp;nbsp;del&amp;nbsp;Estero|Province}}

&amp;emsp; {{../GHcC|Mesopotamia|Argentina}}:&amp;nbsp; {{../GHcD|Misiones|Province}} {{../GHcD|Entre Ríos|Province}} {{../GHcD|Corrientes|Province}}

&amp;emsp; {{../GHcC|Cuyo|Argentina}}:&amp;nbsp; {{../GHcD|San Juan|Province, Argentina}} {{../GHcD|La Rioja|Province, Argentina}} {{../GHcD|Mendoza|Province}} {{../GHcD|San Luis|Province}}

&amp;emsp; {{../GHc|Pampas}}:&amp;nbsp; {{../GHcD|Córdoba|Province, Argentina}} {{../GHcD|Santa&amp;nbsp;Fe|Province}} {{../GHcD|La&amp;nbsp;Pampa|Province}} {{../GHcD|Buenos&amp;nbsp;Aires|Province}}

&amp;emsp; {{../GHc|Patagonia}}:&amp;nbsp; {{../GHcD|Rio&amp;nbsp;Negro|Province}} {{../GHcD|Neuquén|Province}} {{../GHcD|Chubut|Province}} {{../GHcD|Santa&amp;nbsp;Cruz|Province, Argentina}} {{../GHcD|Tierra&amp;nbsp;del&amp;nbsp;Fuego|Province, Argentina}}

A {{../GHc|List of cities in Argentina}} (Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcB|Buenos Aires}} {{../GHcC|Córdoba|Argentina}} {{../GHcA|Rosario}} {{../GHcC|Mendoza|Argentina}} {{../GHcH|La&amp;nbsp;Plata|description}} {{../GHcd|San Miguel de|Tucumán}} {{../GHcA|Mar&amp;nbsp;del&amp;nbsp;Plata}}

===Bolivia===
{{../GHc1|Argentina|Venezuela|Chile|Brazil}} {{../GHca|Bolivia|'''History'''}}

Nine {{../GHcE|Departments|of Bolivia}}: {{../GHcD|Beni|Department}} {{../GHcD|Chuquisaca|Department}} {{../GHcD|Cochabamba|Department}} ''{{../GHcE|La&amp;nbsp;Paz|Department (Bolivia)}}'' ''{{../GHcD|Oruro|Department}}'' ''{{../GHcD|Pando|Department}}'' ''{{../GHcD|Potosí|Department}}'' ''{{../GHcE|Santa&amp;nbsp;Cruz|Department (Bolivia)}}'' ''{{../GHcD|Tarija|Department}}'' (''italics&amp;nbsp;→&amp;nbsp;no history'')

{{../GhC|Cities|Bolivia#Largest_cities_and_towns}}(Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcD|Santa&amp;nbsp;Cruz|de la Sierra}} {{../GHcB|El&amp;nbsp;Alto}} {{../GHcA|La Paz}} {{../GHcB|Cochabamba}} {{../GHcC|Oruro|Bolivia}} {{../GHcB|Sucre}} {{../GHcB|Tarija}} {{../GHcH|Potosí|silver_extraction}}

===Brazil===
{{../GHc1|Bolivia|Argentina|Colombia|Chile}} '''{{../GHca|Brazil|History}}'''

&amp;thinsp;{{../GhC|States|List of Brazilian states by population density}}:&amp;nbsp; (&amp;nbsp;{{../GHcb|Federal District (Brazil)|Distrito&amp;nbsp;Federal}}&amp;nbsp;)&amp;nbsp; (Pop&lt;sup&gt;n&lt;/sup&gt;⇓)&amp;nbsp; {{../GHCc|São&amp;nbsp;Paulo|state}} {{../GHcB|Minas&amp;nbsp;Gerais}} {{../GHCc|Rio&amp;nbsp;de&amp;nbsp;Janeiro|state}}

===Chile===
{{../GHc1|Brazil|Bolivia|Ecuador|Colombia}} {{../GHca|Chile|'''History'''}}

===Colombia===
{{../GHc1|Chile|Brazil|French Guiana|Ecuador}} {{../GHca|Colombia|'''History'''}}

===Ecuador===
{{../GHc1|Colombia|Chile|Guyana|French Guiana}} {{../GHca|Ecuador|'''History'''}}

===French Guiana===
{{../GHc1|Ecuador|Colombia|Nicaragua|Guyana}} {{../GHca|French Guiana|'''History'''}}

===Guyana===
{{../GHc1|French Guiana|Ecuador|Paraguay|Nicaragua}} '''{{../GHca|Guyana|History}}'''

===Nicaragua===
{{../GHc1|Guyana|French Guiana|Peru|Paraguay}} {{../GHca|Nicaragua|'''History'''}}

===Paraguay===
{{../GHc1|Nicaragua|Guyana|Suriname|Peru}} {{../GHca|Paraguay|'''History'''}}

===Peru===
{{../GHc1|Paraguay|Nicaragua|Uruguay|Suriname}} {{../GHca|Peru|'''History'''}}

===Suriname===
{{../GHc1|Peru|Paraguay|Venezuela|Uruguay}} {{../GHca|Suriname|'''History'''}}

===Uruguay===
{{../GHc1|Suriname|Peru|Argentina|Venezuela}} {{../GHca|Uruguay|'''History'''}}

===Venezuela===
{{../GHc1|Uruguay|Suriname|Bolivia|Argentina}} {{../GHca|Venezuela|'''History'''}}</text>
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      <text bytes="4312" sha1="gnkh5vvm5eusezgpu2st5tr0a8zf4lx" xml:space="preserve">==South America==
&amp;emsp;The overall history of South America is given {{../GHC|History of South America}}.&amp;nbsp;
The history of the Americas as a whole is given {{../GHC|History of the Americas}}, and the Wikipedia '''portal''' for Latin America is {{../GHC|Portal:Latin America}}.

&amp;emsp; Otherwise, links to the history of the individual countries and their constituents follow in alphabetical sequence of the countries.&amp;nbsp;

===Argentina===

{{../GHc1|Venezuela|Uruguay|Brazil|Bolivia}} Its {{../GHca|Argentina|'''History'''}} and of its &lt;span style=&quot;font-weight:bold&gt;{{../GHcD|Provinces|of Argentina}}&lt;/span&gt;.

Provinces within {{../GHcE|Regions|of Argentina}} (these are a bit confused, notionally W⇒E then N⇒S).

&amp;emsp; {{../GHcF|Argentine|Northwest}}:&amp;nbsp; {{../GHcD|Jujuy|Province}} {{../GHcC|Salta|Argentina}} {{../GHcD|Tucumán|Province}} {{../GHcD|Catamarca|Province}}

&amp;emsp; {{../GHc|Gran Chaco}}&amp;nbsp; {{../GHcD|Formosa|Province}} {{../GHcD|Chaco|Province}} {{../GHcD|Santiago&amp;nbsp;del&amp;nbsp;Estero|Province}}

&amp;emsp; {{../GHcC|Mesopotamia|Argentina}}:&amp;nbsp; {{../GHcD|Misiones|Province}} {{../GHcD|Entre Ríos|Province}} {{../GHcD|Corrientes|Province}}

&amp;emsp; {{../GHcC|Cuyo|Argentina}}:&amp;nbsp; {{../GHcD|San Juan|Province, Argentina}} {{../GHcD|La Rioja|Province, Argentina}} {{../GHcD|Mendoza|Province}} {{../GHcD|San Luis|Province}}

&amp;emsp; {{../GHc|Pampas}}:&amp;nbsp; {{../GHcD|Córdoba|Province, Argentina}} {{../GHcD|Santa&amp;nbsp;Fe|Province}} {{../GHcD|La&amp;nbsp;Pampa|Province}} {{../GHcD|Buenos&amp;nbsp;Aires|Province}}

&amp;emsp; {{../GHc|Patagonia}}:&amp;nbsp; {{../GHcD|Rio&amp;nbsp;Negro|Province}} {{../GHcD|Neuquén|Province}} {{../GHcD|Chubut|Province}} {{../GHcD|Santa&amp;nbsp;Cruz|Province, Argentina}} {{../GHcD|Tierra&amp;nbsp;del&amp;nbsp;Fuego|Province, Argentina}}

A {{../GHc|List of cities in Argentina}} (Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcB|Buenos Aires}} {{../GHcC|Córdoba|Argentina}} {{../GHcA|Rosario}} {{../GHcC|Mendoza|Argentina}} {{../GHcH|La&amp;nbsp;Plata|description}} {{../GHcd|San Miguel de|Tucumán}} {{../GHcA|Mar&amp;nbsp;del&amp;nbsp;Plata}}

===Bolivia===
{{../GHc1|Argentina|Venezuela|Chile|Brazil}} {{../GHca|Bolivia|'''History'''}}

Nine {{../GHcE|Departments|of Bolivia}}: {{../GHcD|Beni|Department}} {{../GHcD|Chuquisaca|Department}} {{../GHcD|Cochabamba|Department}} ''{{../GHcE|La&amp;nbsp;Paz|Department (Bolivia)}}'' ''{{../GHcD|Oruro|Department}}'' ''{{../GHcD|Pando|Department}}'' ''{{../GHcD|Potosí|Department}}'' ''{{../GHcE|Santa&amp;nbsp;Cruz|Department (Bolivia)}}'' ''{{../GHcD|Tarija|Department}}'' (''italics&amp;nbsp;→&amp;nbsp;no history'')

{{../GhC|Cities|Bolivia#Largest_cities_and_towns}}(Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcD|Santa&amp;nbsp;Cruz|de la Sierra}} {{../GHcB|El&amp;nbsp;Alto}} {{../GHcA|La Paz}} {{../GHcB|Cochabamba}} {{../GHcC|Oruro|Bolivia}} {{../GHcB|Sucre}} {{../GHcB|Tarija}} {{../GHcH|Potosí|silver_extraction}}

===Brazil===
{{../GHc1|Bolivia|Argentina|Colombia|Chile}} {{../GHca|Brazil|'''History'''}}

&amp;thinsp;{{../GhC|States|List of Brazilian states by population density}}:&amp;nbsp; (&amp;nbsp;{{../GHcb|Federal District (Brazil)|Distrito&amp;nbsp;Federal}}&amp;nbsp;)&amp;nbsp; (Pop&lt;sup&gt;n&lt;/sup&gt;⇓)&amp;nbsp; {{../GHCc|São&amp;nbsp;Paulo|state}} {{../GHcB|Minas&amp;nbsp;Gerais}} {{../GHCc|Rio&amp;nbsp;de&amp;nbsp;Janeiro|state}}

===Chile===
{{../GHc1|Brazil|Bolivia|Ecuador|Colombia}} {{../GHca|Chile|'''History'''}}

===Colombia===
{{../GHc1|Chile|Brazil|French Guiana|Ecuador}} {{../GHca|Colombia|'''History'''}}

===Ecuador===
{{../GHc1|Colombia|Chile|Guyana|French Guiana}} {{../GHca|Ecuador|'''History'''}}

===French Guiana===
{{../GHc1|Ecuador|Colombia|Nicaragua|Guyana}} {{../GHca|French Guiana|'''History'''}}

===Guyana===
{{../GHc1|French Guiana|Ecuador|Paraguay|Nicaragua}} '''{{../GHca|Guyana|History}}'''

===Nicaragua===
{{../GHc1|Guyana|French Guiana|Peru|Paraguay}} {{../GHca|Nicaragua|'''History'''}}

===Paraguay===
{{../GHc1|Nicaragua|Guyana|Suriname|Peru}} {{../GHca|Paraguay|'''History'''}}

===Peru===
{{../GHc1|Paraguay|Nicaragua|Uruguay|Suriname}} {{../GHca|Peru|'''History'''}}

===Suriname===
{{../GHc1|Peru|Paraguay|Venezuela|Uruguay}} {{../GHca|Suriname|'''History'''}}

===Uruguay===
{{../GHc1|Suriname|Peru|Argentina|Venezuela}} {{../GHca|Uruguay|'''History'''}}

===Venezuela===
{{../GHc1|Uruguay|Suriname|Bolivia|Argentina}} {{../GHca|Venezuela|'''History'''}}</text>
      <sha1>gnkh5vvm5eusezgpu2st5tr0a8zf4lx</sha1>
    </revision>
    <revision>
      <id>2720895</id>
      <parentid>2720894</parentid>
      <timestamp>2025-07-06T11:00:39Z</timestamp>
      <contributor>
        <username>ShakespeareFan00</username>
        <id>6645</id>
      </contributor>
      <minor />
      <origin>2720895</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4347" sha1="dlx749qaaqbchjew2zz7f110xq65ti4" xml:space="preserve">==South America==
&amp;emsp;The overall history of South America is given {{../GHC|History of South America}}.&amp;nbsp;
The history of the Americas as a whole is given {{../GHC|History of the Americas}}, and the Wikipedia '''portal''' for Latin America is {{../GHC|Portal:Latin America}}.

&amp;emsp; Otherwise, links to the history of the individual countries and their constituents follow in alphabetical sequence of the countries.&amp;nbsp;

===Argentina===

{{../GHc1|Venezuela|Uruguay|Brazil|Bolivia}} Its {{../GHca|Argentina|'''History'''}} and of its &lt;span style=&quot;font-weight:bold&gt;{{../GHcD|Provinces|of Argentina}}&lt;/span&gt;.

Provinces within {{../GHcE|Regions|of Argentina}} (these are a bit confused, notionally W⇒E then N⇒S).

&amp;emsp; {{../GHcF|Argentine|Northwest}}:&amp;nbsp; {{../GHcD|Jujuy|Province}} {{../GHcC|Salta|Argentina}} {{../GHcD|Tucumán|Province}} {{../GHcD|Catamarca|Province}}

&amp;emsp; {{../GHc|Gran Chaco}}&amp;nbsp; {{../GHcD|Formosa|Province}} {{../GHcD|Chaco|Province}} {{../GHcD|Santiago&amp;nbsp;del&amp;nbsp;Estero|Province}}

&amp;emsp; {{../GHcC|Mesopotamia|Argentina}}:&amp;nbsp; {{../GHcD|Misiones|Province}} {{../GHcD|Entre Ríos|Province}} {{../GHcD|Corrientes|Province}}

&amp;emsp; {{../GHcC|Cuyo|Argentina}}:&amp;nbsp; {{../GHcD|San Juan|Province, Argentina}} {{../GHcD|La Rioja|Province, Argentina}} {{../GHcD|Mendoza|Province}} {{../GHcD|San Luis|Province}}

&amp;emsp; {{../GHc|Pampas}}:&amp;nbsp; {{../GHcD|Córdoba|Province, Argentina}} {{../GHcD|Santa&amp;nbsp;Fe|Province}} {{../GHcD|La&amp;nbsp;Pampa|Province}} {{../GHcD|Buenos&amp;nbsp;Aires|Province}}

&amp;emsp; {{../GHc|Patagonia}}:&amp;nbsp; {{../GHcD|Rio&amp;nbsp;Negro|Province}} {{../GHcD|Neuquén|Province}} {{../GHcD|Chubut|Province}} {{../GHcD|Santa&amp;nbsp;Cruz|Province, Argentina}} {{../GHcD|Tierra&amp;nbsp;del&amp;nbsp;Fuego|Province, Argentina}}

A {{../GHc|List of cities in Argentina}} (Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcB|Buenos Aires}} {{../GHcC|Córdoba|Argentina}} {{../GHcA|Rosario}} {{../GHcC|Mendoza|Argentina}} {{../GHcH|La&amp;nbsp;Plata|description}} {{../GHcd|San Miguel de|Tucumán}} {{../GHcA|Mar&amp;nbsp;del&amp;nbsp;Plata}}

===Bolivia===
{{../GHc1|Argentina|Venezuela|Chile|Brazil}} {{../GHca|Bolivia|'''History'''}}

Nine {{../GHcE|Departments|of Bolivia}}: {{../GHcD|Beni|Department}} {{../GHcD|Chuquisaca|Department}} {{../GHcD|Cochabamba|Department}} &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcE|La&amp;nbsp;Paz|Department (Bolivia)}}&lt;/span&gt; ''{{../GHcD|Oruro|Department}}'' ''{{../GHcD|Pando|Department}}'' ''{{../GHcD|Potosí|Department}}'' ''{{../GHcE|Santa&amp;nbsp;Cruz|Department (Bolivia)}}'' ''{{../GHcD|Tarija|Department}}'' (''italics&amp;nbsp;→&amp;nbsp;no history'')

{{../GhC|Cities|Bolivia#Largest_cities_and_towns}}(Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcD|Santa&amp;nbsp;Cruz|de la Sierra}} {{../GHcB|El&amp;nbsp;Alto}} {{../GHcA|La Paz}} {{../GHcB|Cochabamba}} {{../GHcC|Oruro|Bolivia}} {{../GHcB|Sucre}} {{../GHcB|Tarija}} {{../GHcH|Potosí|silver_extraction}}

===Brazil===
{{../GHc1|Bolivia|Argentina|Colombia|Chile}} {{../GHca|Brazil|'''History'''}}

&amp;thinsp;{{../GhC|States|List of Brazilian states by population density}}:&amp;nbsp; (&amp;nbsp;{{../GHcb|Federal District (Brazil)|Distrito&amp;nbsp;Federal}}&amp;nbsp;)&amp;nbsp; (Pop&lt;sup&gt;n&lt;/sup&gt;⇓)&amp;nbsp; {{../GHCc|São&amp;nbsp;Paulo|state}} {{../GHcB|Minas&amp;nbsp;Gerais}} {{../GHCc|Rio&amp;nbsp;de&amp;nbsp;Janeiro|state}}

===Chile===
{{../GHc1|Brazil|Bolivia|Ecuador|Colombia}} {{../GHca|Chile|'''History'''}}

===Colombia===
{{../GHc1|Chile|Brazil|French Guiana|Ecuador}} {{../GHca|Colombia|'''History'''}}

===Ecuador===
{{../GHc1|Colombia|Chile|Guyana|French Guiana}} {{../GHca|Ecuador|'''History'''}}

===French Guiana===
{{../GHc1|Ecuador|Colombia|Nicaragua|Guyana}} {{../GHca|French Guiana|'''History'''}}

===Guyana===
{{../GHc1|French Guiana|Ecuador|Paraguay|Nicaragua}} '''{{../GHca|Guyana|History}}'''

===Nicaragua===
{{../GHc1|Guyana|French Guiana|Peru|Paraguay}} {{../GHca|Nicaragua|'''History'''}}

===Paraguay===
{{../GHc1|Nicaragua|Guyana|Suriname|Peru}} {{../GHca|Paraguay|'''History'''}}

===Peru===
{{../GHc1|Paraguay|Nicaragua|Uruguay|Suriname}} {{../GHca|Peru|'''History'''}}

===Suriname===
{{../GHc1|Peru|Paraguay|Venezuela|Uruguay}} {{../GHca|Suriname|'''History'''}}

===Uruguay===
{{../GHc1|Suriname|Peru|Argentina|Venezuela}} {{../GHca|Uruguay|'''History'''}}

===Venezuela===
{{../GHc1|Uruguay|Suriname|Bolivia|Argentina}} {{../GHca|Venezuela|'''History'''}}</text>
      <sha1>dlx749qaaqbchjew2zz7f110xq65ti4</sha1>
    </revision>
    <revision>
      <id>2720896</id>
      <parentid>2720895</parentid>
      <timestamp>2025-07-06T11:01:35Z</timestamp>
      <contributor>
        <username>ShakespeareFan00</username>
        <id>6645</id>
      </contributor>
      <minor />
      <origin>2720896</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4382" sha1="2djko8469sf1m1xis74yaa49ui3a3nj" xml:space="preserve">==South America==
&amp;emsp;The overall history of South America is given {{../GHC|History of South America}}.&amp;nbsp;
The history of the Americas as a whole is given {{../GHC|History of the Americas}}, and the Wikipedia '''portal''' for Latin America is {{../GHC|Portal:Latin America}}.

&amp;emsp; Otherwise, links to the history of the individual countries and their constituents follow in alphabetical sequence of the countries.&amp;nbsp;

===Argentina===

{{../GHc1|Venezuela|Uruguay|Brazil|Bolivia}} Its {{../GHca|Argentina|'''History'''}} and of its &lt;span style=&quot;font-weight:bold&gt;{{../GHcD|Provinces|of Argentina}}&lt;/span&gt;.

Provinces within {{../GHcE|Regions|of Argentina}} (these are a bit confused, notionally W⇒E then N⇒S).

&amp;emsp; {{../GHcF|Argentine|Northwest}}:&amp;nbsp; {{../GHcD|Jujuy|Province}} {{../GHcC|Salta|Argentina}} {{../GHcD|Tucumán|Province}} {{../GHcD|Catamarca|Province}}

&amp;emsp; {{../GHc|Gran Chaco}}&amp;nbsp; {{../GHcD|Formosa|Province}} {{../GHcD|Chaco|Province}} {{../GHcD|Santiago&amp;nbsp;del&amp;nbsp;Estero|Province}}

&amp;emsp; {{../GHcC|Mesopotamia|Argentina}}:&amp;nbsp; {{../GHcD|Misiones|Province}} {{../GHcD|Entre Ríos|Province}} {{../GHcD|Corrientes|Province}}

&amp;emsp; {{../GHcC|Cuyo|Argentina}}:&amp;nbsp; {{../GHcD|San Juan|Province, Argentina}} {{../GHcD|La Rioja|Province, Argentina}} {{../GHcD|Mendoza|Province}} {{../GHcD|San Luis|Province}}

&amp;emsp; {{../GHc|Pampas}}:&amp;nbsp; {{../GHcD|Córdoba|Province, Argentina}} {{../GHcD|Santa&amp;nbsp;Fe|Province}} {{../GHcD|La&amp;nbsp;Pampa|Province}} {{../GHcD|Buenos&amp;nbsp;Aires|Province}}

&amp;emsp; {{../GHc|Patagonia}}:&amp;nbsp; {{../GHcD|Rio&amp;nbsp;Negro|Province}} {{../GHcD|Neuquén|Province}} {{../GHcD|Chubut|Province}} {{../GHcD|Santa&amp;nbsp;Cruz|Province, Argentina}} {{../GHcD|Tierra&amp;nbsp;del&amp;nbsp;Fuego|Province, Argentina}}

A {{../GHc|List of cities in Argentina}} (Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcB|Buenos Aires}} {{../GHcC|Córdoba|Argentina}} {{../GHcA|Rosario}} {{../GHcC|Mendoza|Argentina}} {{../GHcH|La&amp;nbsp;Plata|description}} {{../GHcd|San Miguel de|Tucumán}} {{../GHcA|Mar&amp;nbsp;del&amp;nbsp;Plata}}

===Bolivia===
{{../GHc1|Argentina|Venezuela|Chile|Brazil}} {{../GHca|Bolivia|'''History'''}}

Nine {{../GHcE|Departments|of Bolivia}}: {{../GHcD|Beni|Department}} {{../GHcD|Chuquisaca|Department}} {{../GHcD|Cochabamba|Department}} &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcE|La&amp;nbsp;Paz|Department (Bolivia)}}&lt;/span&gt; &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcD|Oruro|Department}}&lt;/span&gt; ''{{../GHcD|Pando|Department}}'' ''{{../GHcD|Potosí|Department}}'' ''{{../GHcE|Santa&amp;nbsp;Cruz|Department (Bolivia)}}'' ''{{../GHcD|Tarija|Department}}'' (''italics&amp;nbsp;→&amp;nbsp;no history'')

{{../GhC|Cities|Bolivia#Largest_cities_and_towns}}(Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcD|Santa&amp;nbsp;Cruz|de la Sierra}} {{../GHcB|El&amp;nbsp;Alto}} {{../GHcA|La Paz}} {{../GHcB|Cochabamba}} {{../GHcC|Oruro|Bolivia}} {{../GHcB|Sucre}} {{../GHcB|Tarija}} {{../GHcH|Potosí|silver_extraction}}

===Brazil===
{{../GHc1|Bolivia|Argentina|Colombia|Chile}} {{../GHca|Brazil|'''History'''}}

&amp;thinsp;{{../GhC|States|List of Brazilian states by population density}}:&amp;nbsp; (&amp;nbsp;{{../GHcb|Federal District (Brazil)|Distrito&amp;nbsp;Federal}}&amp;nbsp;)&amp;nbsp; (Pop&lt;sup&gt;n&lt;/sup&gt;⇓)&amp;nbsp; {{../GHCc|São&amp;nbsp;Paulo|state}} {{../GHcB|Minas&amp;nbsp;Gerais}} {{../GHCc|Rio&amp;nbsp;de&amp;nbsp;Janeiro|state}}

===Chile===
{{../GHc1|Brazil|Bolivia|Ecuador|Colombia}} {{../GHca|Chile|'''History'''}}

===Colombia===
{{../GHc1|Chile|Brazil|French Guiana|Ecuador}} {{../GHca|Colombia|'''History'''}}

===Ecuador===
{{../GHc1|Colombia|Chile|Guyana|French Guiana}} {{../GHca|Ecuador|'''History'''}}

===French Guiana===
{{../GHc1|Ecuador|Colombia|Nicaragua|Guyana}} {{../GHca|French Guiana|'''History'''}}

===Guyana===
{{../GHc1|French Guiana|Ecuador|Paraguay|Nicaragua}} '''{{../GHca|Guyana|History}}'''

===Nicaragua===
{{../GHc1|Guyana|French Guiana|Peru|Paraguay}} {{../GHca|Nicaragua|'''History'''}}

===Paraguay===
{{../GHc1|Nicaragua|Guyana|Suriname|Peru}} {{../GHca|Paraguay|'''History'''}}

===Peru===
{{../GHc1|Paraguay|Nicaragua|Uruguay|Suriname}} {{../GHca|Peru|'''History'''}}

===Suriname===
{{../GHc1|Peru|Paraguay|Venezuela|Uruguay}} {{../GHca|Suriname|'''History'''}}

===Uruguay===
{{../GHc1|Suriname|Peru|Argentina|Venezuela}} {{../GHca|Uruguay|'''History'''}}

===Venezuela===
{{../GHc1|Uruguay|Suriname|Bolivia|Argentina}} {{../GHca|Venezuela|'''History'''}}</text>
      <sha1>2djko8469sf1m1xis74yaa49ui3a3nj</sha1>
    </revision>
    <revision>
      <id>2720897</id>
      <parentid>2720896</parentid>
      <timestamp>2025-07-06T11:02:59Z</timestamp>
      <contributor>
        <username>ShakespeareFan00</username>
        <id>6645</id>
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      <minor />
      <origin>2720897</origin>
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      <format>text/x-wiki</format>
      <text bytes="4522" sha1="c8oawqr0thnhak0h1fqu96i8g6etpky" xml:space="preserve">==South America==
&amp;emsp;The overall history of South America is given {{../GHC|History of South America}}.&amp;nbsp;
The history of the Americas as a whole is given {{../GHC|History of the Americas}}, and the Wikipedia '''portal''' for Latin America is {{../GHC|Portal:Latin America}}.

&amp;emsp; Otherwise, links to the history of the individual countries and their constituents follow in alphabetical sequence of the countries.&amp;nbsp;

===Argentina===

{{../GHc1|Venezuela|Uruguay|Brazil|Bolivia}} Its {{../GHca|Argentina|'''History'''}} and of its &lt;span style=&quot;font-weight:bold&gt;{{../GHcD|Provinces|of Argentina}}&lt;/span&gt;.

Provinces within {{../GHcE|Regions|of Argentina}} (these are a bit confused, notionally W⇒E then N⇒S).

&amp;emsp; {{../GHcF|Argentine|Northwest}}:&amp;nbsp; {{../GHcD|Jujuy|Province}} {{../GHcC|Salta|Argentina}} {{../GHcD|Tucumán|Province}} {{../GHcD|Catamarca|Province}}

&amp;emsp; {{../GHc|Gran Chaco}}&amp;nbsp; {{../GHcD|Formosa|Province}} {{../GHcD|Chaco|Province}} {{../GHcD|Santiago&amp;nbsp;del&amp;nbsp;Estero|Province}}

&amp;emsp; {{../GHcC|Mesopotamia|Argentina}}:&amp;nbsp; {{../GHcD|Misiones|Province}} {{../GHcD|Entre Ríos|Province}} {{../GHcD|Corrientes|Province}}

&amp;emsp; {{../GHcC|Cuyo|Argentina}}:&amp;nbsp; {{../GHcD|San Juan|Province, Argentina}} {{../GHcD|La Rioja|Province, Argentina}} {{../GHcD|Mendoza|Province}} {{../GHcD|San Luis|Province}}

&amp;emsp; {{../GHc|Pampas}}:&amp;nbsp; {{../GHcD|Córdoba|Province, Argentina}} {{../GHcD|Santa&amp;nbsp;Fe|Province}} {{../GHcD|La&amp;nbsp;Pampa|Province}} {{../GHcD|Buenos&amp;nbsp;Aires|Province}}

&amp;emsp; {{../GHc|Patagonia}}:&amp;nbsp; {{../GHcD|Rio&amp;nbsp;Negro|Province}} {{../GHcD|Neuquén|Province}} {{../GHcD|Chubut|Province}} {{../GHcD|Santa&amp;nbsp;Cruz|Province, Argentina}} {{../GHcD|Tierra&amp;nbsp;del&amp;nbsp;Fuego|Province, Argentina}}

A {{../GHc|List of cities in Argentina}} (Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcB|Buenos Aires}} {{../GHcC|Córdoba|Argentina}} {{../GHcA|Rosario}} {{../GHcC|Mendoza|Argentina}} {{../GHcH|La&amp;nbsp;Plata|description}} {{../GHcd|San Miguel de|Tucumán}} {{../GHcA|Mar&amp;nbsp;del&amp;nbsp;Plata}}

===Bolivia===
{{../GHc1|Argentina|Venezuela|Chile|Brazil}} {{../GHca|Bolivia|'''History'''}}

Nine {{../GHcE|Departments|of Bolivia}}: {{../GHcD|Beni|Department}} {{../GHcD|Chuquisaca|Department}} {{../GHcD|Cochabamba|Department}} &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcE|La&amp;nbsp;Paz|Department (Bolivia)}}&lt;/span&gt; &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcD|Oruro|Department}}&lt;/span&gt; &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcD|Pando|Department}}&lt;/span&gt; &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcD|Potosí|Department}}&lt;/span&gt; &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcE|Santa&amp;nbsp;Cruz|Department (Bolivia)}}&lt;/span&gt; &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcD|Tarija|Department}}&lt;/span&gt; (''italics&amp;nbsp;→&amp;nbsp;no history'')

{{../GhC|Cities|Bolivia#Largest_cities_and_towns}}(Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcD|Santa&amp;nbsp;Cruz|de la Sierra}} {{../GHcB|El&amp;nbsp;Alto}} {{../GHcA|La Paz}} {{../GHcB|Cochabamba}} {{../GHcC|Oruro|Bolivia}} {{../GHcB|Sucre}} {{../GHcB|Tarija}} {{../GHcH|Potosí|silver_extraction}}

===Brazil===
{{../GHc1|Bolivia|Argentina|Colombia|Chile}} {{../GHca|Brazil|'''History'''}}

&amp;thinsp;{{../GhC|States|List of Brazilian states by population density}}:&amp;nbsp; (&amp;nbsp;{{../GHcb|Federal District (Brazil)|Distrito&amp;nbsp;Federal}}&amp;nbsp;)&amp;nbsp; (Pop&lt;sup&gt;n&lt;/sup&gt;⇓)&amp;nbsp; {{../GHCc|São&amp;nbsp;Paulo|state}} {{../GHcB|Minas&amp;nbsp;Gerais}} {{../GHCc|Rio&amp;nbsp;de&amp;nbsp;Janeiro|state}}

===Chile===
{{../GHc1|Brazil|Bolivia|Ecuador|Colombia}} {{../GHca|Chile|'''History'''}}

===Colombia===
{{../GHc1|Chile|Brazil|French Guiana|Ecuador}} {{../GHca|Colombia|'''History'''}}

===Ecuador===
{{../GHc1|Colombia|Chile|Guyana|French Guiana}} {{../GHca|Ecuador|'''History'''}}

===French Guiana===
{{../GHc1|Ecuador|Colombia|Nicaragua|Guyana}} {{../GHca|French Guiana|'''History'''}}

===Guyana===
{{../GHc1|French Guiana|Ecuador|Paraguay|Nicaragua}} '''{{../GHca|Guyana|History}}'''

===Nicaragua===
{{../GHc1|Guyana|French Guiana|Peru|Paraguay}} {{../GHca|Nicaragua|'''History'''}}

===Paraguay===
{{../GHc1|Nicaragua|Guyana|Suriname|Peru}} {{../GHca|Paraguay|'''History'''}}

===Peru===
{{../GHc1|Paraguay|Nicaragua|Uruguay|Suriname}} {{../GHca|Peru|'''History'''}}

===Suriname===
{{../GHc1|Peru|Paraguay|Venezuela|Uruguay}} {{../GHca|Suriname|'''History'''}}

===Uruguay===
{{../GHc1|Suriname|Peru|Argentina|Venezuela}} {{../GHca|Uruguay|'''History'''}}

===Venezuela===
{{../GHc1|Uruguay|Suriname|Bolivia|Argentina}} {{../GHca|Venezuela|'''History'''}}</text>
      <sha1>c8oawqr0thnhak0h1fqu96i8g6etpky</sha1>
    </revision>
    <revision>
      <id>2720898</id>
      <parentid>2720897</parentid>
      <timestamp>2025-07-06T11:03:40Z</timestamp>
      <contributor>
        <username>ShakespeareFan00</username>
        <id>6645</id>
      </contributor>
      <minor />
      <origin>2720898</origin>
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      <format>text/x-wiki</format>
      <text bytes="4522" sha1="c1jj4ylm2nml4fns02a0l3c7u5cchhv" xml:space="preserve">==South America==
&amp;emsp;The overall history of South America is given {{../GHC|History of South America}}.&amp;nbsp;
The history of the Americas as a whole is given {{../GHC|History of the Americas}}, and the Wikipedia '''portal''' for Latin America is {{../GHC|Portal:Latin America}}.

&amp;emsp; Otherwise, links to the history of the individual countries and their constituents follow in alphabetical sequence of the countries.&amp;nbsp;

===Argentina===

{{../GHc1|Venezuela|Uruguay|Brazil|Bolivia}} Its {{../GHca|Argentina|'''History'''}} and of its &lt;span style=&quot;font-weight:bold&gt;{{../GHcD|Provinces|of Argentina}}&lt;/span&gt;.

Provinces within {{../GHcE|Regions|of Argentina}} (these are a bit confused, notionally W⇒E then N⇒S).

&amp;emsp; {{../GHcF|Argentine|Northwest}}:&amp;nbsp; {{../GHcD|Jujuy|Province}} {{../GHcC|Salta|Argentina}} {{../GHcD|Tucumán|Province}} {{../GHcD|Catamarca|Province}}

&amp;emsp; {{../GHc|Gran Chaco}}&amp;nbsp; {{../GHcD|Formosa|Province}} {{../GHcD|Chaco|Province}} {{../GHcD|Santiago&amp;nbsp;del&amp;nbsp;Estero|Province}}

&amp;emsp; {{../GHcC|Mesopotamia|Argentina}}:&amp;nbsp; {{../GHcD|Misiones|Province}} {{../GHcD|Entre Ríos|Province}} {{../GHcD|Corrientes|Province}}

&amp;emsp; {{../GHcC|Cuyo|Argentina}}:&amp;nbsp; {{../GHcD|San Juan|Province, Argentina}} {{../GHcD|La Rioja|Province, Argentina}} {{../GHcD|Mendoza|Province}} {{../GHcD|San Luis|Province}}

&amp;emsp; {{../GHc|Pampas}}:&amp;nbsp; {{../GHcD|Córdoba|Province, Argentina}} {{../GHcD|Santa&amp;nbsp;Fe|Province}} {{../GHcD|La&amp;nbsp;Pampa|Province}} {{../GHcD|Buenos&amp;nbsp;Aires|Province}}

&amp;emsp; {{../GHc|Patagonia}}:&amp;nbsp; {{../GHcD|Rio&amp;nbsp;Negro|Province}} {{../GHcD|Neuquén|Province}} {{../GHcD|Chubut|Province}} {{../GHcD|Santa&amp;nbsp;Cruz|Province, Argentina}} {{../GHcD|Tierra&amp;nbsp;del&amp;nbsp;Fuego|Province, Argentina}}

A {{../GHc|List of cities in Argentina}} (Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcB|Buenos Aires}} {{../GHcC|Córdoba|Argentina}} {{../GHcA|Rosario}} {{../GHcC|Mendoza|Argentina}} {{../GHcH|La&amp;nbsp;Plata|description}} {{../GHcd|San Miguel de|Tucumán}} {{../GHcA|Mar&amp;nbsp;del&amp;nbsp;Plata}}

===Bolivia===
{{../GHc1|Argentina|Venezuela|Chile|Brazil}} {{../GHca|Bolivia|'''History'''}}

Nine {{../GHcE|Departments|of Bolivia}}: {{../GHcD|Beni|Department}} {{../GHcD|Chuquisaca|Department}} {{../GHcD|Cochabamba|Department}} &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcE|La&amp;nbsp;Paz|Department (Bolivia)}}&lt;/span&gt; &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcD|Oruro|Department}}&lt;/span&gt; &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcD|Pando|Department}}&lt;/span&gt; &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcD|Potosí|Department}}&lt;/span&gt; &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcE|Santa&amp;nbsp;Cruz|Department (Bolivia)}}&lt;/span&gt; &lt;span style=&quot;font-style:italic&quot;&gt;{{../GHcD|Tarija|Department}}&lt;/span&gt; (''italics&amp;nbsp;→&amp;nbsp;no history'')

{{../GhC|Cities|Bolivia#Largest_cities_and_towns}}(Pop&lt;sup&gt;n&lt;/sup&gt;⇓) :&amp;nbsp; {{../GHcD|Santa&amp;nbsp;Cruz|de la Sierra}} {{../GHcB|El&amp;nbsp;Alto}} {{../GHcA|La Paz}} {{../GHcB|Cochabamba}} {{../GHcC|Oruro|Bolivia}} {{../GHcB|Sucre}} {{../GHcB|Tarija}} {{../GHcH|Potosí|silver_extraction}}

===Brazil===
{{../GHc1|Bolivia|Argentina|Colombia|Chile}} {{../GHca|Brazil|'''History'''}}

&amp;thinsp;{{../GhC|States|List of Brazilian states by population density}}:&amp;nbsp; (&amp;nbsp;{{../GHcb|Federal District (Brazil)|Distrito&amp;nbsp;Federal}}&amp;nbsp;)&amp;nbsp; (Pop&lt;sup&gt;n&lt;/sup&gt;⇓)&amp;nbsp; {{../GHCc|São&amp;nbsp;Paulo|state}} {{../GHcB|Minas&amp;nbsp;Gerais}} {{../GHCc|Rio&amp;nbsp;de&amp;nbsp;Janeiro|state}}

===Chile===
{{../GHc1|Brazil|Bolivia|Ecuador|Colombia}} {{../GHca|Chile|'''History'''}}

===Colombia===
{{../GHc1|Chile|Brazil|French Guiana|Ecuador}} {{../GHca|Colombia|'''History'''}}

===Ecuador===
{{../GHc1|Colombia|Chile|Guyana|French Guiana}} {{../GHca|Ecuador|'''History'''}}

===French Guiana===
{{../GHc1|Ecuador|Colombia|Nicaragua|Guyana}} {{../GHca|French Guiana|'''History'''}}

===Guyana===
{{../GHc1|French Guiana|Ecuador|Paraguay|Nicaragua}} {{../GHca|Guyana|'''History'''}}

===Nicaragua===
{{../GHc1|Guyana|French Guiana|Peru|Paraguay}} {{../GHca|Nicaragua|'''History'''}}

===Paraguay===
{{../GHc1|Nicaragua|Guyana|Suriname|Peru}} {{../GHca|Paraguay|'''History'''}}

===Peru===
{{../GHc1|Paraguay|Nicaragua|Uruguay|Suriname}} {{../GHca|Peru|'''History'''}}

===Suriname===
{{../GHc1|Peru|Paraguay|Venezuela|Uruguay}} {{../GHca|Suriname|'''History'''}}

===Uruguay===
{{../GHc1|Suriname|Peru|Argentina|Venezuela}} {{../GHca|Uruguay|'''History'''}}

===Venezuela===
{{../GHc1|Uruguay|Suriname|Bolivia|Argentina}} {{../GHca|Venezuela|'''History'''}}</text>
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      <text bytes="167313" sha1="rr6wzkwuchaecg4n6k7rbv9hllsouyo" xml:space="preserve">[[File:Leslie Ward - Vanity Fair, Newspapermen, ^Algy^, The Hon Algernon Henry Bourke, Januray 20, 1898 - B1979.14.521 - Yale Center for British Art.jpg|thumb|Hon. Algernon Bourke, ''Vanity Fair'', 1898]]

==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
** Button Bourke&lt;ref&gt;&quot;A Tory 'Reformer' at the India Office.&quot; ''India'' 10 November 1911, Friday: 4 [of 12], Col. 1b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004300/19111110/007/0004#. Print: same title, p. 228.&lt;/ref&gt;
** Algy Bourke
* Mrs. Gwendolen Bourke
** Gwendolen&lt;ref&gt;General Register Office. ''England and Wales Civil Registration Indexes''. London, England: General Register Office. FreeBMD. ''England &amp; Wales, Civil Registration Marriage Index, 1837-1915''[database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2006.&lt;/ref&gt;{{rp|Marriage Index}} &lt;ref name=&quot;:15&quot; /&gt;{{rp|''Morning Post'' article about her name}} &lt;ref&gt;General Register Office. ''England and Wales Civil Registration Indexes''. London, England: General Register Office. FreeBMD. ''England &amp; Wales, Civil Registration Marriage Index, 1837-1915''[database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2006.&lt;/ref&gt;{{rp|Electoral Register}}
** Guendoline&lt;ref name=&quot;:1&quot; /&gt; [The National Portrait Gallery, London, uses this spelling for Lafayette's portrait of Bourke in costume for the ball.&lt;ref name=&quot;:23&quot; /&gt;]
** Gwendoline&lt;ref name=&quot;:14&quot;&gt;City of Westminster Archives Centre; London, England; ''Westminster Church of England Parish Registers''; Reference: ''SPWP/PR/1/2''. Ancestry.com. ''Westminster, London, England, Church of England Births and Baptisms, 1813-1919'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2020.&lt;/ref&gt;{{rp|Births and Baptisms}}
* Shelley Bontein and Emilie Sloane-Stanley Bontein
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father and then brother, and other Bourkes

== Overview ==

=== Algernon Bourke ===
Although the Hon. Algernon Henry Bourke was born in Dublin in 1854 and came from a family whose title is in the Peerage of Ireland,&lt;ref name=&quot;:6&quot;&gt;1911 England Census.&lt;/ref&gt; he seems to have spent much of his adult life generally in England and especially in London. He was &quot;a noted fisherman.&quot;&lt;ref&gt;&quot;London Correspondence.&quot; ''Freeman's Journal'' 21 December 1897, Tuesday: 5 [of 8], Col. 5c [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000056/18971221/027/0005. Same print title, n.p.&lt;/ref&gt;

Because he was the son of the [[Social Victorians/People/Mayo|Earl of Mayo]], perhaps, or perhaps because he was so involved in projects that got reported on, he was mentioned a great deal in the newspapers, but after his bankruptcy, he seems to have receded in prominence, in part because he was living outside of the U.K., and apparently separately from his wife, Gwendolen Bourke.

Bourke ran as the Conservative candidate for Parliament from Clapham (population, c. 70,000) in 1885, a race he did not win. As a candidate he is described like this:&lt;blockquote&gt;Acted as a newspaper correspondent during the Zulu war. Subsequently Poor-law inspector in the West of Ireland. &quot;A loyal supporter of Church and State.&quot; Desires to reduce the School Board expenditure, and revive trade; and is opposed to Mr. Chamberlain's &quot;police of hasty and experimental reform.&quot;&lt;ref&gt;&quot;Clapham (70,000).&quot; ''South London Chronicle'' 17 October 1885, Saturday: 5 [of 8], Col. 5a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000443/18851017/113/0005. Print title ''South London Chronicle and Southwark and Lambeth Ensign'', p. 5.&lt;/ref&gt;&lt;/blockquote&gt;The London ''Weekly Dispatch'' says he is &quot;a dashing and unscrupulous young Tory.&quot;&lt;ref&gt;&quot;The Political Campaign in London.&quot; ''Weekly Dispatch'' (London) 15 November 1885, Sunday: 9 [of 16], Col. 3c [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003358/18851115/069/0009. Same print title and p.&lt;/ref&gt;

&quot;Algy&quot; Bourke was &quot;Man of the Day&quot; (No. DCCII [522) for ''Vanity Fair'' in 1898, caricatured by Leslie Ward (above right):&lt;blockquote&gt;Son of the great and murdered Lord Mayo, he is contemporary with the outbreak of the Crimean War, he is a Member of the London Stock Exchange, he has a beautiful wife and a daughter, and, being a very fashionable young man, he was once refused as their Member by the worthy electors of Clapham. He was an Eton boy, of course: and less naturally he went to Cambridge; where he was made President of the Beefsteak, the Amateur Dramatic, the Athenaeum, the True Blue, and the Hibernian Clubs. When he came down he tried journalism and went to Zululand as a ''Daily Telegraph'' ‘‘special”; after which he was improved into an Inspector of Workhouses [2, Col. 2c – 3, Col. 1a] in Ireland: which may account for his proficiency as a caterer. For seven years he worked under the late Mr. Chinnery on ''The Times'': being popularly supposed to look after that journal's morals. He is a good man of business, and a great organiser who has made White's Club pay even if it be less “smart&quot; than it was. He has done much for Willis’s since he took it in hand; he did well with his Battersea venture, and he thinks that he only failed with the Summer Club in Kensington Gardens because people would not go to the wrong side of the Park. Moreover, he runs a Club at Brighton, and he is Chairman of the Grand Hotel at Monte Carlo: whither he once organised a cheap trip. Altogether he is a veritable Clubman, and a very successful arranger of amusements, associations, and restaurants.

He is a popular fellow who is known to all of us; and though he is a little inclined to be quarrelsome, no one can get much the better of him. He is also a quick grasper of facts and a good talker. His favourite sports are fishing and the organising of associations for the introduction of salmon to the Thames. By way of being an art critic, he has made an interesting collection of engravings of the members of White’s Club from its foundation; but his friends say that he is not a well-dressed man. He has also written a history of White’s, and he is now writing one of Brooks's Club. He is a genial person, who looks as if the world agreed with him well.

He is an aquisition [sic] to a house party; and they call him “Algy.”&lt;ref&gt;&quot;Men of the Day.&quot; — No. DCCII [522]. The Hon. Algernon Henry Bourke.&quot; ''Vanity Fair'' 20 January 1898, Thursday: 2 [of 4], Col. 2c – 3, Col. 3a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9900020/18980120/010/0002 and https://www.britishnewspaperarchive.co.uk/viewer/BL/9900020/18980120/005/0003. Same print title, pp. 41–42. Portrait is full page, on p. 1.&lt;/ref&gt;&lt;/blockquote&gt;The Hon. Algernon Bourke and Mr. Algernon Bourke, depending on the newspaper article, were the same person. Calling him Mr. Bourke in the newspapers, especially when considered as a businessman or (potential) member of Parliament, does not rule out the son of an earl, who would normally be accorded the honorific of ''Honorable''.

=== Gwendolen Sloane-Stanley Bourke ===

Mrs. Gwendolen Bourke exhibited at dog shows successfully and was a [[Social Victorians/Timeline/1900s#Society Sportswomen|noted deerstalker]] and &quot;an appreciative listener to good music.&quot;&lt;ref&gt;&quot;Vanity Fair.&quot; ''Lady of the House'' 15 June 1899, Thursday: 4 [of 44], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004836/18990615/019/0004.&lt;/ref&gt; Her personal beauty is often mentioned in reports, and ''The World'' says she was &quot;a magnificent woman.&quot;&lt;ref&gt;&quot;Beauties of To-Day. From the ''World''.&quot; ''Clifton Society'' 24 June 1897, Thursday: 14 [of 16], Col. 2c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002164/18970624/066/0014. Same print and p.&lt;/ref&gt; She is the first listed in the ''Graphic''&lt;nowiki/&gt;'s 1891 &quot;Leading Ladies of Society&quot;:&lt;blockquote&gt;The Hon. Mrs. Algernon Bourke is a daughter (Gwendoline Irene Emily) of the late Hans Sloane Stanley, Esq., of Poultons, Southampton, and 49, Cadogan Square, S.W. She married, on December 15th, 1887, the Hon. Algernon Bourke, third son of the sixth Earl of Mayo, Governor-General of India (who was assassinated in 1872), and nephew of Lord Connemara, Governor of Madras. Mr. Bourke is a member of the London Stock Exchange, and resides at 33, Cadogan Terrace, S.W.&lt;ref&gt;&quot;Leading Ladies of Society.&quot; The Graphic 28 March 1891, Saturday: 6 [of 28], Col. 2c [of 3]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18910328/019/0006. Print: same title, p. 346.&lt;/ref&gt;&lt;/blockquote&gt;She attended many social events without her husband, especially into the 20th century, usually with an appreciative description of what she wore. She was a sponsor of Irish art needlework as well. Unlike her husband's, Gwendolen's social status seems to have risen as time passed, and she appears in stories associated with the Princess of Wales, and then later with Queen Alexandra.

=== The Sloane-Stanley Family ===
Gwendolen's family consisted of a younger brother, Cyril Sloane-Stanley, as well as her parents, Hans Sloane-Stanley and Emilie Edwards Sloane-Stanley. Exactly one year after she and Algernon Bourke married, Hans Sloane-Stanley died (in 1888), leaving an estate worth £33,704 7s. 5d.&lt;ref name=&quot;:17&quot;&gt;Principal Probate Registry; London, England; ''Calendar of the Grants of Probate and Letters of Administration made in the Probate Registries of the High Court of Justice in England''. Ancestry.com. ''England &amp; Wales, National Probate Calendar (Index of Wills and Administrations), 1858-1995'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt; (1888, 321) Her mother remarried almost exactly a year after that, to James Shelly Bontein. Bontein's father had been Gentleman Usher and Clerk of the Robes to Queen Victoria.&lt;ref name=&quot;:18&quot;&gt;&quot;Marriages.&quot; &quot;Births, Marriages, and Deaths.&quot; ''Belfast News-Letter'' 6 December 1889, Friday: 1 [of 8], Col. 1a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/18891206/001/0001. Same print title and p.&lt;/ref&gt;

Shortly after his death ''Truth'' described Gwendolen and Cyril's father Hans Sloane-Stanley:&lt;blockquote&gt;The death of Mr. Sloane Stanley, of Paultons Park, is much regretted in South Hants, as he was one of the most popular landlords in the county, and was greatly esteemed. Mr. Sloane Stanley was well known in yachting circles, and for many years he was Commodore of the Royal Southern Yacht Club, and owned the schooner ''Star of the West''. He was one of the very few owners who continued to keep up the old custom of giving his crew a laying-up supper at the close of each season. There were great festivities at Paultons only a few months ago, when Miss Sloane Stanley was married to Mr. Algernon Bourke.&lt;ref&gt;&quot;Entre Nous.&quot; ''Truth'' 27 December 1888, Thursday: 6 [of 48], Col. 2b [of 2]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18881227/023/0006# https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18881227/023/0006]. Same print title, p. 1136.&lt;/ref&gt;&lt;/blockquote&gt;When he died in 1944, Cyril Sloane-Stanley's estate was quite a bit larger than his father's had been 50 years before. The probate was divided between what was limited to &quot;settled land&quot; and what was &quot;save and except settled land.&quot; What was not settled land totalled £356,114 12s. 10d. and went to John Everett, company director; the Hon. Elwyn Villiers Rhys, captain, H.M. army; and William Adam de Geijer, retired captain, H.M. army.&lt;ref name=&quot;:17&quot; /&gt; (1944, 430) His daughter Lavender was married to John Everett, and Diane was married to Elwyn Villiers Rhys. What was settled land totalled £168,975 and went to William Adam de Geijer, retired captain, H.M. army, and George Lawrence Stewart, solicitor.&lt;ref name=&quot;:17&quot; /&gt; (1944, 430)

The Sloane-Stanleys descend from Hans Sloane (1660–1753), whose 71,000-item collections &quot;provid[ed] the foundation of the British Museum, the British Library, and the Natural History Museum, London.&quot;&lt;ref name=&quot;:19&quot;&gt;{{Cite journal|date=2025-01-07|title=Hans Sloane|url=https://en.wikipedia.org/wiki/Hans_Sloane|journal=Wikipedia https://en.wikipedia.org/wiki/Hans_Sloane|language=en|via=}}&lt;/ref&gt; Much of this Hans Sloane's wealth came from his medical practice in Jamaica, where he went as physician to the Governor General of Jamaica, the 2nd Duke of Albemarle, and where he married &quot;a wealthy heiress of sugar plantations&quot; worked by enslaved Jamaicans.&lt;ref name=&quot;:19&quot; /&gt; His great-nephew, Hans Sloane, inherited Paultons, near Romsey, &quot;and in recognition of this he adopted the additional surname of Stanley in 1821.&quot;&lt;ref&gt;{{Cite journal|date=2023-10-06|title=Hans Sloane (MP)|url=https://en.wikipedia.org/wiki/Hans_Sloane_(MP)|journal=Wikipedia https://en.wikipedia.org/wiki/Hans_Sloane_(MP)|language=en}}&lt;/ref&gt;

== Acquaintances, Friends and Enemies ==

=== Algernon Bourke ===

* Best man at [[Social Victorians/Timeline/1887#Wedding of Algernon Bourke and Gwendolen Sloane Stanley|his wedding]]: the Hon. Michael Sandys
* [[Social Victorians/People/Montrose|Marcus Henry Milner]], &quot;one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys&quot;&lt;ref name=&quot;:8&quot;&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 2a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;
* Caroline, Duchess of Montrose — her &quot;legal advisor&quot; on the day of her marriage to Marcus Henry Milner&lt;ref&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 1b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;

=== Gwendolen Bourke ===

* Bridesmaids at [[Social Victorians/Timeline/1887#Wedding of Algernon Bourke and Gwendolen Sloane Stanley|her wedding]]: Lady Florence Bourke, Miss Nora Bourke, Miss Edwards, and Miss Ewart
* Lord and Lady Alington, Belvedere House, Scarborough
* [[Social Victorians/People/William James|Evelyn James]] 

== Organizations ==

=== Gwendolen Bourke ===

* Member, the Ladies Committee for the [[Social Victorians/London Clubs#Prince's Skating Club|Prince's Skating Club]], which also included [[Social Victorians/People/Princess Louise|Princess Louise]] (Duchess of Argyll), the [[Social Victorians/People/Portland|Duchess of Portland]], [[Social Victorians/People/Londonderry|Lady Londonderry]], [[Social Victorians/People/Campbell|Lady Archibald Campbell]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], and [[Social Victorians/People/Asquith|Mrs. Asquith]]&lt;ref name=&quot;:11&quot;&gt;&quot;What the 'World' Says.&quot; ''Northwich Guardian'' 01 November 1902, Saturday: 6 [of 8], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001975/19021101/134/0006. Print title: The ''Guardian'', p. 6.&lt;/ref&gt; (in 1902, at least)

=== Algernon Bourke ===
* [[Social Victorians/Schools#Eton|Eton]]
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1881: Partner, with 2 uncles, in Brunton, Bourke, and Co.&lt;ref&gt;&quot;From Our London Correspondent.&quot; ''Manchester Courier'' 24 August 1881, Wednesday: 5 [of 8], Col. 4a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000206/18810824/030/0005. Print: ''Manchester Courier and Lancaster General Advertiser'', p. 5.&lt;/ref&gt; (one of the [[Social Victorians/British Aristocracy#Sons of Peers on the Stock Exchange|sons of peers on the Stock Exchange]])
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* 1886: Battersea Friendly Angling Society&lt;ref&gt;&quot;Battersea Friendly Angling Society.&quot; ''Fishing Gazette'' 17 April 1886, Saturday: 6 [of 20], Col. 2a [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002553/18860417/030/0006. Same print title, p. 218.&lt;/ref&gt;
* 27 February 1886: one of the Vice Presidents of the [[Social Victorians/London Clubs#Bolingbroke Reading-Room and Institute|Bolingbroke Reading-Room and Institute]]
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt; ( – 1901 [at least])
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Willis's Rooms (described in 1895):&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;
*The [[Social Victorians/London Clubs#Pelican|Pelican Club]], known for its boxing (1891)

==== Boards of Directors ====
*1883: One of the directors, the Franco-English Tunisian Esparto Fibre Supply Company, Ltd.&lt;ref&gt;''Money Market Review'', 20 Jan 1883 (Vol 46): 124.&lt;/ref&gt;
*1891: One of the founders, the Discount Banking Company, Ltd., which says Algernon Bourke is a director of District Messenger Services and News Company, Ltd.&lt;ref&gt;&quot;Public Company.&quot; ''Nottingham Journal'' 31 October 1891, Saturday: 4 [of 8], Col. 8a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001896/18911031/099/0004. Print title: ''The Nottingham Daily Express'', p. 4.&lt;/ref&gt;
*1894: One of the directors, the Frozen Lake, Ltd., with Admiral Maxse, Lord [[Social Victorians/People/Beresford|Marcus Beresford]], [[Social Victorians/People/Williams|Hwfa Williams]]&lt;ref&gt;&quot;The Frozen Lake, Limited.&quot; ''St James's Gazette'' 08 June 1894, Friday: 15 [of 16], Col. 4a [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/18940608/085/0015. Print p. 15.&lt;/ref&gt;&lt;blockquote&gt;London is to have new amusement this winter, for which Mr Algernon Bourke, who has taught us that it is possible to eat as well in St. James’s as on the Boulevards, and Mr Hwfa Williams, of Sandown fame, are jointly responsible. The &quot;Frozen Lake,&quot; under which title a real ice-skating rink is about to be constructed under their auspices, will no doubt be gladly welcomed by all skaters, and the venture is likely to prove a success.&lt;ref&gt;&quot;Society Gossip.&quot; ''Weston-super-Mare Gazette, and General Advertiser'' 6 June 1894, Wednesday: 4 [of 4], Col. 4b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001444/18940606/044/0004. Print title: ''Weston-super-Mare Gazette'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

==== Committees ====

*Member, General Committee, [[Social Victorians/London Clubs#Baths|the Baths Club]] (1892)
*Member, Men's Committee of the [[Social Victorians/London Clubs#Prince's Skating Club|Prince's Skating Club]], which also included Lord Edward Cecil, Lord Redesdale, Mr. [[Social Victorians/People/Lyttelton|Alfred Lyttelton]], Sir Edgar Vincent, Sir William Hart Dyke, and Mr. [[Social Victorians/People/Grenfell|W. H. Grenfell]]&lt;ref name=&quot;:11&quot; /&gt; (1902, at least)
*[[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)
* Member of an &quot;influential committee&quot; headed by the Lord Mayor &quot;to restore salmon to the Thames&quot; (June 1899)&lt;ref&gt;&quot;Salmon in the Thames.&quot; ''Berks and Oxon Advertiser'' 30 June 1899, Friday: 5 [of 8], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002298/18990630/079/0005. Print n.p.&lt;/ref&gt;

== Timeline ==

=== 1870s ===
'''1872 February 8''', Richard Bourke, 6th Earl of Mayo was assassinated while inspecting a &quot;convict settlement at Port Blair in the Andaman Islands ... by Sher Ali Afridi, a former Afghan soldier.&quot;&lt;ref&gt;{{Cite journal|date=2024-12-01|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo.&lt;/ref&gt; The Hon. Algernon's brother Dermot became the 7th Earl at 19 years old.

'''1876 November 24, Friday''', the Hon. Algernon Bourke was one of 6 men (2 students, one of whom was Bourke; 2 doctors; a tutor and another man) from Cambridge who gave evidence as witnesses in an inquest about the death from falling off a horse of a student.&lt;ref&gt;&quot;The Fatal Accident to a Sheffield Student at Cambridge.&quot; ''Sheffield Independent'' 25 November 1876, Saturday: 7 [of 12], Col. 5a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000181/18761125/040/0007. Print title: ''Sheffield and Rotherham Independent'', n. p.&lt;/ref&gt;

'''1879 December 27, Saturday – 29, Monday''', Algernon Bourke was in Kilrush as a Local Government Board Inspector:&lt;blockquote&gt;Among many distinguished visitors at the Vandeleur Arms Hotel, Kilrush this week was the Hon. Algernon Bourke Local Government Board Inspector who arrived on Saturday, and sojourned there until 2 o'clock on Monday, when the honourable gentleman left by Steamer tor Limerick.&lt;ref&gt;&quot;Fashionable Intelligence.&quot; ''Kilrush Herald and Kilkee Gazette'' 01 January 1880, Thursday: 2 [of 5], Col. 3a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003186/18800101/011/0002. Print title ''Kilrush Herald'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;

=== 1880s ===
'''4 February 1880, Wednesday''', Hon. Algernon Bourke attended the [[Social Victorians/Timeline/1880#Grand Ball at Palmerstown House Hosted by the Earl of Mayo|grand ball at Palmerstown House hosted by the Earl of Mayo]]. 

'''1880 March 30, Tuesday''', Algernon Bourke was working in the judicial system in Newcastle, County Limerick, possibly as Poorhouse Inspector:&lt;blockquote&gt;A sworn enquiry was held to-day at the Workhorse, Newcastle West, by the Hon Algernon Bourke, L.G.I., to enquire into charges preferred by Dr. Pierce, Medical Office, against Dr. O'Shaughnesay. The enquiry was adjourned till Thursday next. Mr Moran, sol., Rathkeale, was engaged for Dr. O'Shaughnessy.&lt;ref&gt;&quot;Sworn Enquiry.&quot; &quot;Limerick County. Newcastle West Intelligence.&quot; ''Bassett's Chronicle'' 31 March 1880, Wednesday: 3 [of 4], Col. 3b–c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003471/18800331/044/0003.  Print title ''Bassett's Daily Chronicle'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;'''1880 April 17, Saturday''', in-jokes dominate this report mentioning Algernon Bourke in the context of the Kildare and National Hunt races in Dublin:&lt;blockquote&gt;And in mopy Upper Mount-street, where young Algernon Bourke, of the Onety-oneth, had promised to call for, and afterwards spin down to the races in his mail phaeton, the Blake girls; and in fastidious Fitzwilliam-place, and exclusive &quot;Murryan-squeer,&quot; from which dashing army men, in their neatly-appointed, well horsed drags were to &quot;tool&quot; down sweet young Dublin lasses of the ''crême d la crême'' [sic], many an anxious forecasting of the weather was taken, lest by an unpropitious shower that last triumph of Mrs. Manning, or the Forrests, or Miss Sedford, or any of the ''grandes dames de la mode'' should be rendered as worthless as a Confederate &quot;greenback.&quot; But by ten o'clock all doubts were happily set aside, and up struck the lovely April day in all its spring-time glory and then the road, oh, the road!&lt;ref&gt;&quot;To Punchestown and Back by the Old Road.&quot; ''Illustrated Sporting and Dramatic News'' 17 April 1880, Saturday: 6 [of 24], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001857/18800417/013/0006. Same print title, p. 102.&lt;/ref&gt;&lt;/blockquote&gt;'''1881 May 10, Tuesday''', Algernon Bourke attended the [[Social Victorians/Timeline/1881#1881 May 10, Tuesday|wedding of Marion Lascelles, eldest daughter of the Hon. Egremont W. Lascelles, brother of the Earl of Harewood, and Lieutenant Henry Dent Brocklehurst, of the Second Life Guards, nephew of Mr. Philip Brocklehurst, of Swithamley Park, Macclesfield]]. His gift was an &quot;old enamelled watch set in pearls.&quot;&lt;ref&gt;&quot;Nuptial Rejoicings at Middlethorpe Manor. Marriage of Miss Lascelles and Lieut. Brocklehurst.&quot; ''Yorkshire Gazette'' 14 May 1881, Saturday: 9 [of 12], Cols. 3a–4a [of 6]. ''British Newspaper Archive''https://www.britishnewspaperarchive.co.uk/viewer/bl/0000266/18810514/057/0009. Print same title and p.&lt;/ref&gt;

'''1881 May 23, Monday, 2:00 p.m.''', Algernon Bourke is listed among the Honourables at the [[Social Victorians/Timeline/1881#Queen's Levee at St. James's Palace|Queen's Levee at St. James's Palace]].

'''1881 July 14, Thursday afternoon, beginning about 2 p.m.''', Algernon Bourke was invited to a Garden Party at Marlborough House hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. Members of the family of the [[Social Victorians/People/Mayo|Earl of Mayo]] were also among the 1,500 or so invited guests.

'''1881 July 22, Friday''', Algernon Bourke was invited to an [[Social Victorians/Timeline/1881#22 July 1881, Friday|evening party at Marlborough House hosted by the Prince and Princess of Wales]].

'''1881 September 17, Saturday''', Algernon Bourke was reported among the company at Doncaster during race week.&lt;ref&gt;&quot;List of the Company.&quot; ''York Herald'' 17 September 1881, Saturday: 8 [of 16], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000499/18810917/183/0008. Same print title and p.&lt;/ref&gt;

'''1881 November 22, Tuesday''', Algernon Bourke was sued in Dublin by Henry Naylor because he &quot;had declined to pay&quot; for a £35 piano.&lt;ref&gt;&quot;Henry Naylor v. the Hon. Algernon Bourke.&quot; &quot;Exchequer Division.&quot; &quot;High Court of Justice.&quot; ''Belfast Morning News'' 23 November 1881, Wednesday: 3 [of 4], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000428/18811123/015/0003. Same print title, n.p.&lt;/ref&gt;

'''1881 December 8, Thursday''', Algernon Bourke was part of a [[Social Victorians/Timeline/1881#Battue at Palmerstown|battue at Palmerstown]], when the group bagged 172 pheasants, hares and rabbits.

'''1882 March 7, Tuesday''', Algernon Bourke attended the [[Social Victorians/Timeline/1882#7 March 1882, Tuesday|fashionable wedding of Reginald Chandos-Pole and Violet Denison]].

'''1882 March 15, Wednesday''', Algernon Bourke attended [[Social Victorians/Timeline/1882#The Marchioness of Salisbury's Assembly|the Marchioness of Salisbury's first reception of the season]].

'''1882 July 13, Thursday''', Algernon Bourke was invited to the [[Social Victorians/1882-07-13 Marlborough House Garden Party|Garden Party at Marlborough House for Queen Victoria]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. The more than 1,000 people invited also included a number of people from the family of the [[Social Victorians/People/Mayo|Earl of Mayo]].

'''1882 September 28, Saturday''', Algernon Bourke attended the [[Social Victorians/Timeline/1882#The Wedding of John M'Donald and Georgiana Lambart|wedding of John M'Donald and Georgiana Lambart]].

'''1883 March 21, Wednesday''', the Evening Irish Times announced that Algernon Bourke &quot;has arrived at Kingstown from England.&quot;&lt;ref&gt;&quot;Court and Fashion.&quot; ''Evening Irish Times'' 21 March 1883, Wednesday: 7 [of 8], Col. 5a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003464/18830321/086/0007. Same print title and p.&lt;/ref&gt;

'''23 July 1883, Monday, noon''', the Hon. Algernon Bourke was invited to a [[Social Victorians/Timeline/1883#Garden Party at Marlborough House, at Noon|garden party at Marlborough House]] hosted by the Prince and Princess of Wales.

'''31 October 1883, Wednesday''', Algernon Bourke attended the wedding of [[Social Victorians/Timeline/1883#Wedding of Lady Cecelia Hay and Captain George Webbe|Lady Cecelia Hay and Captain George Webbe]].&lt;p&gt;

'''1884 February 16, Saturday''', Algernon Bourke attended [[Social Victorians/Timeline/1884#16 February 1884, Saturday|the funeral of Thomas Chenery, editor of the ''Times'']].

'''1884 April 4, Saturday''', Algernon Bourke was (may have been?) one of the [[Social Victorians/Timeline/1884#5 April 1884, Saturday|&quot;Supporters of the Pall&quot; at the funeral]] of [[Social Victorians/People/Leopold|Prince Leopold George Duncan Albert, Duke of Albany]] at St. George's, Windsor.

'''1884 April 26, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1884#26 April 1884, Saturday|dinner party at the Lord Mayor's Mansion House for conservatives to meet Sir Stafford Northcote]].

'''1884 May 3, Saturday''', the &quot;Rochester Conservatives&quot; announced that they would &quot;bring forward the Hon. Algernon Bourke, brother of Lord Mayo, as their second candidate,&quot;&lt;ref&gt;&quot;Election Intelligence.&quot; ''Yorkshire Gazette'' 03 May 1884, Saturday: 4 [of 12], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000266/18840503/011/0004.&lt;/ref&gt; but because he would not be the first candidate, Bourke declined.&lt;ref&gt;&quot;Rochester.&quot; London ''Daily Chronicle'' 09 May 1884, Friday: 3 [of 8], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/18840509/049/0003.&lt;/ref&gt;

'''1884 June 18, Wednesday''', Mr. Algernon Bourke was on a committee to watch a [[Social Victorians/Timeline/1884#18 June 1884, Wednesday|Mr. Bishop's &quot;thought-reading&quot; experiment]], which was based on a challenge by Henry Labourchere made the year before. This &quot;experiment&quot; took place before a fashionable audience.

'''1884 July 25, Friday, afternoon''', the Hon. Algernon Bourke was invited to a [[Social Victorians/Timeline/1884#Garden Party at Marlborough House hosted by the Prince and Princess of Wales|Garden Party at Marlborough House hosted by the Prince and Princess of Wales]].

'''1885 January 22, Thursday''', Algernon Bourke's gift to [[Social Victorians/Timeline/1885#Wedding of George Buckle and Alicia Payn|George Buckle and Alicia Payn for their wedding]] was an antique cabinet.

'''1885 July 7, Tuesday''', Algernon Bourke attended [[Social Victorians/Timeline/1885#7 July 1885, Tuesday|Eva Bourke's wedding to Windham Wyndham-Quin]] at St. Mary Abbots, Kensington.

'''1885 July 13, Monday''', Algernon Bouurke was at Victoria Station as part of the [[Social Victorians/Timeline/1885#Arrival of Lord Wolseley in London from Egypt|crowd greeting Lord Wolseley on his return from Egypt]].

'''1885 July 24, Friday''', the Hon. Algernon Bourke was invited to a [[Social Victorians/1885-07-24 Marlborough House Ball|ball at Marlborough House]] hosted by the Prince and Princess of Wales.

'''1885 September 26, Saturday''', Algernon Bourke took part in the [[Social Victorians/Timeline/1885#26 September 1885, Saturday|Ealing Conservative Club fete and meeting]] supporting Salisbury's government and condemning &quot;the dictates of one man&quot; — Gladstone — for Gordon's death.

'''1885 October 3, Saturday''', the Hon. Algernon Bourke was named as the Conservative candidate for Clapham in the Battersea and Clapham borough after the Redistribution Bill determined the electoral districts for South London.&lt;ref&gt;&quot;South London Candidates.&quot; ''South London Press'' 03 October 1885, Saturday: 9 [of 16], Col. 5b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18851003/096/0009. Print p. 9.&lt;/ref&gt; On Sunday 15 November 1885 the London ''Weekly Dispatch'' supported Moulton, the Liberal candidate, who ultimately won the election:&lt;blockquote&gt;

Though a successful lawyer, Mr. Moulton is much more than that. He is a thorough and independent student of political science, who may be trusted to do good service to the Liberal cause with brain as well as with tongue. It will be matter for hearty congratulation if he defeats the Hon. Algernon Henry Bourke, who is a dashing and unscrupulous young Tory, and a nephew of the well-known politician with the same surname.&lt;ref&gt;&quot;The Political Campaign in London. VI. — The South-West Divisions.&quot; ''Weekly Dispatch'' (London) 15 November 1885, Sunday: 9 [of 16], Col. 3c [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003358/18851115/069/0009. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

On Saturday 21 November 1885 the ''South London Press'' reported on posters for Bourke's candidacy:&lt;blockquote&gt;

The Hon. Algernon Bourke, Conservative candidate for Clapham, has a very industrious billsticker, who pastes up his patron’s bills in every possible place where they can be seen to advantage. It is unfortunate, however, that choosing the flank wall of an auctioneer’s the modern &quot;Sam Slap&quot; has produced some curious combinations, such as — &quot;Vote for Bourke,&quot; &quot;Now on View;&quot; &quot;Electors of Clapham, Vote for Mr. Bourke, and&quot; &quot;Be Sold Without Reserve;&quot; &quot;Mr, Bourke will&quot; &quot;Advance Money to&quot; &quot;the Electors of Clapham;&quot; &quot;Great Conservative Meeting. The British Constitution will be&quot; &quot;Offered for Sale this Evening,&quot; &amp;c.&lt;ref&gt;&quot;Pick-up Notes.&quot; ''South London Press'' 21 November 1885, Saturday: 10 [of 16], Col. 1b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18851121/155/0010. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

'''1885 November 3, Tuesday, 11:00 a.m.''', Algernon Bourke attended the [[Social Victorians/Mayo-Ponsonby Wedding 1885-11-03|wedding of his brother, Dermot, 7th  Earl of Mayo and Geraldine Ponsonby]]. He gave them 2 Sheraton secretaires.

'''1886 January 5, Tuesday, late''', the Hon. Algernon Bourke attended the [[Social Victorians/Timeline/1886#Twelfth Night|Twelfth Night celebration at the Drury Lane theatre]].

'''1886 March 13, Saturday evening''', an Hon. Mr. Bourke attended a [[Social Victorians/1886-03-13 Reception at the French Embassy|reception at the French Embassy]], possibly Algernon Bourke or possibly [[Social Victorians/People/Mayo|one of his brothers]].

'''1886 July 10, Saturday''', Hon. Algernon Bourke was invited to a [[Social Victorians/Timeline/1886#Garden Party at Marlborough House Given to the Queen|garden party at Marlborough House given to the Queen]]. Gwendolen Sloane Stanley is not mentioned but Mr. and Mrs. Hans Sloane Stanley are, as are Mr. and Mrs. F. Sloane Stanley.&lt;p&gt;

'''1886 July 21, Wednesday''', Algernon Bourke was invited to the [[Social Victorians/1886-07-21 Marlborough House Ball|Ball at Marlborough House]], as were a [[Social Victorians/People/Bourke#The Sloane-Stanleys 2|Mr. and Mrs. F. Sloane-Stanley]], possibly the parents of Gwendolen Sloane-Stanley (if the &quot;F&quot; is a mistake), who married Bourke on 15 December 1887. Gwendolen is not mentioned as having been invited.

'''1886 July 27, Tuesday''', Algernon Bourke attended a service honoring a memorial at St. Paul's for his father, who had been assassinated.&lt;ref&gt;&quot;Memorial to the Late Earl of Mayo.&quot; ''Northern Whig'' 28 July 1886, Wednesday: 6 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000434/18860728/143/0006. Print p. 6.&lt;/ref&gt;

'''1886 September 2, Thursday''', Mr. Algernon Bourke was part of a group of mostly aristocratic men taking part in [[Social Victorians/Timeline/1886#Augustus Harris's A Run of Luck|a &quot;trial-rehearsal&quot; as part of Augustus Harris's production]] ''A Run of Luck'', about sports.

'''1886 October 2, Saturday''', the Duke of Beaufort and the Hon. Algernon Bourke arrived in Yougal: &quot;His grace has taken a residence at Lismore for a few weeks, to enjoy some salmon fishing on the Blackwater before the close of the season.&quot;&lt;ref&gt;&quot;Chippenham.&quot; ''Wilts and Gloucestershire Standard'' 02 October 1886, Saturday: 8 [of 8], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001955/18861002/142/0008. Print p. 8.&lt;/ref&gt;

'''1886 October 11, Monday''', Algernon Bourke may have been taking part in a [[Social Victorians/Timeline/1886#Performance of Run of Luck|performance of ''Run of Luck'' at the Drury Lane]].

'''1886 October 23, Saturday''', Algernon Bourke was [[Social Victorians/Timeline/1886#Party at Wemyss Castle, Fife|staying at Wemyss Castle, Fife]].

'''1886 December 30, Thursday''', Algernon Bourke was back in London and attending the [[Social Victorians/Timeline/1886#Augustus Harris's The Forty Thieves|&quot;Forty Thieves&quot; pantomime at the Drury Lane Theatre]].

'''1887 January 5, Wednesday''', the Hon. Algernon Bourke was one of the chief mourners at the [[Social Victorians/Timeline/1887#Funeral of Lady Margaret Harriett Bourke|funeral of Lady Margaret Harriett Bourke]].

'''1887 March 1, 2:00 p.m.''', Algernon Bourke is listed among the Messieurs attending the [[Social Victorians/Timeline/1887#Queen's Levee at St. James's Palace|Queen's Levee at St. James's Palace]].&lt;p&gt;

'''1887 May''', a &quot;signalling incident&quot; in 1907 [[Social Victorians/Timeline/1887#May 1887|caused the Waterford ''Evening News'' to recall a similar event]] that had occurred 20 years earlier, in which Algernon Bourke, as special correspondent for the ''Times'', caused the incident to be publicized:&lt;blockquote&gt;During the manoeuvres in connection with the 1887 Jubilee of Queen Victoria a signal was observed going up from [[Social Victorians/People/Beresford|Lord Charles [Beresford]]]'s ship. It was a message to his wife, Lady Beresford, to the effect that, as he should be late for dinner, she was not to wait. Beyond the hilarity this domestic signal evoked, nothing more would have been heard of it, but Mr. Algernon Bourke (Lord Mayo's brother) was acting as special correspondent for the &quot;Times,&quot; and that paper the next morning contained a full and humorous report of the incident. Then there was trouble.&lt;ref&gt;&quot;Signalling Incident.&quot; ''Evening News'' (Waterford) 13 November 1907, Wednesday: 1 [of 4], Col. 6c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004557/19071113/021/0001.&lt;/ref&gt;&lt;/blockquote&gt;

'''1887 June 15, Wednesday''', the Hon. Algernon Bourke attended a [[Social Victorians Foreign Office Reception 1887-06-15|reception at the Foreign Office in honor of Queen Victoria's Golden Jubilee]].

'''1887 July 6, Wednesday''', Algernon Bourke was invited to and, presumably, attended the State Ball at Buckingham Palace.&lt;ref&gt;&quot;The State Ball at Buckingham Palace.&quot; ''Morning Post'' 08 July 1887, Friday: 3 [of 8], Col. 5a–6c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18870708/013/0003. Same print title and p.&lt;/ref&gt; (Col. 1c)

'''1887 August 6, Saturday''', the ''Brighton Gazette'' says that the &quot;Hon. Mrs and Mr Algernon Bourke&quot; were staying at the Royal Crescent Hotel in Brighton, but they didn't marry until 15 December 1887.&lt;ref&gt;&quot;Royal Crescent Hotel.&quot; ''Brighton Gazette'' 6 August 1887, Saturday: 3 [of 8], Col. 5c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000938/18870806/047/0003. Print title ''Brighton Gazette and Sussex Telegraph'', p. 3.&lt;/ref&gt; Perhaps an elder relative, because she is mentioned first?

'''1887 November 9, Wednesday''', the ''Hampshire Advertiser County Newspaper'' announced that&lt;blockquote&gt;A marriage is arranged, and will take place early in January, between Mr. Algernon Bourke, third son of the late Earl of Mayo, and Miss Guendolen Sloane Stanley, only daughter of Mr. Hans Sloane Stanley, of Paultons.&lt;ref&gt;&quot;Romsey, Nov. 9.&quot; ''Hampshire Advertiser'' 9 November 1887, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18871109/034/0003. Print title ''Hampshire Advertiser County Newspaper'', p. 3.&lt;/ref&gt;&lt;/blockquote&gt;Shortly after, the papers announced that the wedding would not take place.

'''1887 December 15, Thursday''', Hon. [[Social Victorians/Timeline/1887#Wedding of Algernon Bourke and Gwendolen Sloane Stanley|Algernon Bourke and Gwendolen Stanley were married at St. Paul's]], Knightsbridge, by Bourke's uncle the Hon. and Rev. George Bourke. Only family members attended because of &quot;the recent death of a near relative of the bride.&quot;&lt;ref&gt;&quot;Court Circular.&quot; ''Morning Post'' 16 December 1887, Friday: 5 [of 8], Col. 7c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18871216/066/0005.&lt;/ref&gt; Who the &quot;near relative of the bride&quot; was not in her nuclear family, and perhaps that explains the cancellation of the wedding and then the changing of the wedding date and not some problem in the couple.

'''1888 – 1899 January 1''', the Hon. Algernon Bourke was &quot;proprietor&quot; of [[Social Victorians/London Clubs#White's|White's Club, St. James's Street]].&lt;ref name=&quot;:9&quot;&gt;&quot;The Hon. Algernon Bourke's Affairs.&quot; ''Eastern Morning News'' 19 October 1899, Thursday: 6 [of 8], Col. 7c [of7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001152/18991019/139/0006. Print p. 6.&lt;/ref&gt;

'''1888 January 21, Saturday''', Gwendolen Bourke attended the wedding of [[Social Victorians/Timeline/1888#Hamilton-Ewart Wedding|Florence Ewart and Henry Hamilton]].

'''1888 March 7, Wednesday''', assuming that this date is not a week after the actual date, [[Social Victorians/People/Beresford|Lady Charles Beresford]] held a [[Social Victorians/Timeline/1888#1888 March 7, Wednesday|notable and well-attended &quot;at home&quot;]] that Gwendolen Bourke attended, reported for being dressed in white and being among the beautiful women present.

'''6 April 1888, Friday''', Algernon and Gwendolen Bourke attended the [[Social Victorians/Timeline/1888#6 April 1888, Friday|New Forest United Hunt ball at the New Forest Hall, Lyndhurst]].

'''1888 May 2, Wednesday''', Algernon and Gwendolen Bourke attended the [[Social Victorians/Timeline/1888#The Marchioness of Salisbury's Reception|Marchioness of Salisbury's reception]] at the Salisbury home on Arlington-street.

'''1888 May 22, Tuesday''', the Dowager Countess of Mayo presented Gwendolen Bourke at the [[Social Victorians/Timeline/1888#Queen's Drawing Room|Queen's drawing-room]] hosted by the Princess of Wales. This is Gwendolen Bourke's dress:&lt;blockquote&gt;Empire robe de cour of white satin duchesse, lined with rich pink silk, sufficiently bright to give a beautiful shell-like tint through the satin; tulle underdress, with upper skirt, embroidered with pearl, and caught up in Greek folds with large pink Tosca roses; white satin bodice, with Josephine pink sash tied at side, Headdress, veil and plumes; ornaments, diamonds.&lt;ref&gt;&quot;Dresses at the Drawing-Room.&quot; ''Epsom Journal'' 22 May 1888, Tuesday: 3 [of 6], Col. 5b–c [of 6]. ''British Newspapers Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004837/18880522/034/0003. Print: title ''Local Journal'', p. 3.&lt;/ref&gt;&lt;/blockquote&gt;

Another description:&lt;blockquote&gt;Mrs. Algernon Bourke's train was of white satin lined with pink, which showed through with charmingly shell-like effect. The dress, fashioned after those of the Empire period, was of white satin embroidered with pearls. A very broad sash of pink satin made the waist seem quaintly short, a trying thing to any but the young and tall, both of which qualifications Mrs. Bourke most happily possesses. She carried a lovely posy of La France roses.&lt;ref&gt;&quot;Gossip on Dress.&quot; ''Boston Spa News'' 25 May 1888, Friday: 2 [of 8], Col. 1b–2b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003395/18880525/014/0002. Print title The News, n.p.&lt;/ref&gt; (Col. 1c)&lt;/blockquote&gt;'''1888 June 8, Friday''', Hon. Algernon and Mrs. Bourke attended a [[Social Victorians/Timeline/1888#Dinner and Dance Hosted by Lord and Lady Wimborne at Hamilton House|dinner and dance Hosted by Lord and Lady Wimborne at Hamilton House]] featuring Prince and Princess Christian of Schleswig-Holstein, and for the ball, the King of Sweden and Norway and the Prince and Princess of Wales and their daughters were present.

'''1888 June 19, Tuesday''', Gwendolen Bourke was one of the principal guests at the wedding of [[Social Victorians/Timeline/1888#19 June 1888, Tuesday|Captain Philip Green and Miss Mabel Emilie Scott]].

'''1888 July 26''', [[Social Victorians/People/Montrose|Caroline Graham Stirling-Crawford]] (known as Mr. Manton for her horse-breeding and -racing operations) and Marcus Henry Milner married.&lt;ref name=&quot;:12&quot;&gt;&quot;Hon. Caroline Agnes Horsley-Beresford.&quot; {{Cite web|url=https://thepeerage.com/p6863.htm#i68622|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt; According to the ''Nottingham Evening Post'' of 31 July 1888,&lt;blockquote&gt;LONDON GOSSIP.

(From the ''World''.)

The marriage of &quot;Mr. Manton&quot; was the surprise as well the sensation of last week. Although some wise people noticed a certain amount of youthful ardour in the attentions paid by Mr. Marcus Henry Milner to Caroline Duchess of Montrose at '''Mrs. Oppenheim's ball''', nobody was prepared for the sudden ''dénouement''; '''and it''' were not for the accidental and unseen presence [[Social Victorians/People/Mildmay|a well-known musical amateur]] who had received permission to practice on the organ, the ceremony performed at half-past nine on Thursday morning at St. Andrew's, Fulham, by the Rev. Mr. Propert, would possibly have remained a secret for some time to come. Although the evergreen Duchess attains this year the limit of age prescribed the Psalmist, the bridegroom was only born in 1864. Mr. &quot;Harry&quot; Milner (familiarly known in the City as &quot;Millions&quot;) was one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys, and Mr. Algernon Bourke, the head of the house (who, of course, takes a fatherly interest in the match) went down to Fulham to give away the Duchess. The ceremony was followed by a ''partie carrée'' luncheon at the Bristol, and the honeymoon began with a visit to the Jockey Club box at Sandown. Mr. Milner and the Duchess of Montrose have now gone to Newmarket. The marriage causes a curious reshuffling of the cards of affinity. Mr. Milner is now the stepfather of the [[Social Victorians/People/Montrose|Duke of Montrose]], his senior by twelve years; he is also the father-in-law of [[Social Victorians/People/Lady Violet Greville|Lord Greville]], Mr. Murray of Polnaise, and [[Social Victorians/People/Breadalbane|Lord Breadalbane]].&lt;ref name=&quot;:8&quot; /&gt;&lt;/blockquote&gt;

'''1888 December 1st week''', according to &quot;Society Gossip&quot; from the ''World'', the Hon. Algernon Bourke was suffering from malaria, presumably which he caught when he was in South Africa:&lt;blockquote&gt;I am sorry to hear that Mr. Algernon Bourke, who married Miss Sloane-Stanley a short time ago, has been very dangerously ill. Certain complications followed an attack of malarian fever, and last week his mother, the Dowager Lady Mayo, and his brother, Lord Mayo, were hastily summoned to Brighton. Since then a change for the better has taken place, and he is now out of danger.&lt;ref&gt;&quot;Society Gossip. What the ''World'' Says.&quot; ''Hampshire Advertiser'' 08 December 1888, Saturday: 2 [of 8], Col. 5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18881208/037/0002. Print title: ''The Hampshire Advertiser County Newspaper''; print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;

'''1888 December 20, Thursday''', the Sloane-Stanley family, including Gwendolen Bourke, attended the [[Social Victorians/Timeline/1888#20 December 1888, Thursday|funeral of Hans Sloane Stanley]]. Algernon Bourke did not attend because he was still too ill.

'''1889 January 22, 2:30 p.m., Tuesday''', Algernon and Gwendolen Bourke sent a gift for the [[Social Victorians/Cecil Lambton Wedding 1889 January 22|wedding of Lady Eleanor Lambton and Lord Robert]] Cecil, a pair of antique mirrors.

'''1889 May 18, Saturday''', Algernon Bourke attended the [[Social Victorians/Timeline/1889#18 May 1889, Saturday|opening of the Italian Opera season at Covent Garden]].

'''1889 May 27, Monday, 11 p.m.''', the dancing commenced at [[Social Victorians/Timeline/1889#The Queen's State Ball at Buckingham Palace|the Queen's State Ball at Buckingham Palace]], with both the Hon. Algernon and the Hon. Gwendolen Bourke present.

'''1889 June 8, Saturday''', the Hon. Algernon Bourke contributed some art he owned to the collection of the Royal Institute of Painters in Water-Colours' [[Social Victorians/Timeline/1889#8 June 1889, Saturday|exhibition of &quot;the works of the 'English Humourists in Art.'&quot;]]

'''1889 July 2, Tuesday''', Gwendolen and Algernon Bourke sat in the Muriettas' box at a [[Social Victorians/Timeline/1889#The Shah at a Covent Garden Opera Performance|gala performance at Covent Garden also attended by the Prince and Princess of Wales, a number of other royals and the Shah]].&lt;p&gt;

'''1889 27 July, Saturday''', Gwendolen and Algernon Bourke attended a [[Social Victorians/Timeline/1889#Garden Party Hosted by Mr. and Mrs. Augustus Harris|garden party hosted by Mr. and Mrs. Augustus Harris]], which was attended by a people from the theatre and arts worlds.&lt;p&gt;

'''1889 December 2, Monday''', Gwendolen Bourk's mother, Emilie Sloane-Stanley, married James Shelly Bontein:&lt;blockquote&gt;&lt;p&gt;

BONTEIN—STANLEY — December 2, at St. George's, Hanover Square, London, by the Rev. G. S. de Sansmarez, James Shelly, only son of the late James Bontein, Gentleman Usher and Clerk of the Robes to the Queen, to Emilie Josephine, widow of Hans Sloane Stanley, of Paultons.&lt;ref name=&quot;:18&quot; /&gt;&lt;/blockquote&gt;'''1889 December 17, Tuesday''', Hon. Algernon and Mrs. Bourke gave a gift to [[Dangan-Neville Wedding|Lady Violet Nevill for her wedding to Henry Wellesley, Viscount Dangan]] and so were probably in attendance.

=== 1890s ===
'''1890 January 9, Thursday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1890#The York Hunt Ball|fancy-dress Hunt Ball in York]]. She&lt;blockquote&gt;looked a picture in a Gainsborough gown. The white satin skirt was flounced with sable and veiled with ''chiffon'', the setuage of which was left to show without being hemmed up. There was a broad sash of rose-pink silk and each buttonhole was filled round with crimped lisse.&lt;ref&gt;&quot;Our London Letter.&quot; ''Irish Society'' (Dublin) 11 January 1890, Saturday: 17 [of 24], Col. 2a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001939/18900111/042/0017. Same print title, p. 29.&lt;/ref&gt;&lt;/blockquote&gt;'''1890 February''' '''12, Wednesday''', Hon. Algernon and Mrs. Bourke attended [[Social Victorians/Timeline/1890#Lady Constance Leslie's Reception|Lady Constance Leslie's reception]] at her house in Stratford-place.

'''1890 April 9, Wednesday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1890#The New Forest United Hunt Ball|the New Forest United Hunt Ball]].

'''1890 June 3, Tuesday''', Gwendolen Bourke attended the 2:30 p.m. [[Social Victorians/Timeline/1890#Münster-Hay Wedding|wedding of Count Alexander Münster and Lady Muriel Henrietta Constance Hay]]. She is also listed as having attended a [[Social Victorians/Timeline/1890#Dinner and Concert Hosted by Mrs. Arthur Williams and Ball by Mrs. Menzies|ball hosted by Mrs. J. Menzies (daughter of Mrs. Arthur Wilson)]] that Prince Eddie, the Duke of Clarence and Avondale, also attended, that night.  

'''1890 July 4, Friday, 11 p.m.''', the Hon. Algernon and Gwendolen Bourke attended [[Social Victorians/Timeline/1890#The Queen's State Ball at Buckingham Palace|the Queen's State Ball at Buckingham Palace]]. The dancing commenced shortly after 11:00. 

'''1890 July 15, Tuesday''', Hon. Algernon and Mrs. Bourke were invited to a [[Social Victorians/Timeline/1890#Garden Party at Marlborough House to Meet the Queen|garden party at Marlborough House to meet the Queen]]. 

'''1890 July 19, Saturday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1890#Wedding of James Francis Harry St. Clair-Erskine and Violet Aline Vyner|wedding of James Francis Harry St. Clair-Erskine and Violet Aline Vyner]], the two of them giving &quot;four small silver dessert dishes&quot; and Gwendolen giving an &quot;enamel and diamond pin.&quot;&lt;ref&gt;&quot;Marriage of Lord Loughborough with Miss Vyner.&quot; ''Fife Free Press'' 26 July 1890, Saturday: 2 [of 8], Col. 1a–2b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001110/18900726/015/0002. Same print title and p.&lt;/ref&gt; (Col. 2b)

'''1890 July 24, Thursday''', Algernon and Gwendolen Bourke attended a [[Social Victorians/Timeline/1890#Dinner and Dance Hosted by Lord Alington|dance hosted by Lord Alington]] attended also by the Prince and Princess of Wales and Princesses Victoria and Maud.

'''1890 September 6, Saturday''', the ''Country Gentleman'' (as it was called at the time) reported that &quot;Muckross, the only deer forest in Ireland, it may be said, has this year been rented by Mr. Algernon Bourke, who will next week be joined there for the stalking season by his brother, Lord Mayo.&quot;&lt;ref&gt;&quot;Shooting. Moors, Forests, and Fishings.&quot; ''Sporting Gazette'' 06 September 1890, Saturday: 11 [of 38], Col. 1c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002525/18900906/065/0011. Print: ''Country Gentleman'', p. 1251.&lt;/ref&gt; On 11 October 1890 the ''St. James's Gazette'' says,&lt;blockquote&gt;The Earl of Durham has been staying at Muchross, county Kerry, on a visit to the Hon. A. Bourke, who has rented the celebrated shootings and fishings on that estate for the autumn.&lt;ref&gt;&quot;Court and Society.&quot; ''St James's Gazette'' 11 October 1890, Saturday: 12 [of 16], Col. 1b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/18901011/064/0012. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;'''1890 October 25, Saturday''', the Hon. Algernon and Mrs. Bourke gave a gold-mounted box to [[Social Victorians/Loder De Vere Beauclerk Wedding|Lady Louise De Vere Beauclerk on her wedding to Gerald Loder, M.P.]], so they were probably present at the wedding, or at least the reception. Mrs. Bontein [sic Bontine], Gwendolen's mother, gave a silver box, suggesting the relationship was through the women.

'''1890 November 29, 11:30 Saturday morning''', Algernon Bourke's gift for the [[Social Victorians/Dudley-Beckwith Wedding 1890-11-29|wedding of the Hon. Francis Dudley and Miss Forbes Beckwith]] was some cases of a Bordeaux wine: &quot;three dozen Cantenac, 1875 vintage.&quot;&lt;ref&gt;&quot;Marriage of Lord Leigh's Heir. Descriptive Sketch of the Ceremony, and Full List of Guests and Presents.&quot; ''Leamington Spa Courier'' 6 December 1890, Saturday: 6 [of 10], Cols. 1a–4a. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0000319/18901206/021/0006. Same print title and p.&lt;/ref&gt;{{rp|Col. 3b}} Gwendolen Bourke is not listed as having been invited to the reception, but this list from the ''Leamington Spa Courier'' has some gaps.

'''1890 December 4, Thursday''', Gwendolen and Algernon Bourke attended the [[Mure-Portal Wedding 1890-12-04|wedding of Miss Mure and Mr. S. J. Portal]]. Their gift is not recorded.

'''1891 January''', Algernon Bourke took party in a [[Social Victorians/Timeline/1891#Shooting Party in Kallarnet, Totton|shooting party in Kallarnet, Totton]].

'''1891 June 24, Wednesday''', the Hon. Algernon and Mrs. Bourke attended a [[Social Victorians/Timeline/1891#Dinner and Ball Hosted by Lord and Lady Wimborne|dinner and ball Hosted by Lord and Lady Wimborne]] featuring Princess Mary Adelaide, the Duke of Teck, and Princess Victoria.

'''1891 July 9, Thursday''', Algernon and Gwendolen Bourke were invited to a [[Social Victorians/1891-07-09 Garden Party|large Garden Party at Marlborough House]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]] in honor of Queen Victoria and the German Emperor and Empress. The more than 3,000 people invited also included a number of people from the [[Social Victorians/People/Mayo|family of the Earl of Mayo]].

'''1891 July 22, Wednesday''', Gwendolen Bourke attended a [[Social Victorians/Timeline/1891#Dinner and Dance at Alington House|dance at the Earl and Countess Alington]]'s that also included the Prince and Princess of Wales.

'''1891 October 22, Thursday''', Hon. and Mrs. Bourke attended at least the reception of the [[Social Victorians/Timeline/1891#Le Strange Astley Wedding|Le Strange—Astley Wedding]], although perhaps the couple is not the Algernon Bourkes.

'''1891 November 22, Sunday''', the London ''Weekly Dispatch'' reports a performance by American &quot;Lady Magnet&quot; Mrs. Abbott, who claimed to be able to lift anybody using only her magnetic properties. An enthusiastic &quot;committee of some fifteen gentlemen presented a written and signed testimonial&quot; supporting Mrs. Abbott, &quot;the Hon. Algernon Bourke, Professor Atkinson, Dr. Hides, and three other doctors who prefer to remain incog., being among the signatories. All the medical gentlemen concerned assured the ''Evening News and Post'' reporter of their complete and unconditional surrender. One of them went so far as to say that he had come with the full determination of disbelieving, but had been quite able to act up to his resolve.&quot;&lt;ref&gt;&quot;The Lady Magnet. Draws Crowds of People Who Divide in Opinion about Her.&quot; ''Weekly Dispatch'' (London) 22 November 1891, Sunday: 16 [of 16], Cols. 3a–4b [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003358/18911122/203/0016. Print: same title and p.&lt;/ref&gt;

'''1892''', the Hon. Algernon Bourke privately published his ''The History of White's'', the exclusive gentleman's club.

'''1892 January 27, Saturday''', Algernon and Gwendolen Bourke attended the very fashionable [[Social Victorians/Timeline/1892#The Wedding of Lord Henry Cavendish Bentinck, M.P., and Lady Olivia Taylour|wedding of Lord Henry Cavendish Bentinck, M.P., and Lady Olivia Taylour]]. Their gift was not noted in the list.

'''1892 February''' '''10, Wednesday''', Gwendolen Bourke attended the [[Social Victorians/1892-02-10 Alington Leigh Wedding|very fashionable wedding of Henry, Lord Alington and Evelyn Henriette Leigh]] [[Social Victorians/1892-02-10 Alington Leigh Wedding|in St. Paul's, Knightsbridge]]

'''1892 April''' '''10, Wednesday, about 2:30 p.m.''', Gwendolen Bourke attended [[Social Victorians/1892-02-10 Alington Leigh Wedding|the very fashionable wedding between Henry Sturt, Lord Alington and Evelyn Leigh]]. Her gift was a &quot;tortoiseshell and gold heart-shaped tray.&quot;&lt;ref name=&quot;:02&quot;&gt;&quot;Lord Alington to Miss Leigh.&quot; ''Gentlewoman'' 20 February 1892, Saturday: 21 [of 46], Cols. 1a–3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18920220/092/0021. Same print title, p. 237.&lt;/ref&gt; (Col. 3a) 

'''1892 June 25, Saturday''', the ''Gentlewoman''&lt;nowiki/&gt;'s &quot;Overheard by the Little Bird&quot; says &quot;That pretty Mrs. Algernon Bourke has been staying here, but returned to England in time for Ascot.&quot;&lt;ref&gt;Little Bird, The. &quot;Overheard by the Little Bird.&quot; ''Gentlewoman'' 25 June 1892, Saturday: 32 [of 60], Col. 3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18920625/157/0032. Same print title, p. 860.&lt;/ref&gt; 

'''1892 December 13, Tuesday''', the ''Gentlewoman'' says Gwendolen Bourke is lovely in its coverage of [[Social Victorians/Timeline/1892#Wedding of Miss Eleanor M. Ewart and Captain Guy Withington|Eleanor M. Ewart and Captain Guy Withington's wedding]]. 

'''1892 December 22, Thursday''', Algernon Bourke attended the [[Social Victorians/Timeline/1892#22 December 1892, Thursday|monthly meeting of the Zoological Society in Hanover-square]].&lt;p&gt;

'''1893 February 11, Tuesday''', Algernon Bourke opened Willis's Restaurant:&lt;blockquote&gt;Mr. Algernon Bourke has in his time done many things, and has generally done them well. His recently published history of White's Club is now a standard work. White's Club itself was a few years ago in its agony when Mr. Bourke stepped in and gave it a renewed lease of life. Under Mr. Bourke's auspices &quot;Willis's Restaurant&quot; opened its doors to the public on Tuesday last in a portion of the premises formerly so well known as Willis's Rooms. This new venture is to rival the Amphitryon in the matter of cuisine and wines; but it is not, like the Amphitryon, a club, but open to the public generally. Besides the restaurant proper, there are several ''cabinets particuliers'', and these are decorated with the very best of taste, and contain some fine portraits of the Georges.&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Letter from the Linkman.&quot; ''Truth'' 20 April 1893, Thursday: 25 [of 56], Col. 1a [of 2]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025# https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025]. Print p. 855.&lt;/ref&gt;&lt;/blockquote&gt;

'''1893 February 7, Tuesday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1893#1893 February 7, Tuesday|the reception after Lady Emily Cadogan's wedding]].

'''1893 February 20, Monday''', the Hon. Algernon Bourke is listed as having attended the [[Social Victorians/Timeline/1893#Queen's Levee at St. James's Palace|Queen's Levee at St. James's Palace]] held by the Prince of Wales; because wives generally are not listed, it seems likely Gwendolen Bourke attended as well.

'''1893 February 28, Tuesday, 3:00 p.m.''', Gwendolen Bourke attended a [[Social Victorians/Queens Drawing Room 1893-02-28|Queen's Drawing Room at Buckingham Palace]].&lt;p&gt;

'''1893 March 22, Wednesday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1893#22 March 1893, Wednesday|Lady Wimborne's reception]].

'''1893 April 1, Saturday''', Algernon Bourke published a letter to the editor of the ''Times'', reprinted in the ''Kildare Observer'', arguing against Gladstone's Home Rule bill on the grounds that Ireland would not be able to take out a loan on its own behalf because of its obligations to the U.K., including what was called its share of the national debt.&lt;ref&gt;&quot;Irish Unionist Alliance.&quot; ''Kildare Observer and Eastern Counties Advertiser'' 01 April 1893, Saturday: 6 [of 8], Col. 4c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001870/18930401/062/0006. Print: The ''Kildare Observer'', n.p.&lt;/ref&gt;

'''1893 May 13, Saturday''', Algernon Bourke was seen at [[Social Victorians/Timeline/1893#13 May 1893, Saturday|exhibitions of art and furniture for sale by Christie's and on display by Lord Clifden]].

'''1893 July 13, Thursday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1893#The Countess of Listowel's Garden Party|Countess of Listowel's Garden Party]] [[Social Victorians/Timeline/1893#The Countess of Listowel's Garden Party|at her residence, Kingston House, Princes-gate]], accompanied by Miss Adeane.

'''1893 July 14, Friday''', Gwendolen Bourke attended [[Social Victorians/Sandown Races 1893-07-14|the races at Sandown]] wearing a dark-blue-and-white outfit and black hat that got described in the newspaper.

'''1893 August 1, Tuesday – August 4, Friday''', Gwendolen Bourke, at least, was at [[Social Victorians/Timeline/1893#1 August 1893, Tuesday – 4 August 1893, Friday|the Goodwood races]], mentioned in the ''Gentlewoman'' for her beauty, although none of the dresses were noted.

'''1893 November 4–11, Wednesday–Saturday''', Gwendolen Bourke was at a [[Social Victorians/Timeline/1893#Ralph and Mary Sneyd Hosted a Shooting Party|shooting party at Keele Hall hosted by Ralph and Mary Sneyd]].

'''1893 November 30, Thursday''', with Sir Walter Gilbey the Hon. Algernon Bourke &quot;assisted&quot; in &quot;forming [a] collection&quot; of engravings by George Morland that was exhibited at Messrs. J. and W. Vokins’s, Great Portland-street.&lt;ref&gt;&quot;The George Morland Exhibition at Vokins's.&quot; ''Sporting Life'' 30 November 1893, Thursday: 4 [of 4], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000893/18931130/058/0004.&lt;/ref&gt;

'''1893 December 14, Thursday, afternoon''', Gwendolen Bourke attended the [[Social Victorians/1893-12-14 Wedding Adele Grant and George, 7th Earl of Essex|wedding of American Adele Grant and George, 7th Earl of Essex]] and gave a &quot;pearl and gold box.&quot;&lt;ref name=&quot;:22&quot;&gt;&quot;Wedding of the Earl of Essex.&quot; ''Herts Advertiser'' 16 December 1893, Saturday; 8 [of 8], Col. 1a–4b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000415/18931216/125/0008. Print title: ''The Herts Advertiser and St Albans Times'', p. 8.&lt;/ref&gt;{{rp|Col. 3c}} Mr. and Mrs. Shelley Bontein also attended, and Mrs. Bontein gave a &quot;green leather bag and purse, with coronet and monogram in gold.&quot;&lt;ref name=&quot;:22&quot; /&gt;{{rp|3b}}

'''1894 January 27, Saturday''', Psyche in &quot;The Social Peepshow&quot; in the ''Gentlewoman'' reported on a [[Social Victorians/Timeline/1894#27 January 1894, Saturday|ball hosted by Lord and Lady Dunraven at Adare Manor]] that Gwendolen Bourke attended.

'''1894 January 31, Wednesday''', Algernon and Gwendolen Bourke, who was dressed more stylishly than most, attended the [[Social Victorians/Timeline/1894#Also 31 January 1894, Wednesday|Kildare Hunt Ball]] hosted by Dermot, [[Social Victorians/People/Mayo|Earl of Mayo]] and Geraldine, Countess of Mayo.

'''1894 February 24, Saturday''', ''The Field'' reported on a series of tennis matches; Algernon Bourke attended the one played at the Prince's Club.&lt;ref&gt;&quot;Tennis.&quot; ''Field'' 24 February 1894, Saturday: 39 [of 72], Col. 1c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002446/18940224/349/0039. Print title ''The Field, The Country Gentleman's Newspaper'', p. 249.&lt;/ref&gt;

'''1894 March 31, Saturday''', Psyche, in the &quot;Social Peepshow&quot; column in the ''Gentlewoman'', says that &quot;Mr. Algernon Bourke has still further embellished Willis's restaurant hard by [the St. James's Theatre], by the addition of some valuable old tapestry that lately came to the hammer at Christie's.&quot;&lt;ref&gt;Psyche. &quot;The Social Peepshow.&quot; ''Gentlewoman'' 31 March 1894, Saturday: 16 [of 56], Col. 2b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18940331/081/0016. Same print title, p. 408.&lt;/ref&gt;

'''1894 April 13, Friday''', Gwendolen Bourke set sail on the [[Social Victorians/Timeline/1894#P. and O. Line S.S. Rome for Gibraltar|P. and O. Line ''S.S. Rome'' for Gibraltar]] along with her stepfather, Mr. Shelley Bontein, and her brother, Mr. Sloane Stanley.

'''31 May 1894, Thursday''', the Hon. Algernon and Mrs. Bourke attended the [[Social Victorians/Timeline/1894#Reception at Devonshire House|Duchess of Devonshire's reception at Devonshire House]].&lt;p&gt;

'''1894 June 18, Monday''', the London ''Echo'' reported that Algernon Bourke was [[Social Victorians/London Clubs#Brooks'|writing a history of Brooks' Club]].&lt;p&gt;

'''1894 June 20, Wednesday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1894#Princess Louise, Marchioness of Lorne Opened the Annual Sale of the Scottish Home Industries|Annual Sale of the Scottish Home Industries]]; her outfit was described in the article in ''Lady's Pictorial''.

'''1894 August 2, Thursday''', the column &quot;Overheard by the Little Bird&quot; says, &quot;At Willis' [restaurant] — 'What a smart cotillon Mr. and Mrs. Algernon Bourke gave on Thursday evening.&quot;&lt;ref&gt;Bird, The Little. &quot;Overheard by the Little Bird.&quot; ''Gentlewoman'' 04 August 1894, Saturday: 30 [of 56], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18940804/148/0030. Print title same, p. 144.&lt;/ref&gt; Willis's Restaurant, King-street, St. James's, was a restaurant Algernon Bourke opened in 1893.&lt;p&gt;

'''1894 September 7, Saturday''', Algernon and Gwendolen Bourke were at a [[Social Victorians/Timeline/1894#7 September 1894, Saturday|shooting party at Witley]], which had been loaned to one of his brothers by William Ward, 2nd Earl of Dudley.&lt;p&gt;

'''1894 October 22, Thursday''', Algernon and Gwendolen Bourke attended the [[Social Victorians/Timeline/1894#Wedding of Lord Connemara and Mrs. Coleman|luncheon after the wedding of Lord Connemara and Mrs. Coleman]].

'''1894 November 3, Saturday''', Psyche, in &quot;The Social Peepshow&quot; for the Gentlewoman, reported that Gwendolen Bourke had been [[Social Victorians/Timeline/1894#3 November 1894, Saturday|seen shopping in London]].

'''1895 January 5, Saturday, 2:00 p.m.''', Algernon and Gwendolen Bourke gave an old mother-of-pearl workbox to [[Wolverton-Ward Wedding 1895-01-05|Lady Edith Ward for her wedding to Frederick Glyn, Lord Wolverton]] and presumably attended the wedding and reception afterwards.&lt;p&gt;

'''1895 February 23, Saturday''', the Hon. Algernon Bourke attended the [[Social Victorians/Timeline/1895#23 February 1895, Saturday|fashionable wedding of Laurence Currie and Edith Sibyl Mary Finch]]. Gwendolen Bourke is not listed as having attended, but she is not noted as absent, either. Daphne Bourke was born on 5 April 1895, probably explaining Gwendolen's absence.

'''1895 March 24, Sunday – 30 March, Saturday''', Algernon Bourke was [[Social Victorians/Timeline/1895#24, Sunday – 30 March 1895, Saturday|enjoying the sunny weather in Brighton]].

'''1895 April 27, Saturday''', Algernon Bourke attended the [[Social Victorians/Timeline/1895#1895 April 27, Saturday|wedding of Norah Bourke and Henry E. A. Lindsay]]. Again, Gwendolen Bourke is not listed as having attended. Daphne Bourke was born on 5 April 1895, and Psyche, writing the &quot;Social Peepshow&quot; column in the Gentlewoman, says,&lt;blockquote&gt;

I regret to hear of the serious illness of Mrs. Algernon Bourke, whose first child was born a fortnight ago. It is feared that the attack is of the nature of typhoid, but happily the patient's strength keeps up. Mrs. Bourke is at her mother's house in Clarges-street.&lt;ref&gt;Psyche. &quot;The Social Peepshow.&quot; ''Gentlewoman'' 27 April 1895, Saturday: 28 [of 84], Col. 2c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18950427/147/0028. Same print title, p. 506.&lt;/ref&gt;&lt;/blockquote&gt;

'''1895 July 13, Saturday''', Algernon Bourke donated 10s. to the ''Daily Telegraph'' National Shilling Testimonial to W. G. Grace.&lt;ref&gt;&quot;''Daily Telegraph'' National Shilling Testimonial to W. G. Grace.&quot; ''Daily Telegraph &amp; Courier'' (London) 13 July 1895, Saturday: 7 [of 12], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18950713/079/0007. Print: ''Daily Telegraph'', p. 7.&lt;/ref&gt;

'''1895 August 24, Saturday''', &quot;Marmaduke&quot; in the ''Graphic'' says that Algernon Bourke &quot;opened a cyclists' club in Chelsea.&quot;&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Court and Club.&quot; The ''Graphic'' 24 August 1895, Saturday: 11 [of 32], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18950824/017/0011. Print p. 223.&lt;/ref&gt;

'''1895 October''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#24 October 1902, Friday|opened the Prince's ice-skating rink for the]] season.if the newspapers were right that 1902 was the 7th season. He also was planning a bicycling club for Kensington Gardens to open the following season.&lt;ref&gt;Mackenzie, Ethel Morell (Miss). &quot;Pins and Needles.&quot; ''Hull Daily News'' 12 October 1895, Saturday: 24 [of 40], Col. 1a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003443/18951012/024/0024. Print title: ''Hull News Supplement'', p. 1[6? 8?].&lt;/ref&gt;

'''1895 October 7, Monday''', the Hon. Algernon and Mrs. Bourke attended the [[Social Victorians/Timeline/1895#Adeane-Cator Wedding|Maud Adeane–John Cator wedding]].

'''1895 December 11, Wednesday''', Gwendolen and Algernon Bourke attended a [[Social Victorians/Timeline/1895#Sneyd Party to Meet the Duke of Coburg|shooting party at the Sneyds' to meet the Duke of Coburg]].

'''1895 December 18, Wednesday''', Algernon and Gwendolen Bourke attended the [[Social Victorians/Timeline/1895#Wedding of Lady Albreda Fitzwilliam and the Hon. Charles Bourke|wedding of Lady Albreda Fitzwilliam and the Hon. Charles Bourke]]. Their gift is not noted in the newspaper account.

'''1896 March 17, Tuesday''', Algernon Bourke attended the [[Social Victorians/Timeline/1896#17 March 1896, Tuesday|annual dinner of the Cymmrodorion, or the Honourable Society of Cymmrodorion]], a society for Welsh culture and history.

'''1896 April 21, Monday''', Mr. and Mrs. A. Bourke sent a gift — a &quot;box for miniature&quot; — for [[Social Victorians/Timeline/1896#Monday, 1896 April 27|the wedding of Lady Angela St. Clair Erskine and James Stewart Forbes]].

'''1896 May 21, Thursday''', the Hon. and Mrs. Algernon Bourke attended [[Social Victorians/Timeline/1896#Mrs. C. H. Wilson's Ball|Mrs. C. H. Wilson's ball in Grosvenor-square, London]].

'''1896 May 26, Tuesday,  through 28 May, Thursday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1896#Coming of Age of Mr Sloane Stanley|3-day celebration in honor of the coming of age of her brother, Cyril Sloane Stanley]].

'''1896 June 15, Monday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1896#Dinner and Dance Hosted by the Countess of Huntingdon|dance hosted by the Earl and Countess of Huntingdon]] after their dinner party.

'''1896 July 13, Monday''', Algernon Bourke (listed among the &quot;Honourables&quot;) and Mrs. A. Bourke (Listed among the &quot;Honourable Ladies&quot;) were invited to the [[Social Victorians/Timeline/1896#Queen's Garden Party at Buckingham Palace|Queen's Garden Party at Buckingham Palace]].

'''1896 June 29, Monday''', the Hon. Mrs. Algernon Bourke attended the [[Social Victorians/Cadogan-Scott Wedding 1896-06-29|wedding and reception of Lady Sophie Cadogan and Sir Samuel Scott]]. Algernon Bourke published a letter to the editor of the ''Daily Telegraph'' about White's Club — and thus Bourke's — &quot;[[Social Victorians/London Clubs#Summer Club|Summer Club]]&quot; in Kensington Park, the subject of a little controversy.

'''1896 July 21, Tuesday''', the Hon. Algernon and Mrs. Bourke attended a [[Social Victorians/Timeline/1896#Dinner Hosted by Sir Horace and Lady Farquhar|dinner hosted by Sir Horace and Lady Farquhar in Grosvenor-square]].

'''1896 August 5, Wednesday''', Algernon and Gwendolen Bourke attended at the [[Social Victorians/Timeline/1896#5 August 1896|wedding of the Hon. Terence Bourke and Miss Eveline Haines]] and gave the bride an &quot;enamel muff chain.&quot;&lt;p&gt;

'''1896 August 10, Monday''', the Morning Leader reported that the Hon. Algernon Bourke, for the Foreign Office, received Li Hung Chang at St. Paul's:&lt;blockquote&gt;At St. Paul's Li Hung was received by Field-Marshal Simmons, Colonel Lane, the Hon. Algernon Bourke, of the Foreign Office (who made the necessary arrangements for the visit) and Canon Newbolt, on behalf of the Dean and Chapter. A crowd greeted Li with a cheer as he drove up in Lord Lonsdale’s striking equipage, and his Excellency was carried up the steps in an invalid chair by two stalwart constables. He walked through the centre door with his suite, and was immediately conducted by Canon Newbolt to General Gordon’s tomb in the north aisle, where a detachment of boys from the Gordon Home received him as a guard of honor.

Li inspected the monument with marked interest, and drew the attention of his suite to the remarkable likeness to the dead hero. He laid a handsome wreath of royal purple asters, lilies, maidenhair fern, and laurel, tied with a broad band of purple silk, on the tomb.

The visit was not one of inspection of the building, but on passing the middle aisle the interpreter called the attention of His Excellency to the exquisite architecture and decoration of the chancel. Li shook hands in hearty English fashion with Canon Newbolt and the other gentlemen who had received him, and, assisted by his two sons, walked down the steps to his carriage. He returned with his suite to Carlton House-terrace by way of St. Paul’s Churchyard, Cannon-st., Queen Victoria-st., and the Embankment.&lt;ref&gt;&quot;At St. Paul's.&quot; ''Morning Leader'' 10 August 1896, Monday: 7 [of 12], Col. 2b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18960810/134/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1896 August 19, Wednesday''', the ''Edinburgh Evening News'' reported on the catering that White's Club and Mr Algernon Bourke arranged for the visiting Li Hung Chang:&lt;blockquote&gt;It is probably not generally known (says the &quot;Chef&quot;) that Mr Algernon Bourke, manager of White's Club, London, has undertaken to the whole of the catering for our illustrious visitor front the Flowery Land. Li Hung Chang has five native cooks in his retinue, and the greatest good fellowship exists between them and their English ''confreres'', although considerable difficulty is experienced in conversation in understanding one another's meaning. There are between 40 and and 50 to cater for daily, besides a staff about 30; that Mr Lemaire finds his time fully occupied. The dishes for his Excellency are varied and miscellaneous, and from 14 to 20 courses are served at each meal. The bills of fare contain such items as bird's-nest soup, pigs' kidneys stewed in cream, boiled ducks and green ginger, sharks' fins, shrimps and prawns stewed with leeks and muscatel grapes, fat pork saute with peas and kidney beans. The meal usually winds with fruit and sponge cake, and freshly-picked green tea as liqueur.&lt;ref&gt;&quot;Li Hung Chang's Diet.&quot; ''Edinburgh Evening News'' 19 August 1896, Wednesday: 3 [of 4], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000452/18960819/057/0003.&lt;/ref&gt;&lt;/blockquote&gt;

'''1896 November 6, Friday''', both Algernon and Gwendolen Bourke were on the committee for the [[Social Victorians/London Clubs#Prince's Skating Club|Prince's Club ice-skating rink]], which [[Social Victorians/Timeline/1896#Opening of the Prince's Club Skating Rink|opened on this day]].

'''1896 November 22, week of''', Mrs. Algernon Bourke was part of a [[Social Victorians/Timeline/1896#Shooting Party at the Charles Wilsons' Warter Priory, Yorkshire|shooting party at the Charles Wilsons' Warter Priory, Yorkshire]].&lt;p&gt;

'''1896 November 25, Wednesday''', Mr. and Mrs. Algernon Bouke attended [[Social Victorians/Timeline/1896#Lord and Lady Burton Hosted a Party for Derby Day|Lord and Lady Burton's party for Derby Day]].&lt;p&gt;

'''1896 December 4, Friday''', the Orleans Club at Brighton was robbed:&lt;blockquote&gt;The old building of the Orleans Club at Brighton, which opens its new club house at 33, Brunswick-terrace to-day, was the scene of a very ingenious burglary during the small hours of yesterday morning. The greater portion of the club property had already been removed to the new premises, but Mr Algernon Bourke, his private secretary, and some of the officials of the club, still occupied bed-rooms at the house in the King’s-road. The corner shop of the street front is occupied by Mr. Marx, a jeweller in a large way of business, and upon his manager arriving at nine o'clock he discovered that the place had been entered through hole in the ceiling, and a great part of a very valuable stock of jewelry extracted. An examination of the morning rooms of the club, which runs over Mr. Marx's establishment reveal a singularly neat  specimen of the burglar's art. A piece of the flooring about 15in square had been removed by a series of holes bored side by side with a centre-bit, at a spot where access to the lofty shop was rendered easy by a tall showcase which stood convemently near. A massive iron girder had been avoided by a quarter of an inch, and this circumstance and the general finish of the operation point to an artist in his profession, who had acquired an intimate knowledge of the premises. The club doors were all found locked yesterday morning, and the means of egress adopted by the thief are at present a mystery.&lt;ref&gt;&quot;Burglary at Brighton.&quot; ''Daily Telegraph &amp; Courier'' (London) 05 December 1896, Saturday: 5 [of 12], Col. 7a [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18961205/090/0005. Print title: ''Daily Telegraph''; p. 5.&lt;/ref&gt;&lt;/blockquote&gt;

'''1896 December 10, Thursday''', Gwendolen Bourke was present to help staff a stall at the [[Social Victorians/Timeline/1896#10 December 1896, Thursday|Irish Industries Exhibition and Sale, Brighton]].

'''1896 December 31, Thursday''', Gwendolen Bourke hosted a New Year's Eve dance:&lt;blockquote&gt;Mrs. Algernon Bourke gave a highly satisfactory and enjoyable dance on Thursday night, when the old year was danced out and the new one danced in. Most of the silver gilters at present in to len were to the fore.&lt;ref&gt;&quot;The Man about Town.&quot; ''Sporting Gazette'' 02 January 1897, Saturday: 7 [of 34], Col. 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002525/18970102/041/0007. Print title ''The County Gentleman'', p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1897 January 9, Saturday''', Psyche in &quot;The Social Peepshow&quot; says that Algernon Bourke's &quot;cheerful countenance was quite in keeping with the [Christmas] season,&quot; seen in London.&lt;ref&gt;Psyche. &quot;The Social Peepshow.&quot; ''Gentlewoman'' 9 January 1897, Saturday: 22 [of 56], Col. 2a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970109/097/0022. Same print title, p. 40.&lt;/ref&gt; 

'''1897 January 13, Wednesday – 18, Monday''', Algernon and Gwendolen Bourke were guests of the [[Social Victorians/Timeline/1897#The Warwickshire Hunt Club Ball|house party associated with the Warwickshire Hunt Ball]] at [[Social Victorians/People/Warwick|Warwick Castle]].

'''1897 January 30, Saturday''', Gwendolen Bourke was reported to have been out shopping in London: &quot;Another charming figure was that of Mrs. Algernon Bourke all in chinchilla, with something of pale blue in a smart toque.&quot;&lt;ref&gt;Psyche. &quot;The Social Peepshow.&quot; ''Gentlewoman'' 30 January 1897, Saturday: 20 [of 59]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970130/107/0020. Same print title, p. 134.&lt;/ref&gt;

'''1897 May 31, Monday''', Hon. Algernon and Mrs. Bourke were present at a [[Social Victorians/Timeline/1897#House Party at Warwick Castle|House Party at Warwick Castle]] hosted by the Earl and Countess of Warwick.

'''1897 June 2, Wednesday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1897#Reception at the Foreign Office|reception at the Foreign Office]].

'''1897 June 12, Saturday''', the ''Gentlewoman'' reported on Gwendolen Bourke's dress and hat at the [[Social Victorians/Timeline/1897#The Duchess of Albany's Bazaar at the Imperial Institute|Duchess of Albany's Bazaar at the Imperial Institute]]. 

'''1897 June 19, Saturday''', Psyche in &quot;The Social Peepshow&quot; column in the ''Gentlewoman'' writes that Gwendolen Bourke was seen driving in London, &quot;in blue, ... looking as usual very handsome.&quot;&lt;ref&gt;Psyche. &quot;The Social Peepshow.&quot; ''Gentlewoman'' 19 June 1897, Saturday: 28 [of 108], Col. 2b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970619/159/0028. Same print title, p. 848.&lt;/ref&gt;

'''1897 June 28, Monday''', Algernon and Gwendolen Bourke were invited to the [[Social Victorians/Diamond Jubilee Garden Party|Garden Party at Buckingham Palace]], the final official event of the London Diamond Jubilee celebrations. Members of the family of the [[Social Victorians/People/Mayo|Earl of Mayo]] were also among the 5,000–6,000 people invited.

'''1897 July 2, Friday''', the Hon. A. and Mrs. A. Bourke and Mr. and Mrs. Bourke attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House.

'''1897 July 8, Thursday, 11:00 p.m.''', Hon. Algernon and Gwendolen Bourke were present at [[Social Victorians/Timeline/1890#Queen's State Ball at Buckingham Palace|the Queen's State Ball at Buckingham Palace]]. The dancing commenced shortly after 11:00 p.m.

'''1897 July 11–16, week of''', a dog of Gwendolen Bourke's won a prize at the [[Social Victorians/Timeline/1897#The Ladies' Kennel Association show in the Royal Botanic Gardens in Regent's Park|Ladies' Kennel Association show in the Royal Botanic Gardens in Regent's Park]]. 

'''1897 July 23, Friday''', both the Hon. Algernon Bourke and Gwendolen Bourke attended the [[Social Victorians/Timeline/1897#Bourke-Curzon Cricket Match at the Queen's Club|Bourke-Curzon cricket match at the Queen's Club]], which Algernon Bourke's team lost. 

'''1897 July 23 — or July 30, Friday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1897#Lady Burton's party at Chesterfield House|Lady Burton's party at Chesterfield House]]. &lt;blockquote&gt;Far the prettiest women in the room were Lady Henry Bentinck (who looked perfectly lovely in pale yellow, with a Iong blue sash; and Mrs. Algernon Bourke, who was as smart as possible in pink, with pink and white ruchings on her sleeves and a tall pink feather in her hair.&lt;ref&gt;&quot;Lady Burton's Party at Chesterfield House.&quot; ''Belper &amp; Alfreton Chronicle'' 30 July 1897, Friday: 7 [of 8], Col. 1c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004151/18970730/162/0007. Print title: ''Belper and Alfreton Chronicle''; n.p.&lt;/ref&gt;&lt;/blockquote&gt;

'''1897 August 2, Monday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1897#Warwick House Party for the Easton Lodge Cricket Week Games|Earl and Countess of Warwick's house party for Easton Lodge cricket week]].

'''1897 August 2, Monday''', Mrs. Algernon Bourke was listed as among [[Social Victorians/Timeline/1897#The Most Beautiful Women in England|the most beautiful women in England]] in an article from ''Vanity Fair'' that was reprinted elsewhere.

'''1897 September 25, Saturday''', according to the ''Pall Mall Gazette'',&lt;blockquote&gt;The [[Social Victorians/People/Mayo|Dowager-Countess of Mayo]] is staying with her son, the Hon. Algernon Bourke, at Bramnber, near Brighton.&lt;ref&gt;&quot;Pall Mall Gazette Office.&quot; ''Pall Mall Gazette'' 25 September 1897, Saturday: 8 [of 10], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18970925/023/0008. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;'''1897 October 2, Saturday''', &quot;Yenatrix&quot; in &quot;Kennel Column&quot; in the ''Gentlewoman'' reported that Gwendolen Bourke had joined the Ladies' Kennel Association.&lt;ref&gt;Yenatrix. &quot;Kennel Column.&quot; ''Gentlewoman'' 02 October 1897, Saturday: 39 [of 61], Col. 2a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18971002/182/0039. Same print title, p. 434.&lt;/ref&gt;

'''1897 October 9, Saturday''', Algernon and Gwendolen Bourke were at [[Social Victorians/Timeline/1897#Harrogate|Harrogate, presumably taking the waters and baths]]. Lady May was on her way to visit Algernon Bourke in Brighton:&lt;blockquote&gt;The Earl of Mayo is expected to return from Sweden on Saturday next. Lady Mayo leaves Bournemouth on Sarurday for Brighton, where she will pay a two days' visit to her brother-in-law, the [[Social Victorians/People/Bourke|Hon. Algernon Bourke]]. The Earl and Countess will then return to Palmerstown, their seat in County Kildare.&lt;ref&gt;&quot;Pall Mall Gazette Office.&quot; ''Pall Mall Gazette'' 7 October 1897, Thursday: 8 [of 12], Col. 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18971007/022/0008. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;&lt;p&gt;

'''1897 October 30, Saturday''', ''Black and White'' published '''J.P.B.'''&lt;nowiki/&gt;'s &quot;The Case of Mrs. Elliott,&quot;&lt;ref name=&quot;:13&quot;&gt;J.P.B. &quot;The Case of Mrs. Elliott.&quot; ''Black &amp; White'' 30 October 1897, Saturday: 12 [of 34], Cols. 1a–2b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004617/18971030/036/0012. Print title ''Black and White'', p. 542.&lt;/ref&gt; an odd short short story in which the Honourable Algernon Bourke Herriott is &quot;rude to Mrs. Elliott,&quot;&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2b}} presumably having proposed sexual relations while her husband is out. J.P.B. links to the biographical Algernon Bourke's career in the stock market in the description of Mrs. Christine Elliott not even simulating interest in her husband's bicycling: &quot;a soul is a grievous burthen for a stockbroker's wife,&quot;&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2a}} suggesting that Mr. Elliott rather than Algernon Bourke Herriott is the stockbroker. The Hon. Algy&lt;blockquote&gt;was a senior member of several junior clubs. A woman had dubbed him once &quot;a rip with a taste for verses.&quot; The description was severe, but not unwarranted. His was a pretty pagan sensualism, though, singing from a wine palate to Church music. For the rest, he had just imagination enough to despise mediocrity.&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2a}}&lt;/blockquote&gt;

'''1897 November 25–26, Thursday–Friday''', Gwendolen Bourke was in Brighton, helping the Countess of Mayo at the [[Social Victorians/Timeline/1897#The Irish Industries' Association Annual Exhibition|bazaar of the Irish Industries' Association]].

'''1897 December 7, Tuesday''', Algernon Bourke attended the [[Social Victorians/Timeline/1897#7 December 1897, Tuesday|7th annual dinner for the Actors' Benevolent Fund]].

'''1897 December 30''', Algernon and Gwendolen Bourke attended a [[Social Victorians/Timeline/1897#Blenheim Palace Party with Amateur Theatricals|party at Blenheim Palace in which people performed tableaux vivants]] that got reported on, many of whom wearing the costumes from the Duchess of Devonshire's ball. The ''Irish Independent'' said Algernon Bourke was &quot;mainly responsible for the living pictures.&quot;&lt;ref&gt;&quot;Mr Algernon Bourke ....&quot; ''Irish Independent'' 05 January 1898, Wednesday: 6 [of 8], Col. 2c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001985/18980105/115/0006.&lt;/ref&gt;

'''1898''', Algernon Bourke called a meeting at White's Club about attempting to [[Social Victorians/Timeline/1900s#The Thames Salmon Experiment|restock the Thames with salmon]]. In 1899 he was on a [[Social Victorians/People/Bourke#Committees|committee led by the Lord Mayor about this topic]] as well.

'''1898 February 3, Thursday''',  Algernon Bourke was among [[Social Victorians/Timeline/1898#The Dundee Evening Telegraph Report on People at Monte Carlo|those visiting Monte Carlo according to the Dundee ''Evening Telegraph'']].

'''1898 March 12, Saturday''', ''The World'' reported on Algernon Bourke's upgrading of the Orleans Club at Brighton:&lt;blockquote&gt;

The Orleans Club at Brighton is flourishing exceedingly, and the new buildings which Mr. Algernon Bourke has just had erected at the back of the comfortable mansion at the corner of Lansdowne-place now provide all that was wanting to make the present habitat of the club all that its members desire. The new billiard-room is rapidly approaching completion, and the coffee-room, excellent and spacious now, was open on Saturday night, when every table was occupied by club diners and their guests, all of whom were enthusiastic over the excellence of this latest addition to the comfort of the house. All interested may be congratulated on what is practically new lease of life to the Orleans Club, than which there is no more comfortable place stay within the four seas.&lt;ref&gt;&quot;From '''The World''.'&quot; ''East &amp; South Devon Advertiser'' 12 March 1898, Saturday: 6 pop 8], Col. 2b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001639/18980312/132/0006. Print title ''The East and South Devon Advertiser'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;

'''1898 March 30, Wednesday''', Algernon Bourke was charged with assaulting a Mr. Potter, but it is not clear from this account what exactly happened:&lt;blockquote&gt;The Hon. Algernon H. Bourke, of Bramber, was summoned, at the instance of Mr. Walter John Potter, clerk to Mr. G. A. Flowers, solicitor, of Steyning, for assault, on the 30th March. — Mr. J. Edward Dell supported the case, and Mr. J. C. Buckwell defended, and pleaded not guilty. — The evidence was to the effect that Mr. Potter had occasion go to defendant's house on Wednesday last to serve a writ. He was going to drop the letter into [Col. 5c–6a] defendant's pocket when he turned and struck him a violent blow on the chest, making witness stagger backwards. Witness put up his hands to keep his balance, and defendant then struck him violently across the head with a weeding spud. — Richard Reed, who was at work for Mr. Bourke on the date named, and was working in garden at the time of the alleged assault, gave corroborative evidence. — Defendant, in the witness box, made a similar statement. — The magistrates differed as to whether the assault was committed, and dismissed the case.&lt;ref&gt;&quot;Steyning.&quot; ''Sussex Express'' 9 April 1898, Saturday: 2 [of 12], Col. 5c–6a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000654/18980409/036/0002. Print: ''The Sussex Express, Surrey Standard, Weald of the Kent Mail, Hants and County Advertiser'', p. 2.&lt;/ref&gt;&lt;/blockquote&gt;'''1898 April 12, Tuesday''', Algernon Bourke was among [[Social Victorians/Timeline/1898#1898 April 12, Tuesday|those visiting Monte Carlo according to the ''Gentlewoman'']].

'''1898 May 25, Wednesday''', Gwendolen Bourke wore pink to [[Social Victorians/1898-05-25 Savoy Dinner Dance Hwfa|Mrs. Hwfa Williams' dinner-dance at the Savoy]].

'''1898 June 7, Tuesday''', the Hon. Algernon and Mrs. A. Bourke were invited to and probably attended the [[Social Victorians/Timeline/1898#7 June 1898, Tuesday|State Ball at Buckingham Palace hosted by the Prince and Princess of Wales]].

'''1898 July 4, Thursday afternoon''', the Hon. Algernon and Mrs. Bourke were invited to and probably attended the [[Social Victorians/Timeline/1898#Garden Party at Marlborough House|Garden Party at Marlborough House given to the Queen and Shah of Persia]].

'''1898 October 29, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1898#Tennis Championship Game at Prince's Club, Knightsbridge|tennis match at Prince's Club, Knightsbridge]].

'''1898 November 22, Tuesday''', Algernon Bourke was present at a [[Social Victorians/Timeline/1898#Shooting Party Hosted by William James|shooting party hosted by Mr. William James]].

'''1898 December 3, Saturday''', Hon. Algernon and Mrs. A. Bourke attended the [[Social Victorians/Timeline/1898#The Funeral of Lady Connemara|funeral of Lady Connemara in Christ Church]], Down street, Piccadilly.&lt;p&gt;

'''1899 January 10, Tuesday''', the Brighton Championship Dog Show opened:&lt;blockquote&gt;Princess of Wales a Winner at the Ladies’ Kennel Club Show.

[Exclusive to &quot;The Leader.&quot;)

The Brighton Championship Dog Show opened in the Dome and Corn Exchange yesterday, and was very well patronised by visitors and exhibitors. Among the latter was H.R.H. the Princess of Wales, who did very well; and others included Princess Sophie Duleep Singh, Countess De Grey, Sir Edgar Boehm, the Hon Mrs. Algernon Bourke, Lady Cathcart, Lady Reid, Mr. Shirley (chairman of the Kennel Club), and the Rev. Hans Hamiiton (president of the Kennel Club).

The entry of bloodhounds is one of the best seen for some time; the Great Danes are another strong lot; deerhounds are a fine entry, all good dogs, and most of the best kennels represented; borzois are another very stylish lot. The bigger dogs are, as usual, in the Corn Exchange and the &quot;toy&quot; dogs in the Dome. To everyone's satsfaction the Princess of Wales carried off two first prizes with Alex in the borzois class.&lt;ref&gt;&quot;Dogs at Brighton.&quot; ''Morning Leader'' 11 January 1899, Wednesday: 8 [of 12], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18990111/142/0008. Print p. 8.&lt;/ref&gt;&lt;/blockquote&gt;

'''1899 January 11, Wednesday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1899#11 January 1899, Wednesday|a luncheon at Stanfield-hall, home of Mr. and Mrs. Basil Montogomery, for Princess Henry of Battenberg]], that also included the Countess of Dudley (sister of Mrs. Montgomery), General Oliphant, and the Mayor and Mayoress of Romsey.

'''1899 January 17–18, Tuesday and Wednesday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1899#Ladies' Kennel Association in Brighton|Ladies' Kennel Association in Brighton]], where she showed an Italian greyhound named Brenda.

'''1899 February 7, Tuesday''', Gwendolen Bourke was a member of the very high-ranking committee organizing the [[Social Victorians/Timeline/1899#Gordon Memorial College Ball|Gordon Memorial College Ball at the Hotel Cecil on 7 February 1899]]. The committee had been planning for the ball, of course, for at least 3 weeks before.

'''1899 February 22, Wednesday – April''', Gwendolen Bourke was part of [[Social Victorians/Timeline/1899#Society in St. Moritz|Society in St. Moritz]]. 1899 March 29, Wednesday, the ''Dundee Advertiser'' says that [[Social Victorians/Timeline/1899#29 March 1899, Wednesday|Cyril Sloane-Stanley was spending part of the winter in St. Moritz]] with his sister Gwendolen Bourke.

'''1899 April 7, Friday, probably''', oddly, Algernon and Gwendolen Bourke are not reported to have attended the [[Social Victorians/Timeline/1899#Funeral of the Hon. Charles Bourke, C.B.|Funeral of the Hon. Charles Bourke, C.B.]] or even to have sent flowers.

'''1899 April 8, Saturday''', the ''Gentlewoman'' reported that Gwendolen Bourke had gone to [[Social Victorians/Timeline/1899#8 April 1899, Saturday|St. Moritz with her brother, Mr. Stanley, who had gotten engaged to Lady Cairns]].

'''1899 April 26, Wednesday''', according to &quot;Local and District News&quot; for Totton, Gwendolen Bourke was &quot;ill with influenza in Paris, and Mrs. Shelley Bontein, her mother, has gone out to nurse her.&quot;&lt;ref&gt;&quot;Local and District News. Totton.&quot; ''Hampshire Advertiser'' 26 April 1899, Wednesday: 4 [of 4], Col. 2b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18990426/037/0004. Print title ''Hampshire Advertiser County Newspaper'', p. 4.&lt;/ref&gt;

'''1899 June 1, Thursday, or 2, Friday''', the Hon. Algernon and Gwendolen Bourke attended the [[Social Victorians/Timeline/1899#Wedding of Roger Cyril Sloane Stanley and Olivia, Countess Cairns|wedding of her brother, Sloane Stanley and Olivia Countess Cairns]] at Holy Trinity Church, Brompton.

'''1899 June 8, Thursday''', Algernon Bourke's money troubles:&lt;blockquote&gt;The Hon. Algernon Bourke, son of the Earl of Mayo, has been appearing before the official receivers in connection with a winding-up order made against Willis’ Restaurant, Limited. The companyf [sic] was formed to acquire the well known restaurant from the Hon. H. A. Bourke. The chairman reminded the creditors that on the last occasion the meeting was adjourned because Mr. Bourke said he thought he would be able in the course of a fortnight to obtain an offer for a sum sufficient to satisfy the creditors and debenture holders. He had received a letter from Mr. Bourke to the effect that he had been unable to complete arrangements. Having looked into the affairs of the company more closely, it appeared to him that Mr. Bourke was legally liable to repay the sum of £5,000 which was advanced to White's Club, and the question would arise whether Mr. Bourke was not also liable to repay the sum of £4,000.&lt;ref&gt;&quot;Mr. Bourke Must Pay.&quot; ''Irish Independent'' 8 June 1899, Thursday: 4 [of 8], Col. 8c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001985/18990608/118/0004. Print title: ''The Irish Weekly Independent'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;'''1899 July 1, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1899#1 July 1899, Saturday|meeting in London at the Duke of Westminster's Grosvenor House]] about preserving Killarney as part of the National Trust and seems to have been acting for someone who wanted to purchase the Muckross Estate.

'''1899 July 5, Wednesday''', Gwendolen Bourke attended a [[Social Victorians/Timeline/1899#Dinner and Dance at Devonshire House|dance at Devonshire House hosted by the Duke and Duchess of Devonshire]].

'''1899 July 6, Thursday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1899#Joan Wilson and Guy Fairfax's Wedding|wedding of Joan Wilson and Guy Fairfax in St. Mark's, near Grosvenor Square]].

'''1899 July 14, Friday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1899#14 July 1899, Friday|Ernest Beckett's dinner party]].

'''1899 July 18, Tuesday''', Gwendolen Bourke attended a [[Social Victorians/Timeline/1899#Ludovici Lecture on Impressionism|lecture on Impressionism by Ludovici hosted by the Countess of Mayo]].

'''1899 July 28, Friday''', [[Social Victorians/London Clubs#White's|White's Club]] was no longer under Algernon Bourke's management and was reconstituting itself after the possibility that it would have to close.

'''1889 July 31, Wednesday''', the Hon. Algernon and Mrs. Bourke attended a [[Social Victorians/Timeline/1889#Fete of the Uxbridge Habitation of the Primrose League|Fete of the Uxbridge Habitation of the Primrose League]] at Hillingdon Court and hosted by the Hon. Algernon and Lady Mary Mills.

'''1899 September 9, Saturday''', the ''Eastern Morning News'' includes Algernon Bourke (&quot;St. James's-street, London, club proprietor&quot;) in a list of men &quot;Receiving Orders,&quot; which it is reprinting from the ''London Gazette''.&lt;ref&gt;&quot;Receiving Orders.&quot; ''Eastern Morning'' News 9 September 1899, Saturday: 5 [of 8], Col. 3c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001152/18990909/074/0005. Same print title and p.&lt;/ref&gt;&lt;p&gt;

'''1899 October 19, Thursday''', the Hon. Algernon Bourke had a bankruptcy hearing:&lt;blockquote&gt;The public examination of the Hon. Algernon Bourke was held before Mr Registrar Giffard yesterday, at the London Bankruptcy Court. The debtor, described as proprietor of a St. James's-street club, furnished a statement of affairs showing unsecured debts £13,694 and debts fully secured £12,800, with assets which are estimated at £4,489 [?]. He stated, in reply to the Official Receiver, that he was formerly a member of the Stock Exchange, but had nothing to do with the firm of which he was a member during the last ten years. He severed his connection with the firm in May last, and believed he was indebted to them to the extent of £2,000 or £3,000. He repudiated a claim which they now made for £37,300. In 1889 he became proprietor of White's Club, St. James's-street, and carried it on until January 1st last, when he transferred it to a company called Recreations, Limited. One of the objects of the company was to raise money on debentures. The examination was formally adjourned.&lt;ref name=&quot;:9&quot; /&gt;&lt;/blockquote&gt;

'''1899 October 20, Friday''', the ''Morning Leader'' mentions Bourke's bankruptcy:&lt;blockquote&gt;Mr. Algernon Bourke, whose bankruptcy is much talked about, has been connected with numerous enterprises in clubland. He raised White's from the slough into which it had sunk after the secession of the Prince of Wales. He started the Willis Restaurant, put fresh life into the Orleans Club at Brighton, arranged a big restaurant for the bicyclists in the time of the bicycle parade, and was concerned at first in the smart and short-lived Trafalgar Bicycle Club. At one time his name spelt success. Latterly his luck has left him. He is a brother of Lord Mayo, a son of the peer who was assassinated at the post of duty, and is one of the best known men about town of the day.&lt;ref&gt;&quot;Club, Stage, and Salon.&quot; ''Morning Leader'' 20 October 1899, Friday: 6 [of 12], Col. 5b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18991020/085/0006. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;'''1899 November 8, Wednesday''', the Hon. Algernon Bourke's bankruptcy case came up again:&lt;blockquote&gt;At Bankruptcy Court, yesterday, the case the Hon. Algernon Bourke again came on for hearing before Mr. Registrar Giffard, and the examination was concluded. The debtor has at various times been proprietor of White’s Club, St. James’s-street, and the Orleans’ Club, Brighton, and also of Willis's Restaurant, King-street, St. James's. He attributed his failure to losses sustained by the conversion of White’s Club and the Orleans' Club into limited companies, to the payment of excessive Interest on borrowed money, and other causes. The liabilities amount to £26,590, of which £13,694 are stated to be unsecured, and assets £4,409.&lt;ref&gt;&quot;Affairs of the Hon. A. Bourke.&quot; ''Globe'' 09 November 1899, Thursday: 2 [of 8], Col. 1c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001652/18991109/020/0002. Print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;

'''1899 December 23, Saturday''', &quot;Mr. Algernon Bourke has departed for a tour in Africa, being at present the guest of his brother in Tunis.&quot;&lt;ref&gt;&quot;The Society Pages.&quot; ''Walsall Advertiser'' 23 December 1899, Saturday: 7 [of 8], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001028/18991223/143/0007. Print p. 7.&lt;/ref&gt;

'''1899 December 29, Friday''', Gwendolen Bourke was at the [[Social Victorians/Timeline/1899#Christmas Party Hosted by the Duke and Duchess of Marlborough|Christmas Party Hosted by the Duke and Duchess of Marlborough]].&lt;p&gt;

'''1899 December 31''', the San Francisco newspaper ''The Wave'' wrote the following about London society:&lt;blockquote&gt;The most prominent untitled people in London may be said to be Mr. and Mrs. [[Social Victorians/People/Williams|Hwfa Williams]], Mr. and Mrs. [[Social Victorians/People/Grenfell|Willie Grenfell]] and Mr. Algy Bourke. That they are passing rich, goes without saying, and that they entertain lavishly, understood — for to be untitled, prominent and successful, argues wealth, hospitality and cleverness.&lt;ref&gt;&quot;London.&quot; The (San Francisco) ''Wave'' 14 January 1899 (Vol. XIX, No. 2): 14. ''The Internet Archive'' https://archive.org/details/wave19unse/page/n20/mode/1up.&lt;/ref&gt;&lt;/blockquote&gt;

=== 1900s ===

'''1900 February 15, Thursday''', Daphne Bourke, the four-year-old daughter of the Hon. Algernon and Mrs. Bourke was a bridesmaid in the [[Social Victorians/Wilson Chesterfield Wedding 1900-02-15|wedding of Enid Wilson and the Earl of Chesterfield]].&lt;ref&gt;&quot;London Day by Day.&quot; ''Daily Telegraph'' 15 February 1900, Thursday: 8 [of 12], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/19000215/175/0008. Name in British Newspaper Archive: ''Daily Telegraph &amp; Courier'' (London). Print p. 8.&lt;/ref&gt; Gwendolen Bourke, &quot;who was in grey, wore a chinchilla toque with violets.&quot;&lt;ref&gt;&quot;Society. Entertainments, Balls, &amp;c.&quot; ''The Queen'' 24 February 1900, Saturday: 40 [of 76], Col. 1a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19000224/235/0040. Print: ''The Queen, The Lady's Newspaper'', p. 308.&lt;/ref&gt;

'''1900 March 10, Saturday''', the ''Weekly Irish Times'' reprinted society gossip from ''The World'':&lt;blockquote&gt;Mrs. Algernon Bourke, who has been staying with her husband's uncle, old Connemara, during Mr. Algernon Bourke's absence abroad, has taken a new house near Portman square, and will be settling there before Easter.&lt;ref&gt;&quot;Society Gossip.&quot; ''Weekly Irish Times'' 10 March 1900, Saturday: 17 [of 20], Col. 1b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001684/19000310/116/0017. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;'''1900 July''' '''17, Tuesday''', Gwendolen Bourke took part in the [[Social Victorians/Timeline/1900s#17 July 1900, Tuesday|Children's Fete in support of the National Society for the Prevention of Cruelty to Children]] on the grounds of the Royal Botanic Society. Daphe was 5 at this time, so it seems logical that she would have been there, too.

'''1900 July 30, Monday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1900s#Barber of Seville at Covent Garden|''The Barber of Seville'' at Covent Garden]].

'''1890 August 6, Friday''', &quot;[[Social Victorians/Timeline/1890#Beautiful Women|Beautiful Women]],&quot; an article in ''Vanity Fair'' that was reprinted elsewhere, mentions Gwendolen Bourke (&quot;Lady Algernon Bourke&quot;) as one of the most beautiful women in England.

'''1900 August 11, Saturday''', Gwendolen Bourke got&lt;blockquote&gt;the pretty little Yorkshire String, an especially tiny mite, weighing only 2&lt;sup&gt;1&lt;/sup&gt;/&lt;sub&gt;2&lt;/sub&gt;lb, and carrying a very promising coat, ... at the Aquarium Show.&lt;ref&gt;&quot;The Witchampton Kennel.&quot; &quot;Ladies Kennels.&quot; ''Ladies' Field'' 11 August 1900, Saturday: 16 [of 60], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0006043/19000811/043/0016. Print title same, p. 390.&lt;/ref&gt;&lt;/blockquote&gt;&lt;p&gt;

'''1900 September 16''', the Hon. Algernon Bourke became the heir presumptive to the Earldom of Mayo when his older brother Captain Hon. Sir Maurice Archibald Bourke died.&lt;p&gt;

'''1900 October 06, Saturday''', the ''Weekly Irish Times'' says that Mr. Algernon Bourke, now heir presumptive to the earldom of Mayo, &quot;has been for some months lately staying with Mr. Terence Bourke in Morocco.&quot;&lt;ref&gt;&quot;Society Gossip.&quot; ''Weekly Irish Times'' 06 October 1900, Saturday: 14 [of 20], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001684/19001006/121/0014. Print p. 14.&lt;/ref&gt;&lt;p&gt;

'''1901 May 30, Thursday''', the Hon. Mrs. Algernon Bourke attended the fashionable [[Social Victorians/Timeline/1900s#1901 May 30, Thursday|Ladies' Kennel Association Dog Show at the Botanic Garden]].

'''1901 July 2, Tuesday''', Gwendolen Bourke — &quot;pretty Mrs. Algernon Bourke, in a mauve gown and and purple tulle toque&quot; — attended a children's party at the Botanic Gardens hosted by the Earl and Countess of Kilmorey.&lt;ref&gt;&quot;The Earl of Kilmorey, K.P.&quot; ''Gentlewoman'' 13 July 1901: Saturday, 50 [of 84], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010713/237/0050. Print: title the same, p. 60.&lt;/ref&gt;

'''1901 July 4, Thursday''', Gwendolen Bourke — dressed &quot;in pale grey, with her pretty little girl,&quot; 6-year-old Daphne — attended a [[Social Victorians/Timeline/1900s#The Countess of Yarborough's Children's Party|children's party hosted by the Countess of Yarborough]].&lt;ref&gt;&quot;The Countess of Yarborough ....&quot; ''Gentlewoman'' 13 July 1901, Saturday: 76 [of 84], Col. 2b, 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010713/381/0076. Print p. xxxvi.&lt;/ref&gt;{{rp|Col. 3a}}

'''1901 July 4–6, Thursday–Saturday''', Gwendolen Bourke helped staff the Perthshire stall&lt;ref&gt;&quot;The Great County Sale.&quot; ''Gentlewoman'' 29 June 1901, Saturday: 43 [of 72], Col. 3a [of 3]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010629/223/0043# https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010629/223/0043]. Same print title, pp. 679.&lt;/ref&gt; at the [[Social Victorians/Timeline/1900s#The Great County Sale|Great County Sale in the Imperial Gardens of the Earl's Court Exhibition]].

'''1901 July 20, Saturday''', the ''Gentlewoman'' published the Hon. Mrs. Algernon Bourke's portrait (identified with &quot;Perthshire&quot;) in its 3rd series of &quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot;&lt;ref&gt;&quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot; ''Gentlewoman'' 20 July 1901, Saturday: 31 [of 60], Col. 4b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010720/141/0031. Print n.p.&lt;/ref&gt; Their daughter Daphne appears in the portrait as well.

'''1901 July 23, Tuesday''', an &quot;Hon. Mrs. Bourke&quot; was in the [[Social Victorians/Timeline/1900s#Lord and Lady Algernon Gordon Lennox|party &quot;entertained by Lord and Lady Algernon Gordon Lennox]].&quot;&lt;p&gt;

'''1901 September 12, Thursday''', Mrs. Gwendolen Bourke wanted her name listed as Mrs. Algernon Bourke in the Electoral Register, apparently a frequent complaint:&lt;blockquote&gt;Mr. Underhill, the Conservative agent, mentioned to the Revising Barrister (Mr. William F. Webster) that the name of the Hon. Mrs. Gwendolen Bourke was on the list in respect of the house, 75, Gloucester-place. The lady had written to him to say that she was the Hon. Mrs. Algernon Bourke and that she wished that name to appear on the register. In reply to the Revising Barrister, Mr. Underhill said that “Algernon” was the name of the lady’s husband.

Mr. Cooke, the rate-collector, said that Mrs. Bourke had asked to be addressed Mrs. Algernon Bourke, but that the Town Clerk thought the address was not a correct one. The lady signed her cheques Gwendolen.”

Mr. Underhill said the agents frequently had indignant letters from ladies because they were not addressed by their husband’s Christian name.

The Revising Barrister — lf a lady gave me the name of Mrs. John Smith I should say I had not got the voter’s name. The name Gwendolen must remain.&lt;ref name=&quot;:15&quot;&gt;&quot;Ladies’ Names.&quot; ''Morning Post'' 12 September 1901, Thursday: 7 [of 10], Col. 3a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19010912/130/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1901 October 26, Friday''', Algernon Bourke was on the Men's Committee of the [[Social Victorians/London Clubs#Prince's Club Ice-skating Rink|Prince's Club Ice-skating Rink]], which had [[Social Victorians/Timeline/1900s#The Prince's Club Ice-skating Rink Opening|its official opening on his day]]. 

'''1902 January''', Algernon Bourke is mentioned in [[Social Victorians/Schools#&quot;More of My Contemporaries at School.&quot;|reminiscences of Eton written by the &quot;Earl of X&quot;]] as being among those in the &quot;world of letters,&quot; and whose brother, later the Earl of Mayo, the Earl of X did not like. 

'''1902 January 25, Saturday''', Mrs. Algernon Bourke gave a box to Lady Helen Stewart-Vane-Tempest in honor of [[Social Victorians/Stewart-Stavordale Wedding 1902-01-25|Lady Helen's wedding to Giles Fox-Strangways, Lord Stavordale]]. 

'''1902 April 26, Saturday''', Mrs. A. Bourke is listed as being at the Norfolk Hotel in Brighton.&lt;ref&gt;&quot;Guide to Visitors at Hotels and Boarding Houses.&quot; ''Brighton Gazette'' 26 April 1902, Saturday: 3 [of 8], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000938/19020426/116/0003. Same print title and p.&lt;/ref&gt; 

'''1902 May, End of''', Gwendolen Bourke attended a [[Social Victorians/Timeline/1900s#End of May 1902|party at Blenheim Palace hosted by the Duke and Duchess of Marlborough]]. 

'''1902 June 11, Monday''', the Hon. Mrs. Algernon Bourke had a dog entered in the [[Social Victorians/Timeline/1900s#Ladies' Kennel Association Show|Ladies' Kennel Association competitions in the Botanic Gardens]]. 

'''1902 September 4, Thursday''', the ''Daily Express'' reported that &quot;Mrs. Algernon Bourke is staying with Lord and Lady Alington at Scarborough.&quot;&lt;ref&gt;&quot;Onlooker.&quot; &quot;My Social Diary.&quot; &quot;Where People Are.&quot; ''Daily Express'' 04 September 1902, Thursday: 5 [of 8], Col. 1b? [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020904/099/0005. Print p. 4, Col. 7b [of 7].&lt;/ref&gt;

'''1902 September 22, Monday''', Gwendolen Bourke was a guest at the [[Social Victorians/Timeline/1900s#Earl and Countess of Mar and Kellie's House Party|large house party hosted by the Earl and Countess of Mar and Kellie]].

'''1902 October 24, Friday''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#Annual Opening of the Prince's Ice-skating Rink|opened the Prince's ice-skating rink for the season]], which he had been doing since 1895.

'''1902 October 25, Saturday''', Algernon Bourke was bequeathed £500 by his uncle [[Social Victorians/People/Mayo|Robert Bourke]], who had died 3 September 1902.&lt;ref&gt;&quot;Will of Lord Connemara.&quot; ''Kildare Observer and Eastern Counties Advertiser'' 25 October 1902, Saturday: 2 [of 8], Col. 4b–c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001870/19021025/037/0002. Print title the ''Kildare Observer'', n.p.&lt;/ref&gt;&lt;p&gt;

'''1902 October 31, Friday''', the [[Social Victorians/Timeline/1900s#Annual Opening of the Prince's Ice-skating Rink|7th opening of the Prince's Skating Club]]. Guendoline Bourke was on the Women's Committee and Algernon Bourke was on the Men's.&lt;p&gt;

'''1902 November 8, Friday, beginning, perhaps''', Gwendolen Bourke was part of the [[Social Victorians/Timeline/1900s#8 November 1902, Saturday|Earl and Countess of Warwick's shooting party at Easton Lodge]].&lt;p&gt;

'''1902 December 9, Tuesday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1900s#9 December 1902, Tuesday|Lady Eva Wyndham-Quin's &quot;at home,&quot; held at the Welch Industrial depot]] for the sale Welsh-made Christmas gifts and cards. Bourke wore &quot;a fur coat and a black picture hat.&quot;&lt;ref&gt;&quot;A Lady Correspondent.&quot; &quot;Society in London.&quot; ''South Wales Daily News'' 11 December 1902, Thursday: 4 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000919/19021211/082/0004. Print p. 4.&lt;/ref&gt;

'''1903 February 6, Friday''', Hon. Mrs A. Bourke was present at a [[Social Victorians/Timeline/1900s#Dinner Party Hosted by Lord Lieutenant of Ireland and the Countess of Dudley|dinner party Hosted by Lord Lieutenant of Ireland and the Countess of Dudley]]. &lt;p&gt;

'''1903 February 9, Monday''', Gwendolen Bourke was present at a [[Social Victorians/Timeline/1900s#Dinner Party Hosted by Lord Lieutenant of Ireland and the Countess of Dudley|house party at Dublin Castle hosted by the Lord Lieutenant and Countess of Dudley that began the Viceregal season]].

'''1903 March 17, Tuesday''', Gwendolen Bourke staffed a booth at a [[Social Victorians/Timeline/1900s#1903 March 17, Tuesday|sale of the Irish Industries Association]] on St. Patrick's Day with [[Social Victorians/People/Mayo|Lady Mayo]], [[Social Victorians/People/Dudley|Georgina Lady Dudley]] and [[Social Victorians/People/Beresford|Miss Beresford]]. A number of other aristocratic women were also present at the sale in other booths, including [[Social Victorians/People/Londonderry|Lady Londonderry]] and [[Social Victorians/People/Lucan|Lady Lucan]].

'''1903 June 19, Friday''', Gwendolen Bourke was invited to the [[Social Victorians/Timeline/1900s#Grand Ball in the Waterloo Chamber at Windsor Castle|grand ball at Windsor Castle]], the end of the Ascot-week festivities.

'''1903 June 23, Tuesday''', Gwendolen and Daphne Bourke were invited to a [[Social Victorians/Timeline/1900s#1903 June 23, Tuesday|children's party at Buckingham Palace for Prince Eddie's birthday]].

'''1903 July 10, Friday, or so''', Gwendolen Bourke attended a [[Social Victorians/Timeline/1900s#Party Hosted by the Duke and Duchess of Marlborough|party hosted by the Duke and Duchess of Marlborough]].

'''1904 May 17, Tuesday''', Gwendolen Bourke had agreed to let Daphne appear in the tableaux vivants arranged by Sir Philip Burne-Jones for the [[Social Victorians/Timeline/1900s#Countess Cadogan's Great Bazaar|Countess of Cadogan's great bazaar]]. Some mothers had had to decline because of the outbreaks of measles and chicken pox.&lt;p&gt;

'''1904 June 30, Thursday''', Gwendolen and Daphne Bourke attended another birthday party for Prince Eddie at Buckingham Palace, and the ''Gentlewoman'' says, &quot;No prettier little girl was to be seen that day than little Miss Daphne Bourke, the daughter of the Hon. Mrs. Algernon Bourke, with her wonderful Irish eyes and colouring, her pretty white frock being relieved with a rose pink sash.&quot;&lt;ref&gt;&quot;Prince Eddie's Birthday.&quot; ''Gentlewoman'' 02 July 1904, Saturday: 68 [of 92]. Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19040702/360/0068. Print: title the same, p. 42.&lt;/ref&gt;&lt;p&gt;

'''1904 September 15, Thursday''', according to what was at the time called the ''Irish Daily Independent and Nation'', Algernon Bourke was living in Venice and not in the UK at this point:&lt;blockquote&gt;Algernon Bourke, who usually lives in Venice, has spent some time in England during the present summer, and has now gone on a fishing expedition to Sweden, accompanied by his brother, Lord Mayo. Lady Mayo has been staying meanwhile in Ireland, and has had a visit from her mother, Lady Maria Ponsonby, who is a sister of Lend Obventry.&lt;ref name=&quot;:10&quot;&gt;&quot;Society Notes.&quot; ''Irish Independent'' 15 September 1904, Thursday: 4 [of 8], Col. 5b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001986/19040915/131/0004. Print title: ''Irish Daily Independent and Nation'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

'''1904 October 22, Saturday''', the ''Gentlewoman'' reported that &quot;Mrs. Algernon Bourke is paying a visit to Venice, which Mr. Bourke has made his headquarters for several years past, as he is connected with some very artistic stone and marble works situated near the Grand Canal.&quot;&lt;ref&gt;&quot;The Social Peepshow.&quot; ''Gentlewoman'' 22 October 1904, Saturday: 24 [of 6ths 8], Col. 2c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19041022/112/0024. Print title same, p. 672.&lt;/ref&gt;

'''1905 February 17, Friday''', the Dundee ''Evening Post'' reported that Algernon Bourke &quot;set up a shop in Venice for the sale of art treasures and old furniture.&quot;&lt;ref&gt;&quot;Social News.&quot; Dundee ''Evening Post'' 17 February 1905, Friday: 6 [of 6], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000582/19050217/105/0006. Print p. 6.&lt;/ref&gt;

'''1905 April 26, Wednesday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1900s#New Forest United Hunt Ball|New Forest United Hunt Ball]], as did her brother Captain R. C. H. Sloane Stanley and his wife Olivia Countess Cairns.&lt;p&gt;

'''1905 June 5, Monday''', Algernon Bourke wrote to the ''Times'' from Venice that &quot;The Venetian wits have suggested a motto for Admiral Togo, Togo Tenga Tutto (Togo takes the lot).&quot;&lt;ref&gt;&quot;Mr. Algernon Bourke.&quot; ''Hull Daily Mail'' 08 June 1905, Thursday: 2 [of 6], Col. 6a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000324/19050608/008/0002. Print title ''Daily Mail'', p. 6.&lt;/ref&gt;&lt;p&gt;

'''1905, last week of July''', Gwendolen Bourke and daughter Daphne Bourke — who was 10 years old — attended [[Social Victorians/Timeline/1900s#Last week of July, 1905|Lady Cadogan's children's party at Chelsea House]]. Daphne was &quot;One of loveliest little girls present.&quot;&lt;ref&gt;&quot;Court and Social News.&quot; ''Belfast News-Letter'' 01 August 1905, Tuesday: 7 [of 10], Col. 6b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/19050801/157/0007. Print p. 7.&lt;/ref&gt;&lt;p&gt;

'''1906 March 9, Friday''', Gwendolen Bourke was a reference for Mr. Frances Burgess, who taught piano, singing, voice production, organ and music theory. Burgess was &quot;Organist and Choirmaster of St. Columbs', North Kensington, Director of the Plainsong and Medieval Music Society's Choir, etc., etc.&quot;&lt;ref name=&quot;:21&quot;&gt;&quot;Mr. Francis Burgess.&quot; ''Kilburn Times'' 9 March 1906, Friday: 3 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001813/19060309/086/0003. Print title: ''Kilburn Times Hampstead and North-western Press'', p. 3.&lt;/ref&gt;&lt;p&gt;

'''1906 December 10, Monday''', Gwendolen Bourke was seen in the tea room, possibly with Lady Grosvenor, at [[Social Victorians/Timeline/1900s#1906 December 10, Monday|Lady Dudley's sale of Irish needlework]].&lt;p&gt;

'''1907 May''', a &quot;naval signalling incident&quot; [[Social Victorians/Timeline/1887#May 1887|caused the Waterford ''Evening News'' to recall a similar event]] that had occurred 20 years earlier, in which Algernon Bourke, as special correspondent for the ''Times'', publicized [[Social Victorians/People/Beresford|Lord Charles Beresford]]'s use of his ship's signalling capabilities to send a message to his wife about being late for dinner:&lt;blockquote&gt;

The naval signalling incident is still in the air. It is expected that the matter will not be threshed out until Emperor William leaves England. A story of a former signalling incident in which [[Social Victorians/People/Beresford|Lord Charles Beresford]] was concerned is going the rounds at the moment.&lt;/blockquote&gt;

'''1907 August 24, Saturday''', Algernon Bourke was present at [[Social Victorians/Timeline/1900s#Polo Week at Eaton Hall, Duke and Duchess of Westminster|Polo Week at Eaton Hall, hosted by the Duke and Duchess of Westminster]].

'''1908 July 30, Thursday''', Gwendolen Bourke was at [[Social Victorians/Timeline/1900s#Glorious Goodwood. Cup Day and Dresses.|Cup Day at the Goodwood races]], wearing salmon-pink with a matching hat.

'''1909 April 20, Tuesday''', Lady Rosemary Cairns — daughter of Olivia Sloan-Stanley, Countess Cairns and Cyril Sloane-Stanley — and Wyndham Portal were [[Social Victorians/Timeline/1900s#20 April 1909, Tuesday|married in St. Margaret's, Westminster]]. Lavender and Diane Sloane-Stanley were bridesmaids.&lt;p&gt;

'''1909 May 22, Saturday''', Algernon Bourke appears to have been living in Pisa. A columnist for the ''Queen'' reported on the Royal School of Art Needlework:&lt;blockquote&gt;Lady Leconfield [?] was there, also her sister-in-law, the [[Social Victorians/People/Mayo|Dowager Lady Mayo]], only just back from her winter on the Continent, when she spent most of the time at Pisa, where her son Mr Algernon Bourke has also been staying. The latter is a great connoisseur as regards [art?] notably in what is really good in the way of old Italian sculpture and carving. He and his handsome wife have a place near to Putney, and this winter again Mr Bourke, as the result of his Italian travels, has been sending home such relics of the old Italian palace gardens as as stone and marble carved vases, garden seats, and what-not of the kind — not all for himself and his own gardens by any means, I fancy; but his friends, relying on his knowledge in such matters, get him when abroad to choose for [them?] the adornment of their English terraces and gardens.&lt;ref&gt;&quot;My Social Diary.&quot; The ''Queen'' 22 May 1909, Saturday: 31 [of 86], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19090522/203/0031. Print p. 871.&lt;/ref&gt;&lt;/blockquote&gt;'''1909 September''', the Hon. Algernon Bourke was among the [[Social Victorians/Timeline/1900s#Visitors in Venice from the U.K.|many visitors from &quot;England&quot; in Venice]] in September.

=== 1910s ===
'''1910 April 20, Wednesday''', the ''Tatler'' printed an &quot;open letter&quot; to Geraldine, Countess of Mayo, as part of its &quot;The Searchlight in Society&quot; series and mentioned Algernon Bourke, saying he had been keeping &quot;a curiosity shop at Venice&quot;:&lt;blockquote&gt;The Bourkes have brains, and a good example is afforded by Mr. Algernon Bourke, next brother to Lord Mayo and heir-presumptive to the title. He is a good-looking man who used to be known as Buttons Bourke, and he married well, as his wife was the rich and pretty Miss Guendolen Sloane Stanley. He may be described as a &quot;Jack of all trades,&quot; but it is not I who will say that he is a master of none. He was once in the Stock Exchange, then he took White's Club in hand and restored it to much of its former prestige. After that he dabbled in smart hotels and restaurants, and the last thing I heard of him was that he kept a curiosity shop at Venice.&lt;ref&gt;Candida. &quot;The Searchlight in Society. Our Open Letter. No. CII. The Countess of Mayo.&quot; The ''Tatler'' 20 April 1910, Wednesday: 18 [of 42], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001852/19100420/023/0018. Print title same, p. 72.&lt;/ref&gt;&lt;/blockquote&gt;

'''1911 November 21, Tuesday''', Gwendolen Bourke assisted the [[Social Victorians/Timeline/1910s#21 November 1911, Tuesday|Duchess of Marlborough at her at-home]] that included a sale of work by the wives of prisoners.&lt;p&gt;

'''1912 September 27, Friday''', Gwendolen and Daphne Bourke were visiting Mr. and Mrs. Shelley Bontein, her mother and stepfather.&lt;ref&gt;&quot;From 'The World.'&quot; ''Berks and Oxon Advertiser'' 27 September 1912, Friday: 2 [of 8], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002298/19120927/014/0002. Same print title, n.p.&lt;/ref&gt;&lt;p&gt;

'''1913 April 23, Wednesday''', the Irish Independent reported that Gwendolen and Daphne Bourke had arrived in London for the season:&lt;blockquote&gt;&lt;p&gt;

The Hon. Mrs. Algernon Bourke and Miss Bourke have arrived for the season at 75 Gloucester place, Portman square, London.&lt;ref&gt;&quot;Social and Personal.&quot; ''Irish Independent'' 23 April 1913, Wednesday: 4 [of 10], Col. 5b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001715/19130423/081/0004. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;&lt;p&gt;

'''1913 May 7, Wednesday''', Gwendolen Bourke presented her daughter Daphne Bourke at court:&lt;blockquote&gt;Mrs. Algernon Bourke presented her daughter, and wore blue and gold broché with a gold lace train.&lt;ref&gt;&quot;Social and Personal.&quot; London ''Daily Chronicle'' 08 May 1913, Thursday: 6 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/19130508/120/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

The ''Pall Mall Gazette'' has a description of Daphne Bourke's dress, but what exactly &quot;chiffon [[Social Victorians/Terminology#Hoops|paniers]]&quot; means in 1913 is not clear:&lt;blockquote&gt;Court dressmakers appear to have surpassed all previous records in their efforts to make the dresses for to-night’s Court as beautiful as possible. Noticeable among these is the dainty presentation gown to be worn by Miss Bourke, who will be presented by her mother, the Hon. Mrs. Algernon Bourke. This has a skirt of soft white satin draped with chiffon [[Social Victorians/Terminology#Hoops|paniers]] and a bodice veiled with chiffon and trimmed with diamanté and crystal embroidery. Miss Bourke’s train, gracefully hung from the shoulders, is of white satin lined with pale rose pink chiffon and embroidered with crystal and diamanté.&lt;ref&gt;&quot;Fashion Day by Day. Lovely Gowns for To-night's Court.&quot; ''Pall Mall Gazette'' 07 May 1913, Wednesday: 13 [of 18], Col. 1a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/19130507/199/0013. Print n.p.&lt;/ref&gt;&lt;/blockquote&gt;The ''London Evening Standard'' describes Gwendolen and Daphne Bourke the same way except with differences in editing:&lt;blockquote&gt;Miss Bourke: Presented by her mother, the Hon. Mrs. Algernon Bourke. Dainty presentation gown of white satin, the skirt draped with chiffon paniers, bodice veiled chiffon and trimmed with diamanté and crystal embroidery. Train gracefully hung from shoulder of white satin embroidered with crystal and diamanté, lined with pale rose pink chiffon.&lt;ref&gt;&quot;Some of the Dresses.&quot; &quot;The King and Queen. Third Court. Most Brilliant of the Year.&quot; ''London Evening Standard'' 08 May 1913, Thursday: 11 [of 18], Col. 4b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/19130508/237/0011. Print title ''The Standard'', p. 11.&lt;/ref&gt;&lt;/blockquote&gt;

According to the ''Lady's Pictorial'', Daphne Bourke's dress was designed and constructed by [[Social Victorians/People/Dressmakers and Costumiers#Messrs Russell and Allen|Messrs. Russell and Allen]], Old Bond-street, W., and the description is identical (except for a couple of commas).&lt;ref&gt;&quot;Their Majesties' Court.&quot; ''Lady's Pictorial'' 17 May 1913, Saturday: 35 [of 64], Col. 2c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005980/19130517/296/0035. Same print title, p. 787.&lt;/ref&gt;

'''1914 May 11, Monday''', Gwendolen and Daphne Bourke attended a [[Social Victorians/Timeline/1910s#Dance at the Ritz Hosted by Mrs. George Marjoribanks|dance at the Ritz hosted by Mrs. George Marjoribanks]].

'''1915 January 1, Friday''', Algernon Bourke is listed as being on the Executive Committee of the [[Social Victorians/Timeline/1910s#1915 January 1, Friday|National Food Fund, publicized by the ''Conservative and Unionist Women's Franchise Review'']].

'''1916 August 25, Friday''', Daphne Bourke's and John Fortescue's engagement was announced:&lt;blockquote&gt;A most attractive prospective bride (says the &quot;Star&quot;) is Mr. and Mrs. Algernon Bourke's only daughter, Miss Daphne Bourke, whose engagement has just taken place to Mr. Fortescue, of the Coldstream Guards. Miss Bourke is tall, dark, and very beautiful; and Mr. Fortescue is one of the family of Boconoc, Cornwall, and Dropmore, Maidenhead. At the latter place the two families have been neighbours, for Mr. and Mrs. Algernon Bourke have a charming country residence at Taplow, while Dropmore is famous for its magnificent gardens.&lt;ref&gt;&quot;Personalia.&quot; ''Uxbridge &amp; W. Drayton Gazette'' 25 August 1916, Friday: 4 [of 8], Col. 5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002285/19160825/043/0004. Print title ''The Advertiser'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;&lt;p&gt;'''1917 June 7, Thursday''', Daphne Bourke and John Grenville Fortescue [[Social Victorians/Timeline/1910s#7 June 1917, Thursday|married in the Coldstream Guards' chapel]].

== Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball ==
According to both the ''Morning Post'' and the ''Times'', the Hon. Algernon Bourke was among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]] at the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]].&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt; Based on the people they were dressed as, Gwendolen Bourke was probably in this procession but it seems unlikely that Algernone Bourke was.

[[File:Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.jpg|thumb|alt=Black-and-white photograph of a standing woman richly dressed in an historical costume with a headdress and a very large fan|Hon. '''Guendoline''' Bourke as Salammbô. ©National Portrait Gallery, London.]]
=== Hon. Guendoline Bourke ===
[[File:Alfons Mucha - 1896 - Salammbô.jpg|thumb|left|alt=Highly stylized orange-and-yellow painting of a bare-chested woman with a man playing a harp at her feet|Alfons Mucha's 1896 ''Salammbô''.]]
Lafayette's portrait (right) of &quot;Guendoline Irene Emily Bourke (née Sloane-Stanley) as Salammbô&quot; in costume is photogravure #128 in the '''Album''' presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot;&gt;&quot;Devonshire House Fancy Dress Ball (1897): photogravures by Walker &amp; Boutall after various photographers.&quot; 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.&lt;/ref&gt; The printing on the portrait says, &quot;The Hon. Mrs. Algernon Bourke as Salammbo.&quot;&lt;ref name=&quot;:23&quot;&gt;&quot;Mrs. Algernon Bourke as Salammbo.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158491/Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.&lt;/ref&gt;

The Lafayette Archive has 2 additional poses from the same session on 5 July 1897 as the one chosen for the Album:

* Same image as the Album photograph but higher resolution than the one the National Portrait Gallery, London, gives permission to post (Neg. No. GP [L] ).
* Standing with fan behind head, includes close-up of skirt fabric and left hand (Neg. No. GP [L] [http://lafayette.org.uk/bou1368-444.html 1368-444]).
* Reclining on pillows and furs, includes close-up of face and headdress (Neg. No. GP [L] [http://lafayette.org.uk/bou1368-442.html 1368-442]).

==== Newspaper Accounts ====
The Hon. Mrs. A. Bourke was dressed as Salambo in the Oriental procession&lt;ref name=&quot;:2&quot; /&gt;&lt;ref name=&quot;:3&quot; /&gt; in a costume made by [[Social Victorians/People/Dressmakers and Costumiers#Mrs. Mason|Mrs. Mason]].

Besides the two that mention her — the ''Morning Post'' and the ''Times'' — only two describe her costume, the London ''Evening Standard'' and the ''Gentlewoman'':
* &quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}

==== Commentary ====

*

==== Salammbô ====
Salammbô is the fictitious protagonist in Gustave Flaubert's 1862 novel ''Salammbô'', set during the Roman war against Carthage.&lt;ref name=&quot;:5&quot;&gt;{{Cite journal|date=2024-04-29|title=Salammbô|url=https://en.wikipedia.org/w/index.php?title=Salammb%C3%B4&amp;oldid=1221352216|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Salammb%C3%B4.&lt;/ref&gt; Salammbô is a Carthaginian priestess of the lunar goddess Tanit. Matho, a Roman mercenary, breaks into Tanit's temple and steals her sacred veil — the spiritual guardian of Carthage. Salammbô sneaks into the enemy encampment to steal the veil back. She meets Matho in his tent, and &quot;believing each other to be divine apparitions,&quot; they make love,&lt;ref name=&quot;:5&quot; /&gt; although it is also a defilement. Salammbô succceds in getting the veil back, but Matho is tortured and executed, which causes her to die of shock, the effect of both having touched the veil. The plot of the opera is not identical to that of the novel.

What Gwendolen Bourke saw as representative of herself in Salammbo is difficult to discern, unless her costume contains references to particular images or productions. Translations and illustrated editions of Flaubert's novel came out steadily beginning in the 1880s. A production of Ernest Reyer's opera ''Salammbô'', based on Flaubert's novel and published in Paris in 1890, opened at the Paris Opéra on 16 May 1892,&lt;ref&gt;{{Cite journal|date=2024-04-11|title=Ernest Reyer|url=https://en.wikipedia.org/w/index.php?title=Ernest_Reyer&amp;oldid=1218353215|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Ernest_Reyer.&lt;/ref&gt; starring Madame Rose Caron, with Mademoiselle Lucienne Bréval performing when Caron was on vacation.&lt;ref&gt;Jullienn, Adolphe. &quot;Mademoiselle Lucienne Bréval de L'Académie Nationale de Musique [or de l'Opéra in the Table of Contents].&quot; ''Le Théatre'' April 1898 (No. 4). Google Books https://www.google.com/books/edition/_/_oxRAQAAMAAJ. Pp. 8–10.&lt;/ref&gt; (8, Col. 2c) This production was widely reviewed and discussed in the papers in the UK, and its production design was notable, especially Caron's costumes, the sets and the very scale of the production. So Bourke or her costumier may have seen the opera, images of the performers or its posters, influencing the design of her costume.

* Rose Caron in her Salammbo costume is here: https://www.gettyimages.com/detail/news-photo/rose-caron-french-soprano-in-costume-in-the-title-role-of-news-photo/1439485238.
* A headshot of Bréval in costume is here: https://books.google.com/books/content?id=_oxRAQAAMAAJ&amp;pg=RA3-PP7&amp;img=1&amp;zoom=3&amp;hl=en&amp;bul=1&amp;sig=ACfU3U2Gv8Os_rEmx2gM9SakJkYLJ9hW7g&amp;ci=6%2C1%2C988%2C1371&amp;edge=0.)
* &quot;Salammbo's hair [was] powdered with a violet dust when she first appeared before the eyes of Matho.&quot;&lt;ref&gt;&quot;Salome.&quot; ''Pall Mall Gazette'' 27 February 1893, Monday: 3 [of 8]. Col. 2b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18930227/010/0003. Same print title and p.&lt;/ref&gt;

Salammbo figured in paintings, sculptures and illustrations of editions of Flaubert's novel before Ernest Reyer's 1890 opera. She is often depicted as nude and highly sexual or sexualized (kissing a huge snake, for example, that she holds aloft).

Gwendolen Bourke's costume and her social life as reported in the newspapers do not suggest that she was a big risk-taker like, for example, the eccentric la Comtesse de Castiglione, who appeared at a ball in a Salammbo costume in 1886, 4 years after Flaubert's novel was first published. In 1889 the ''Edinburgh Evening News'' exaggerates her nudity and doesn't describe the rush in the ballroom to see her but does address the lingering memory:&lt;blockquote&gt;The late Countess Castiglione, whose death in Paris is recorded yesterday, made her first appearance at the Imperial Court in 1866, where her extraordinary beauty made a great impression on Napoleon III., and eventually led to the Empress Eugenie’s undertaking an unexpected and much-talked-of visit to Scotland. The Countess had a face and complexion which would have enchanted Rubens, and her lovely golden hair touched her feet. Even at the present day Paris has not forgotten her costume, or rather absence of costume as Salammbo, in which character she figured at a certain memorable ball at the Tuileries, wearing her hair, her jewels, and very little else. The Empress Eugenie, when she was presented to her thus lightly arrayed, declared that she must be cold, and insisted upon her there and then donning a mantle. Mme. de Castiglione was never again invited to an entertainment over which the Empress Eugenie presided.&lt;ref&gt;&quot;A Countess’ Queer Ball Costume.&quot; ''Edinburgh Evening News'' 2 December 1899, Saturday: 2 [of 6], Col. 7b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000452/18991202/024/0002. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;Given how widely this incident was discussed at the time of the death of la Comtesse in 1889, Gwendolen Bourke might easily have known about it. But she was developing relationships with people like the Princess of Wales, and what Countess Castigiolone did does not sound at all like her. 

===== Scale of the Production of ''Salammbo'' =====

* &quot;In Reyer's opera of 'Salammbo,' lately produced at the Grand Opera in Paris, there were 1,400 persons on the stage in the last act.&quot;&lt;ref&gt;&quot;Facts and Fancies.&quot; ''Louth and North Lincolnshire Advertiser'' 9 July 1892, Saturday: 3 [of 8], Col. 6c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000313/18920709/038/0003. Same print title and p.&lt;/ref&gt;
* &quot;the battle scene in [''Salammbo''] requires no less than 3000 square yards of 'decorative surface' [probably canvas]. This establishes a record, the next largest surface being that of the salles des fetes in 'Don Giovanni.'&quot;&lt;ref&gt;&quot;A French paper gives interesting details....&quot; ''Sevenoaks Chronicle and Kentish Advertiser'' 26 August 1892, Friday: 2 [of 8], Col. 3c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001067/18920826/032/0002. Same print title, n.p.

&lt;/ref&gt;

===== Influence of the Production of ''Salammbo'' =====
Rose Caron's productions were influential, including for the costumes she wore. The 1892 ''Lohengrin'' she starred in was the source of the costumes worn by [[Social Victorians/People/Stonor#Julia Caroline Stonor, Marquise of Hautpoul|Julia Stonor, Marquise of Hautpoul]] and her brother, [[Social Victorians/People/Stonor#Hon. Harry Stonor|Hon. Harry Stonor]].

Women's clothing was influenced by the costumes in the opera, particularly those worn by Rose Caron. One color of intense red was called Salammbo. A bonnet was named the Salammbô:&lt;blockquote&gt;About the smartest thing in bonnets for ordinary complimentary mourning is called the Salammbô, and is copied from a head-dress worn by a leading artiste at one of the Paris theatres. It is made of jet, and has a rose on each side of the front from the centres of which rise two black ospreys.&lt;ref&gt;Mantalini, Miss. &quot;The Shows in the London Shops. With Mems. about Millinery.&quot; ''Pall Mall Budget'' 29 December 1892, Thursday: 22 [of 40], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005967/18921229/092/0022. Same print title, p. 1928.&lt;/ref&gt;&lt;/blockquote&gt;In a long illustrated article describing the wedding of Princess Marie of Edinburgh, the ''Lady's Pictorial'' provides a sketch of &quot;a very pretty [hat] (No. 4) of brown mirror velvet trimmed with mink and a brown velvet bow in front with Salammbo '''fantaisie''&lt;nowiki/&gt;'&quot; that is among the bride's millinery.&lt;ref&gt;&quot;The Marriage of H.R.H. Princess Marie of Edinburgh and H.R.H. Ferdinand Crown Prince of Roumania.&quot; ''Lady's Pictorial'' 14 January 1893, Saturday: 40 [of 76], Col. 3c [of 3]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0005980/18930114/064/0040. Same print title, p. 56.&lt;/ref&gt;

Shoes appeared:&lt;blockquote&gt;At Mrs Merritt's, Savile-street, the stock is particularly attractive, there being so many new styles in shoes this season. One of the latest designs is the Salammbo Shoe, glace kid, with one strap, a jet buckle, and very low French heels. This shoe is especially designed for tender feet, as it is very light in weight.&lt;ref&gt;&quot;House and Home. Local Letter for Women Reader [sic], (By Our Lady Contributor).&quot; ''Hull Daily Mail'' 22 July 1897, Thursday: 5 [of 6], Col. 1b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000324/18970722/069/0005. Same print title, n.p.&lt;/ref&gt;&lt;/blockquote&gt;Patterns for making the Tunique Romaine and Corsage Salammbo were for sale just a few months after the opening:&lt;blockquote&gt;Some of the leading fashionable novelties described in ''Le Follet de Paris'' are almost ahead of the season, but they look so well that it will not be long before our provincial dressmakers have them. A revival and modification of the ancient tunic is one item which is transforming the modern gowns of tailor-built tweeds into long clinging draperies, of simple cut but ineffable grace. We have had the Russian blouse with us now for the last couple of months. Now the reign of Tunique Romaine and Corsage Salambo is upon us.

...

A very successful novelty is the ''corsage'' “Salammbo.” In reality, it is more of a blouse and short tunic than a ''corsage'', as there is no attempt at shaping to the figure. In [sic] consists, indeed, of two straight pieces of material cut round on the shoulders, where the back and front are fastened together by clasps. There is no arm-hole, and the two pieces meet at the waist under the arm, and then hang open on to the skirt. There being no dart, the waist is as wide as the shoulders; the fullness is drawn to the centre under a ''ceinture Russe'', or of oxydised silver. The outlines are trimmed with ''galon'' or some similar garniture. The &quot;Salammbo” ''guimpe'' or ''corsage'' are made of flannel or ''mousseline de laine'' of bright colour, and are worn with fitting bodices or skirts of serge, or woollen of dark colour. They are very effective, and nothing can be easier to make, while their addition to a frock constitutes a separate costume.

The fitting bodices worn under the ''guimpes'' or ''robes'' &quot;Salammbo&quot; are very simply made; being round-waisted, they are without side pieces, and only require a seam under each arm; one in the centre of the back, and one or two darts in front, according to the figure. The skirt is mounted on a round waistband, and the ''ceinture'' worn over this gives the bodice and skirt the effect of a princess dress.&lt;ref&gt;&quot;A Womans Ceilidh.&quot; ''Oban Times and Argyllshire Advertiser'' 3 September 1892, Saturday: 3 [of 8], Col. 6a–b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000462/18920903/078/0003. Print title: ''The Oban Times'', p. 3.&lt;/ref&gt;&lt;/blockquote&gt;Stationery even before the opera opened in Paris:&lt;blockquote&gt;The last fad in fancy stationery is the carte Salammbo, a delightfully smooth surface for writing upon, the envelopes are very small, square, and of the wallet make; the paper folds over once to fit. The newest shades are rose pink, pale English blue, apple green, and the evergreen heliotrope.&lt;ref&gt;&quot;Fashions of the Month.&quot; ''Nottinghamshire Guardian'' 27 February 1892, Saturday: 7 [of 8], Col. 2b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000176/18920227/059/0007. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;Both Modest Mussorgsky and Sergei Rachmaninoff had attempted but not completed operas based on the novel as well.&lt;ref name=&quot;:5&quot; /&gt; Alfons Mucha's 1896 lithograph of Salammbô (above left) was published the year before the ball.

Reyer's opera was first produced in 1890 in Brussels. 

[[File:Algernon Henry Bourke Vanity Fair 20 January 1898.jpg|thumb|alt=Old colored drawing of an elegant elderly man dressed in a 19th-century tuxedo with a cloak, top hat and formal pointed shoes with bows, standing facing 1/4 to his right|''Algy'' — Algernon Henry Bourke — by &quot;Spy,&quot; ''Vanity Fair'' 20 January 1898]]

=== Hon. Algernon Bourke ===
[[File:Hon-Algernon-Henry-Bourke-as-Izaak-Walton.jpg|thumb|left|alt=Black-and-white photograph of a man richly dressed in an historical costume sitting in a fireplace that does not have a fire and holding a tankard|Hon. Algernon Henry Bourke as Izaak Walton. ©National Portrait Gallery, London.]]
'''Lafayette's portrait''' (left) of &quot;Hon. Algernon Henry Bourke as Izaak Walton&quot; in costume is photogravure #129 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot; /&gt; The printing on the portrait says, &quot;The Hon. Algernon Bourke as Izaak Walton.&quot;&lt;ref&gt;&quot;Hon. Algernon Bourke as Izaak Walton.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158492/Hon-Algernon-Henry-Bourke-as-Izaak-Walton.&lt;/ref&gt;

This portrait is amazing and unusual: Algernon Bourke is not using a photographer's set with theatrical flats and props, certainly not one used by anyone else at the ball itself. Isaak Walton (baptised 21 September 1593 – 15 December 1683) wrote ''The Compleat Angler''.&lt;ref&gt;{{Cite journal|date=2021-09-15|title=Izaak Walton|url=https://en.wikipedia.org/w/index.php?title=Izaak_Walton&amp;oldid=1044447858|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Izaak_Walton.&lt;/ref&gt; A cottage Walton lived in and willed to the people of Stafford was photographed in 1888, suggesting that its relationship to Walton was known in 1897, raising a question about whether Bourke could have used the fireplace in the cottage for his portrait. (This same cottage still exists, as the [https://www.staffordbc.gov.uk/izaak-waltons-cottage Isaak Walton Cottage] museum.)

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

=== Mr. and Mrs. Bourke ===
The ''Times'' made a distinction between the Hon. Mr. and Mrs. A. Bourke and Mr. and Mrs. Bourke, including both in the article.&lt;ref name=&quot;:3&quot; /&gt; Occasionally this same article mentions the same people more than once in different contexts and parts of the article, so they may be the same couple. (See [[Social Victorians/People/Bourke#Notes and Question|Notes and Question]] #2, below.)

== Demographics ==

=== The Bourkes ===
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;

==== Residences ====
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1888–1891: 33 Cadogan Terrace, S.W., Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1904: Algernon Bourke was &quot;usually liv[ing] in Venice&quot;&lt;ref name=&quot;:10&quot; /&gt;
*1906: 75, Gloucester-place, W.&lt;ref name=&quot;:21&quot; /&gt;
*Gwendolen Bourke
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

=== The Sloane-Stanleys ===

==== Residences ====

* 1871: Chester Street, St George Hanover Square (Census), with 5 servants, including a cook and a footman.&lt;ref name=&quot;:16&quot;&gt;The National Archives; Kew, London, England; ''1871 England Census''; Class: ''RG10''; Piece: ''104''; Folio: ''21''; Page: ''37''; GSU roll: ''838763''. Ancestry.com. ''1871 England Census'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations Inc, 2004.&lt;/ref&gt;
* 1881–1885&lt;ref&gt;''UK, City and County Directories, 1600s-1900s''. Ancestry.com. ''UK, City and County Directories, 1766 - 1946'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2013.&lt;/ref&gt; [at least]: 14 Halkin Street, W., St. Georges, 14 servants, including a governess, a house steward, an under butler, a footman and a cook.&lt;ref&gt;''Census Returns of England and Wales, 1881''. Kew, Surrey, England: The National Archives of the UK (TNA): Public Record Office (PRO), 1881. Class: ''RG11''; Piece: ''98''; Folio: ''66''; Page: ''37''; GSU roll: ''1341022''. Ancestry.com and The Church of Jesus Christ of Latter-day Saints. ''1881 England Census'' [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2004.&lt;/ref&gt;
* 1888: 49, Cadogan-square, St. Luke, Chelsea&lt;ref&gt;Ancestry.com. ''London, England, Overseer Returns, 1863-1894'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2013.&lt;/ref&gt;
* 1899, Roger Cyril Sloane-Stanley: 4 Down St., St George, Hanover Square&lt;ref&gt;London Metropolitan Archives; London, England; ''Electoral Registers''. Ancestry.com. ''London, England, Electoral Registers, 1832-1965'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt;
* 1911, Roger Cyril Sloane-Stanley: Paultons, Ower, Romsey

== Family ==
*Hon. Algernon Henry Bourke (31 December 1854 – 7 April 1922)&lt;ref&gt;&quot;Hon. Algernon Henry Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p29657.htm#i296561|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
*Gwendolen Irene Emily Sloane-Stanley Bourke (c. 1869 – 30 December 1967)&lt;ref name=&quot;:1&quot;&gt;&quot;Guendoline Irene Emily Stanley.&quot; {{Cite web|url=https://www.thepeerage.com/p51525.htm#i515247|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
#Daphne Marjory Bourke (5 April 1895 – 22 May 1962)

=== Relations ===
*Hon. Algernon Henry Bourke (the 3rd son of the [[Social Victorians/People/Mayo|6th Earl of Mayo]]) was the older brother of Lady Florence Bourke.&lt;ref name=&quot;:0&quot; /&gt;
*Wilfred Blunt was a cousin of Algernon Bourke: his mother's &quot;mother was one of the Blunts of Crabbet Park, Sussex, which makes them kinswomen of Mr. Alfred Scawen Blunt, poet, Egyptophil and counsel for Arabi Pasha in his trial.&quot;&lt;ref&gt;&quot;From ''Truth''.&quot; ''Mid-Lothian Journal'' 23 August 1912, Friday: 8 [of 8], 2c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002721/19120823/147/0008. Print title and p. same.&lt;/ref&gt;

==== Other Bourkes ====
*Hubert Edward Madden Bourke (after 1925, Bourke-Borrowes)&lt;ref&gt;&quot;Hubert Edward Madden Bourke-Borrowes.&quot; {{Cite web|url=https://www.thepeerage.com/p52401.htm#i524004|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p52401.htm#i524004.&lt;/ref&gt;
*Lady Eva Constance Aline Bourke, who married [[Social Victorians/People/Dunraven|Windham Henry Wyndham-Quin]] on 7 July 1885;&lt;ref&gt;&quot;Lady Eva Constance Aline Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p2575.htm#i25747|title=Person Page|website=www.thepeerage.com|access-date=2020-12-02}} https://www.thepeerage.com/p2575.htm#i25747.&lt;/ref&gt; he became 5th Earl of Dunraven and Mount-Earl on 14 June 1926.

=== The Sloane-Stanleys ===
* Emilie Josephine S Stanley ( 21 December 1848 [baptism]&lt;ref&gt;London Metropolitan Archives; &quot;London, England, UK&quot; ; ''London Church of England Parish Registers''; Reference Number: ''P87/Tri/001''. Ancestry.com. ''London, England, Church of England Births and Baptisms, 1813-1923'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt;  – October 1945)
* Hans T Sloane Stanley (11 May 1840 [baptism]&lt;ref&gt;Ancestry.com. ''England, Select Births and Christenings, 1538-1975'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2014.&lt;/ref&gt; – 15 December 1888&lt;ref&gt;Ancestry.com. ''UK and Ireland, Find a Grave® Index, 1300s-Current'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2012.&lt;/ref&gt;)
* James Shell[e?]y Bontein ()
*# Gwendoline&lt;ref name=&quot;:14&quot; /&gt; Irene Emily G Stanley (c. 1870&lt;ref name=&quot;:16&quot; /&gt; – )
*# '''Roger Cyril Hans Sloane Stanley''' (29 April 1875&lt;ref&gt;The National Archives; Kew, Surrey, England; ''WO 42 War Office: Officers' Birth Certificates, Wills and Personal Papers 1755-1908''; Reference: ''WO 42/72''. Ancestry.com. ''UK, Officers' Birth Certificates, Wills and Personal Papers, 1755-1908'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2023.&lt;/ref&gt; – 18 November 1944&lt;ref&gt;''Find a Grave''. Find a Grave®. http://www.findagrave.com/cgi-bin/fg.cgi. Ancestry.com. ''UK and Ireland, Find a Grave® Index, 1300s-Current'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2012.&lt;/ref&gt;)


* Olivia Elizabeth Berens, Countess Cairns&lt;ref&gt;The National Archives of the UK (TNA); Kew, Surrey, England; ''Census Returns of England and Wales, 1911''. Ancestry.com. ''1911 England Census'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2011.&lt;/ref&gt; (c. 1871 – 20 June 1951&lt;ref&gt;&quot;Olivia Elizabeth Berens.&quot; Person Page 3908; person #39077. ''The Peerage: A Genealogical Survey of the Peerage of Britain as well as the Royal Families of Europe''. https://www.thepeerage.com/p3908.htm#i39077.

&lt;/ref&gt;)
* Arthur William Cairns, 2nd Earl Cairns (21 December 1861 – 14 January 1890)&lt;ref name=&quot;:20&quot;&gt;&quot;Arthur William Cairns, 2nd Earl Cairns.&quot; Person Page 3908; Person #39076. ''The Peerage: A Genealogical Survey of the Peerage of Britain as well as the Royal Families of Europe''. https://www.thepeerage.com/p3908.htm#i39076.&lt;/ref&gt;
*# Lady Louise Rosemary Kathleen Virginia Cairns (10 March 1889 – 17 May 1962)&lt;ref name=&quot;:20&quot; /&gt;
* Roger Cyril Hans Sloane Stanley (1875 – 18 November 1944)
*# Lavender Elizabeth (20 May 1900 [baptism]&lt;ref&gt;Hampshire Archives and Local Studies; Winchester, England, UK; ''Anglican Parish Registers''; Reference: ''35M76/PR3''. Ancestry.com. ''Hampshire, England, Church of England Baptisms, 1813-1921''[database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2023.&lt;/ref&gt; – )
*# Diane Sloane Stanley (c. 1905 – )


* Lavender Elizabeth (20 May 1900 [baptism] – )
* John Everett ()


* Diane Sloane Stanley (c. 1905 – )
* Elwyn Villiers Rhys ()

== Writings, Memoirs, Biographies, Papers ==

=== Writings ===
* Bourke, the Hon. Algernon. ''The History of White's''. London: Algernon Bourke [privately published], 1892.
* Bourke, the Hon. Algernon, ed., &quot;with a brief Memoir.&quot; ''Correspondence of Mr Joseph Jekyll with His Sister-in-Law, Lady Gertrude Sloane Stanley, 1818–1838''. John Murray, 1893.
* Bourke, the Hon. Algernon, ed. ''Correspondence of Mr Joseph Jekyll''. John Murray, 1894.

=== Papers ===
* Where are the papers for the Earl of Mayo family? Are Algernon and Gwendolen Bourke's papers with them?

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
#Hans Stanley-Sloane's estate was £33,704 7s. 5d. in the final probate in December 1889,&lt;ref&gt;Principal Probate Registry; London, England; ''Calendar of the Grants of Probate and Letters of Administration made in the Probate Registries of the High Court of Justice in England''. Ancestry.com. ''England &amp; Wales, National Probate Calendar (Index of Wills and Administrations), 1858-1995'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt; which might lead his widow to consider remarrying.
== Footnotes ==
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      <text bytes="167316" sha1="a3lrp33zgn146wi5zcuaj8igrqsra4i" xml:space="preserve">[[File:Leslie Ward - Vanity Fair, Newspapermen, ^Algy^, The Hon Algernon Henry Bourke, Januray 20, 1898 - B1979.14.521 - Yale Center for British Art.jpg|thumb|Hon. Algernon Bourke, ''Vanity Fair'', 1898]]

==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
** Button Bourke&lt;ref&gt;&quot;A Tory 'Reformer' at the India Office.&quot; ''India'' 10 November 1911, Friday: 4 [of 12], Col. 1b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004300/19111110/007/0004#. Print: same title, p. 228.&lt;/ref&gt;
** Algy Bourke
* Mrs. Gwendolen Bourke
** Gwendolen&lt;ref&gt;General Register Office. ''England and Wales Civil Registration Indexes''. London, England: General Register Office. FreeBMD. ''England &amp; Wales, Civil Registration Marriage Index, 1837-1915''[database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2006.&lt;/ref&gt;{{rp|Marriage Index}} &lt;ref name=&quot;:15&quot; /&gt;{{rp|''Morning Post'' article about her name}} &lt;ref&gt;General Register Office. ''England and Wales Civil Registration Indexes''. London, England: General Register Office. FreeBMD. ''England &amp; Wales, Civil Registration Marriage Index, 1837-1915''[database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2006.&lt;/ref&gt;{{rp|Electoral Register}}
** Guendoline&lt;ref name=&quot;:1&quot; /&gt; [The National Portrait Gallery, London, uses this spelling for Lafayette's portrait of Bourke in costume for the ball.&lt;ref name=&quot;:23&quot; /&gt;]
** Gwendoline&lt;ref name=&quot;:14&quot;&gt;City of Westminster Archives Centre; London, England; ''Westminster Church of England Parish Registers''; Reference: ''SPWP/PR/1/2''. Ancestry.com. ''Westminster, London, England, Church of England Births and Baptisms, 1813-1919'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2020.&lt;/ref&gt;{{rp|Births and Baptisms}}
* Shelley Bontein and Emilie Sloane-Stanley Bontein
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father and then brother, and other Bourkes

== Overview ==

=== Algernon Bourke ===
Although the Hon. Algernon Henry Bourke was born in Dublin in 1854 and came from a family whose title is in the Peerage of Ireland,&lt;ref name=&quot;:6&quot;&gt;1911 England Census.&lt;/ref&gt; he seems to have spent much of his adult life generally in England and especially in London. He was &quot;a noted fisherman.&quot;&lt;ref&gt;&quot;London Correspondence.&quot; ''Freeman's Journal'' 21 December 1897, Tuesday: 5 [of 8], Col. 5c [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000056/18971221/027/0005. Same print title, n.p.&lt;/ref&gt;

Because he was the son of the [[Social Victorians/People/Mayo|Earl of Mayo]], perhaps, or perhaps because he was so involved in projects that got reported on, he was mentioned a great deal in the newspapers, but after his bankruptcy, he seems to have receded in prominence, in part because he was living outside of the U.K., and apparently separately from his wife, Gwendolen Bourke.

Bourke ran as the Conservative candidate for Parliament from Clapham (population, c. 70,000) in 1885, a race he did not win. As a candidate he is described like this:&lt;blockquote&gt;Acted as a newspaper correspondent during the Zulu war. Subsequently Poor-law inspector in the West of Ireland. &quot;A loyal supporter of Church and State.&quot; Desires to reduce the School Board expenditure, and revive trade; and is opposed to Mr. Chamberlain's &quot;police of hasty and experimental reform.&quot;&lt;ref&gt;&quot;Clapham (70,000).&quot; ''South London Chronicle'' 17 October 1885, Saturday: 5 [of 8], Col. 5a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000443/18851017/113/0005. Print title ''South London Chronicle and Southwark and Lambeth Ensign'', p. 5.&lt;/ref&gt;&lt;/blockquote&gt;The London ''Weekly Dispatch'' says he is &quot;a dashing and unscrupulous young Tory.&quot;&lt;ref&gt;&quot;The Political Campaign in London.&quot; ''Weekly Dispatch'' (London) 15 November 1885, Sunday: 9 [of 16], Col. 3c [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003358/18851115/069/0009. Same print title and p.&lt;/ref&gt;

&quot;Algy&quot; Bourke was &quot;Man of the Day&quot; (No. DCCII [522) for ''Vanity Fair'' in 1898, caricatured by Leslie Ward (above right):&lt;blockquote&gt;Son of the great and murdered Lord Mayo, he is contemporary with the outbreak of the Crimean War, he is a Member of the London Stock Exchange, he has a beautiful wife and a daughter, and, being a very fashionable young man, he was once refused as their Member by the worthy electors of Clapham. He was an Eton boy, of course: and less naturally he went to Cambridge; where he was made President of the Beefsteak, the Amateur Dramatic, the Athenaeum, the True Blue, and the Hibernian Clubs. When he came down he tried journalism and went to Zululand as a ''Daily Telegraph'' ‘‘special”; after which he was improved into an Inspector of Workhouses [2, Col. 2c – 3, Col. 1a] in Ireland: which may account for his proficiency as a caterer. For seven years he worked under the late Mr. Chinnery on ''The Times'': being popularly supposed to look after that journal's morals. He is a good man of business, and a great organiser who has made White's Club pay even if it be less “smart&quot; than it was. He has done much for Willis’s since he took it in hand; he did well with his Battersea venture, and he thinks that he only failed with the Summer Club in Kensington Gardens because people would not go to the wrong side of the Park. Moreover, he runs a Club at Brighton, and he is Chairman of the Grand Hotel at Monte Carlo: whither he once organised a cheap trip. Altogether he is a veritable Clubman, and a very successful arranger of amusements, associations, and restaurants.

He is a popular fellow who is known to all of us; and though he is a little inclined to be quarrelsome, no one can get much the better of him. He is also a quick grasper of facts and a good talker. His favourite sports are fishing and the organising of associations for the introduction of salmon to the Thames. By way of being an art critic, he has made an interesting collection of engravings of the members of White’s Club from its foundation; but his friends say that he is not a well-dressed man. He has also written a history of White’s, and he is now writing one of Brooks's Club. He is a genial person, who looks as if the world agreed with him well.

He is an aquisition [sic] to a house party; and they call him “Algy.”&lt;ref&gt;&quot;Men of the Day.&quot; — No. DCCII [522]. The Hon. Algernon Henry Bourke.&quot; ''Vanity Fair'' 20 January 1898, Thursday: 2 [of 4], Col. 2c – 3, Col. 3a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9900020/18980120/010/0002 and https://www.britishnewspaperarchive.co.uk/viewer/BL/9900020/18980120/005/0003. Same print title, pp. 41–42. Portrait is full page, on p. 1.&lt;/ref&gt;&lt;/blockquote&gt;The Hon. Algernon Bourke and Mr. Algernon Bourke, depending on the newspaper article, were the same person. Calling him Mr. Bourke in the newspapers, especially when considered as a businessman or (potential) member of Parliament, does not rule out the son of an earl, who would normally be accorded the honorific of ''Honorable''.

=== Gwendolen Sloane-Stanley Bourke ===

Mrs. Gwendolen Bourke exhibited at dog shows successfully and was a [[Social Victorians/Timeline/1900s#Society Sportswomen|noted deerstalker]] and &quot;an appreciative listener to good music.&quot;&lt;ref&gt;&quot;Vanity Fair.&quot; ''Lady of the House'' 15 June 1899, Thursday: 4 [of 44], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004836/18990615/019/0004.&lt;/ref&gt; Her personal beauty is often mentioned in reports, and ''The World'' says she was &quot;a magnificent woman.&quot;&lt;ref&gt;&quot;Beauties of To-Day. From the ''World''.&quot; ''Clifton Society'' 24 June 1897, Thursday: 14 [of 16], Col. 2c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002164/18970624/066/0014. Same print and p.&lt;/ref&gt; She is the first listed in the ''Graphic''&lt;nowiki/&gt;'s 1891 &quot;Leading Ladies of Society&quot;:&lt;blockquote&gt;The Hon. Mrs. Algernon Bourke is a daughter (Gwendoline Irene Emily) of the late Hans Sloane Stanley, Esq., of Poultons, Southampton, and 49, Cadogan Square, S.W. She married, on December 15th, 1887, the Hon. Algernon Bourke, third son of the sixth Earl of Mayo, Governor-General of India (who was assassinated in 1872), and nephew of Lord Connemara, Governor of Madras. Mr. Bourke is a member of the London Stock Exchange, and resides at 33, Cadogan Terrace, S.W.&lt;ref&gt;&quot;Leading Ladies of Society.&quot; The Graphic 28 March 1891, Saturday: 6 [of 28], Col. 2c [of 3]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18910328/019/0006. Print: same title, p. 346.&lt;/ref&gt;&lt;/blockquote&gt;She attended many social events without her husband, especially into the 20th century, usually with an appreciative description of what she wore. She was a sponsor of Irish art needlework as well. Unlike her husband's, Gwendolen's social status seems to have risen as time passed, and she appears in stories associated with the Princess of Wales, and then later with Queen Alexandra.

=== The Sloane-Stanley Family ===
Gwendolen's family consisted of a younger brother, Cyril Sloane-Stanley, as well as her parents, Hans Sloane-Stanley and Emilie Edwards Sloane-Stanley. Exactly one year after she and Algernon Bourke married, Hans Sloane-Stanley died (in 1888), leaving an estate worth £33,704 7s. 5d.&lt;ref name=&quot;:17&quot;&gt;Principal Probate Registry; London, England; ''Calendar of the Grants of Probate and Letters of Administration made in the Probate Registries of the High Court of Justice in England''. Ancestry.com. ''England &amp; Wales, National Probate Calendar (Index of Wills and Administrations), 1858-1995'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt; (1888, 321) Her mother remarried almost exactly a year after that, to James Shelly Bontein. Bontein's father had been Gentleman Usher and Clerk of the Robes to Queen Victoria.&lt;ref name=&quot;:18&quot;&gt;&quot;Marriages.&quot; &quot;Births, Marriages, and Deaths.&quot; ''Belfast News-Letter'' 6 December 1889, Friday: 1 [of 8], Col. 1a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/18891206/001/0001. Same print title and p.&lt;/ref&gt;

Shortly after his death ''Truth'' described Gwendolen and Cyril's father Hans Sloane-Stanley:&lt;blockquote&gt;The death of Mr. Sloane Stanley, of Paultons Park, is much regretted in South Hants, as he was one of the most popular landlords in the county, and was greatly esteemed. Mr. Sloane Stanley was well known in yachting circles, and for many years he was Commodore of the Royal Southern Yacht Club, and owned the schooner ''Star of the West''. He was one of the very few owners who continued to keep up the old custom of giving his crew a laying-up supper at the close of each season. There were great festivities at Paultons only a few months ago, when Miss Sloane Stanley was married to Mr. Algernon Bourke.&lt;ref&gt;&quot;Entre Nous.&quot; ''Truth'' 27 December 1888, Thursday: 6 [of 48], Col. 2b [of 2]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18881227/023/0006# https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18881227/023/0006]. Same print title, p. 1136.&lt;/ref&gt;&lt;/blockquote&gt;When he died in 1944, Cyril Sloane-Stanley's estate was quite a bit larger than his father's had been 50 years before. The probate was divided between what was limited to &quot;settled land&quot; and what was &quot;save and except settled land.&quot; What was not settled land totalled £356,114 12s. 10d. and went to John Everett, company director; the Hon. Elwyn Villiers Rhys, captain, H.M. army; and William Adam de Geijer, retired captain, H.M. army.&lt;ref name=&quot;:17&quot; /&gt; (1944, 430) His daughter Lavender was married to John Everett, and Diane was married to Elwyn Villiers Rhys. What was settled land totalled £168,975 and went to William Adam de Geijer, retired captain, H.M. army, and George Lawrence Stewart, solicitor.&lt;ref name=&quot;:17&quot; /&gt; (1944, 430)

The Sloane-Stanleys descend from Hans Sloane (1660–1753), whose 71,000-item collections &quot;provid[ed] the foundation of the British Museum, the British Library, and the Natural History Museum, London.&quot;&lt;ref name=&quot;:19&quot;&gt;{{Cite journal|date=2025-01-07|title=Hans Sloane|url=https://en.wikipedia.org/wiki/Hans_Sloane|journal=Wikipedia https://en.wikipedia.org/wiki/Hans_Sloane|language=en|via=}}&lt;/ref&gt; Much of this Hans Sloane's wealth came from his medical practice in Jamaica, where he went as physician to the Governor General of Jamaica, the 2nd Duke of Albemarle, and where he married &quot;a wealthy heiress of sugar plantations&quot; worked by enslaved Jamaicans.&lt;ref name=&quot;:19&quot; /&gt; His great-nephew, Hans Sloane, inherited Paultons, near Romsey, &quot;and in recognition of this he adopted the additional surname of Stanley in 1821.&quot;&lt;ref&gt;{{Cite journal|date=2023-10-06|title=Hans Sloane (MP)|url=https://en.wikipedia.org/wiki/Hans_Sloane_(MP)|journal=Wikipedia https://en.wikipedia.org/wiki/Hans_Sloane_(MP)|language=en}}&lt;/ref&gt;

== Acquaintances, Friends and Enemies ==

=== Algernon Bourke ===

* Best man at [[Social Victorians/Timeline/1887#Wedding of Algernon Bourke and Gwendolen Sloane Stanley|his wedding]]: the Hon. Michael Sandys
* [[Social Victorians/People/Montrose|Marcus Henry Milner]], &quot;one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys&quot;&lt;ref name=&quot;:8&quot;&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 2a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;
* Caroline, Duchess of Montrose — her &quot;legal advisor&quot; on the day of her marriage to Marcus Henry Milner&lt;ref&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 1b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;

=== Gwendolen Bourke ===

* Bridesmaids at [[Social Victorians/Timeline/1887#Wedding of Algernon Bourke and Gwendolen Sloane Stanley|her wedding]]: Lady Florence Bourke, Miss Nora Bourke, Miss Edwards, and Miss Ewart
* Lord and Lady Alington, Belvedere House, Scarborough
* [[Social Victorians/People/William James|Evelyn James]] 

== Organizations ==

=== Gwendolen Bourke ===

* Member, the Ladies Committee for the [[Social Victorians/London Clubs#Prince's Skating Club|Prince's Skating Club]], which also included [[Social Victorians/People/Princess Louise|Princess Louise]] (Duchess of Argyll), the [[Social Victorians/People/Portland|Duchess of Portland]], [[Social Victorians/People/Londonderry|Lady Londonderry]], [[Social Victorians/People/Campbell|Lady Archibald Campbell]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], and [[Social Victorians/People/Asquith|Mrs. Asquith]]&lt;ref name=&quot;:11&quot;&gt;&quot;What the 'World' Says.&quot; ''Northwich Guardian'' 01 November 1902, Saturday: 6 [of 8], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001975/19021101/134/0006. Print title: The ''Guardian'', p. 6.&lt;/ref&gt; (in 1902, at least)

=== Algernon Bourke ===
* [[Social Victorians/Schools#Eton|Eton]]
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1881: Partner, with 2 uncles, in Brunton, Bourke, and Co.&lt;ref&gt;&quot;From Our London Correspondent.&quot; ''Manchester Courier'' 24 August 1881, Wednesday: 5 [of 8], Col. 4a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000206/18810824/030/0005. Print: ''Manchester Courier and Lancaster General Advertiser'', p. 5.&lt;/ref&gt; (one of the [[Social Victorians/British Aristocracy#Sons of Peers on the Stock Exchange|sons of peers on the Stock Exchange]])
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* 1886: Battersea Friendly Angling Society&lt;ref&gt;&quot;Battersea Friendly Angling Society.&quot; ''Fishing Gazette'' 17 April 1886, Saturday: 6 [of 20], Col. 2a [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002553/18860417/030/0006. Same print title, p. 218.&lt;/ref&gt;
* 27 February 1886: one of the Vice Presidents of the [[Social Victorians/London Clubs#Bolingbroke Reading-Room and Institute|Bolingbroke Reading-Room and Institute]]
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt; ( – 1901 [at least])
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Willis's Rooms (described in 1895):&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;
*The [[Social Victorians/London Clubs#Pelican|Pelican Club]], known for its boxing (1891)

==== Boards of Directors ====
*1883: One of the directors, the Franco-English Tunisian Esparto Fibre Supply Company, Ltd.&lt;ref&gt;''Money Market Review'', 20 Jan 1883 (Vol 46): 124.&lt;/ref&gt;
*1891: One of the founders, the Discount Banking Company, Ltd., which says Algernon Bourke is a director of District Messenger Services and News Company, Ltd.&lt;ref&gt;&quot;Public Company.&quot; ''Nottingham Journal'' 31 October 1891, Saturday: 4 [of 8], Col. 8a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001896/18911031/099/0004. Print title: ''The Nottingham Daily Express'', p. 4.&lt;/ref&gt;
*1894: One of the directors, the Frozen Lake, Ltd., with Admiral Maxse, Lord [[Social Victorians/People/Beresford|Marcus Beresford]], [[Social Victorians/People/Williams|Hwfa Williams]]&lt;ref&gt;&quot;The Frozen Lake, Limited.&quot; ''St James's Gazette'' 08 June 1894, Friday: 15 [of 16], Col. 4a [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/18940608/085/0015. Print p. 15.&lt;/ref&gt;&lt;blockquote&gt;London is to have new amusement this winter, for which Mr Algernon Bourke, who has taught us that it is possible to eat as well in St. James’s as on the Boulevards, and Mr Hwfa Williams, of Sandown fame, are jointly responsible. The &quot;Frozen Lake,&quot; under which title a real ice-skating rink is about to be constructed under their auspices, will no doubt be gladly welcomed by all skaters, and the venture is likely to prove a success.&lt;ref&gt;&quot;Society Gossip.&quot; ''Weston-super-Mare Gazette, and General Advertiser'' 6 June 1894, Wednesday: 4 [of 4], Col. 4b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001444/18940606/044/0004. Print title: ''Weston-super-Mare Gazette'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

==== Committees ====

*Member, General Committee, [[Social Victorians/London Clubs#Baths|the Baths Club]] (1892)
*Member, Men's Committee of the [[Social Victorians/London Clubs#Prince's Skating Club|Prince's Skating Club]], which also included Lord Edward Cecil, Lord Redesdale, Mr. [[Social Victorians/People/Lyttelton|Alfred Lyttelton]], Sir Edgar Vincent, Sir William Hart Dyke, and Mr. [[Social Victorians/People/Grenfell|W. H. Grenfell]]&lt;ref name=&quot;:11&quot; /&gt; (1902, at least)
*[[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)
* Member of an &quot;influential committee&quot; headed by the Lord Mayor &quot;to restore salmon to the Thames&quot; (June 1899)&lt;ref&gt;&quot;Salmon in the Thames.&quot; ''Berks and Oxon Advertiser'' 30 June 1899, Friday: 5 [of 8], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002298/18990630/079/0005. Print n.p.&lt;/ref&gt;

== Timeline ==

=== 1870s ===
'''1872 February 8''', Richard Bourke, 6th Earl of Mayo was assassinated while inspecting a &quot;convict settlement at Port Blair in the Andaman Islands ... by Sher Ali Afridi, a former Afghan soldier.&quot;&lt;ref&gt;{{Cite journal|date=2024-12-01|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo.&lt;/ref&gt; The Hon. Algernon's brother Dermot became the 7th Earl at 19 years old.

'''1876 November 24, Friday''', the Hon. Algernon Bourke was one of 6 men (2 students, one of whom was Bourke; 2 doctors; a tutor and another man) from Cambridge who gave evidence as witnesses in an inquest about the death from falling off a horse of a student.&lt;ref&gt;&quot;The Fatal Accident to a Sheffield Student at Cambridge.&quot; ''Sheffield Independent'' 25 November 1876, Saturday: 7 [of 12], Col. 5a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000181/18761125/040/0007. Print title: ''Sheffield and Rotherham Independent'', n. p.&lt;/ref&gt;

'''1879 December 27, Saturday – 29, Monday''', Algernon Bourke was in Kilrush as a Local Government Board Inspector:&lt;blockquote&gt;Among many distinguished visitors at the Vandeleur Arms Hotel, Kilrush this week was the Hon. Algernon Bourke Local Government Board Inspector who arrived on Saturday, and sojourned there until 2 o'clock on Monday, when the honourable gentleman left by Steamer tor Limerick.&lt;ref&gt;&quot;Fashionable Intelligence.&quot; ''Kilrush Herald and Kilkee Gazette'' 01 January 1880, Thursday: 2 [of 5], Col. 3a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003186/18800101/011/0002. Print title ''Kilrush Herald'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;

=== 1880s ===
'''4 February 1880, Wednesday''', Hon. Algernon Bourke attended the [[Social Victorians/Timeline/1880#Grand Ball at Palmerstown House Hosted by the Earl of Mayo|grand ball at Palmerstown House hosted by the Earl of Mayo]]. 

'''1880 March 30, Tuesday''', Algernon Bourke was working in the judicial system in Newcastle, County Limerick, possibly as Poorhouse Inspector:&lt;blockquote&gt;A sworn enquiry was held to-day at the Workhorse, Newcastle West, by the Hon Algernon Bourke, L.G.I., to enquire into charges preferred by Dr. Pierce, Medical Office, against Dr. O'Shaughnesay. The enquiry was adjourned till Thursday next. Mr Moran, sol., Rathkeale, was engaged for Dr. O'Shaughnessy.&lt;ref&gt;&quot;Sworn Enquiry.&quot; &quot;Limerick County. Newcastle West Intelligence.&quot; ''Bassett's Chronicle'' 31 March 1880, Wednesday: 3 [of 4], Col. 3b–c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003471/18800331/044/0003.  Print title ''Bassett's Daily Chronicle'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;'''1880 April 17, Saturday''', in-jokes dominate this report mentioning Algernon Bourke in the context of the Kildare and National Hunt races in Dublin:&lt;blockquote&gt;And in mopy Upper Mount-street, where young Algernon Bourke, of the Onety-oneth, had promised to call for, and afterwards spin down to the races in his mail phaeton, the Blake girls; and in fastidious Fitzwilliam-place, and exclusive &quot;Murryan-squeer,&quot; from which dashing army men, in their neatly-appointed, well horsed drags were to &quot;tool&quot; down sweet young Dublin lasses of the ''crême d la crême'' [sic], many an anxious forecasting of the weather was taken, lest by an unpropitious shower that last triumph of Mrs. Manning, or the Forrests, or Miss Sedford, or any of the ''grandes dames de la mode'' should be rendered as worthless as a Confederate &quot;greenback.&quot; But by ten o'clock all doubts were happily set aside, and up struck the lovely April day in all its spring-time glory and then the road, oh, the road!&lt;ref&gt;&quot;To Punchestown and Back by the Old Road.&quot; ''Illustrated Sporting and Dramatic News'' 17 April 1880, Saturday: 6 [of 24], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001857/18800417/013/0006. Same print title, p. 102.&lt;/ref&gt;&lt;/blockquote&gt;'''1881 May 10, Tuesday''', Algernon Bourke attended the [[Social Victorians/Timeline/1881#1881 May 10, Tuesday|wedding of Marion Lascelles, eldest daughter of the Hon. Egremont W. Lascelles, brother of the Earl of Harewood, and Lieutenant Henry Dent Brocklehurst, of the Second Life Guards, nephew of Mr. Philip Brocklehurst, of Swithamley Park, Macclesfield]]. His gift was an &quot;old enamelled watch set in pearls.&quot;&lt;ref&gt;&quot;Nuptial Rejoicings at Middlethorpe Manor. Marriage of Miss Lascelles and Lieut. Brocklehurst.&quot; ''Yorkshire Gazette'' 14 May 1881, Saturday: 9 [of 12], Cols. 3a–4a [of 6]. ''British Newspaper Archive''https://www.britishnewspaperarchive.co.uk/viewer/bl/0000266/18810514/057/0009. Print same title and p.&lt;/ref&gt;

'''1881 May 23, Monday, 2:00 p.m.''', Algernon Bourke is listed among the Honourables at the [[Social Victorians/Timeline/1881#Queen's Levee at St. James's Palace|Queen's Levee at St. James's Palace]].

'''1881 July 14, Thursday afternoon, beginning about 2 p.m.''', Algernon Bourke was invited to a Garden Party at Marlborough House hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. Members of the family of the [[Social Victorians/People/Mayo|Earl of Mayo]] were also among the 1,500 or so invited guests.

'''1881 July 22, Friday''', Algernon Bourke was invited to an [[Social Victorians/Timeline/1881#22 July 1881, Friday|evening party at Marlborough House hosted by the Prince and Princess of Wales]].

'''1881 September 17, Saturday''', Algernon Bourke was reported among the company at Doncaster during race week.&lt;ref&gt;&quot;List of the Company.&quot; ''York Herald'' 17 September 1881, Saturday: 8 [of 16], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000499/18810917/183/0008. Same print title and p.&lt;/ref&gt;

'''1881 November 22, Tuesday''', Algernon Bourke was sued in Dublin by Henry Naylor because he &quot;had declined to pay&quot; for a £35 piano.&lt;ref&gt;&quot;Henry Naylor v. the Hon. Algernon Bourke.&quot; &quot;Exchequer Division.&quot; &quot;High Court of Justice.&quot; ''Belfast Morning News'' 23 November 1881, Wednesday: 3 [of 4], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000428/18811123/015/0003. Same print title, n.p.&lt;/ref&gt;

'''1881 December 8, Thursday''', Algernon Bourke was part of a [[Social Victorians/Timeline/1881#Battue at Palmerstown|battue at Palmerstown]], when the group bagged 172 pheasants, hares and rabbits.

'''1882 March 7, Tuesday''', Algernon Bourke attended the [[Social Victorians/Timeline/1882#7 March 1882, Tuesday|fashionable wedding of Reginald Chandos-Pole and Violet Denison]].

'''1882 March 15, Wednesday''', Algernon Bourke attended [[Social Victorians/Timeline/1882#The Marchioness of Salisbury's Assembly|the Marchioness of Salisbury's first reception of the season]].

'''1882 July 13, Thursday''', Algernon Bourke was invited to the [[Social Victorians/1882-07-13 Marlborough House Garden Party|Garden Party at Marlborough House for Queen Victoria]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. The more than 1,000 people invited also included a number of people from the family of the [[Social Victorians/People/Mayo|Earl of Mayo]].

'''1882 September 28, Saturday''', Algernon Bourke attended the [[Social Victorians/Timeline/1882#The Wedding of John M'Donald and Georgiana Lambart|wedding of John M'Donald and Georgiana Lambart]].

'''1883 March 21, Wednesday''', the Evening Irish Times announced that Algernon Bourke &quot;has arrived at Kingstown from England.&quot;&lt;ref&gt;&quot;Court and Fashion.&quot; ''Evening Irish Times'' 21 March 1883, Wednesday: 7 [of 8], Col. 5a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003464/18830321/086/0007. Same print title and p.&lt;/ref&gt;

'''23 July 1883, Monday, noon''', the Hon. Algernon Bourke was invited to a [[Social Victorians/Timeline/1883#Garden Party at Marlborough House, at Noon|garden party at Marlborough House]] hosted by the Prince and Princess of Wales.

'''31 October 1883, Wednesday''', Algernon Bourke attended the wedding of [[Social Victorians/Timeline/1883#Wedding of Lady Cecelia Hay and Captain George Webbe|Lady Cecelia Hay and Captain George Webbe]].&lt;p&gt;

'''1884 February 16, Saturday''', Algernon Bourke attended [[Social Victorians/Timeline/1884#16 February 1884, Saturday|the funeral of Thomas Chenery, editor of the ''Times'']].

'''1884 April 4, Saturday''', Algernon Bourke was (may have been?) one of the [[Social Victorians/Timeline/1884#5 April 1884, Saturday|&quot;Supporters of the Pall&quot; at the funeral]] of [[Social Victorians/People/Leopold|Prince Leopold George Duncan Albert, Duke of Albany]] at St. George's, Windsor.

'''1884 April 26, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1884#26 April 1884, Saturday|dinner party at the Lord Mayor's Mansion House for conservatives to meet Sir Stafford Northcote]].

'''1884 May 3, Saturday''', the &quot;Rochester Conservatives&quot; announced that they would &quot;bring forward the Hon. Algernon Bourke, brother of Lord Mayo, as their second candidate,&quot;&lt;ref&gt;&quot;Election Intelligence.&quot; ''Yorkshire Gazette'' 03 May 1884, Saturday: 4 [of 12], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000266/18840503/011/0004.&lt;/ref&gt; but because he would not be the first candidate, Bourke declined.&lt;ref&gt;&quot;Rochester.&quot; London ''Daily Chronicle'' 09 May 1884, Friday: 3 [of 8], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/18840509/049/0003.&lt;/ref&gt;

'''1884 June 18, Wednesday''', Mr. Algernon Bourke was on a committee to watch a [[Social Victorians/Timeline/1884#18 June 1884, Wednesday|Mr. Bishop's &quot;thought-reading&quot; experiment]], which was based on a challenge by Henry Labourchere made the year before. This &quot;experiment&quot; took place before a fashionable audience.

'''1884 July 25, Friday, afternoon''', the Hon. Algernon Bourke was invited to a [[Social Victorians/Timeline/1884#Garden Party at Marlborough House hosted by the Prince and Princess of Wales|Garden Party at Marlborough House hosted by the Prince and Princess of Wales]].

'''1885 January 22, Thursday''', Algernon Bourke's gift to [[Social Victorians/Timeline/1885#Wedding of George Buckle and Alicia Payn|George Buckle and Alicia Payn for their wedding]] was an antique cabinet.

'''1885 July 7, Tuesday''', Algernon Bourke attended [[Social Victorians/Timeline/1885#7 July 1885, Tuesday|Eva Bourke's wedding to Windham Wyndham-Quin]] at St. Mary Abbots, Kensington.

'''1885 July 13, Monday''', Algernon Bouurke was at Victoria Station as part of the [[Social Victorians/Timeline/1885#Arrival of Lord Wolseley in London from Egypt|crowd greeting Lord Wolseley on his return from Egypt]].

'''1885 July 24, Friday''', the Hon. Algernon Bourke was invited to a [[Social Victorians/1885-07-24 Marlborough House Ball|ball at Marlborough House]] hosted by the Prince and Princess of Wales.

'''1885 September 26, Saturday''', Algernon Bourke took part in the [[Social Victorians/Timeline/1885#26 September 1885, Saturday|Ealing Conservative Club fete and meeting]] supporting Salisbury's government and condemning &quot;the dictates of one man&quot; — Gladstone — for Gordon's death.

'''1885 October 3, Saturday''', the Hon. Algernon Bourke was named as the Conservative candidate for Clapham in the Battersea and Clapham borough after the Redistribution Bill determined the electoral districts for South London.&lt;ref&gt;&quot;South London Candidates.&quot; ''South London Press'' 03 October 1885, Saturday: 9 [of 16], Col. 5b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18851003/096/0009. Print p. 9.&lt;/ref&gt; On Sunday 15 November 1885 the London ''Weekly Dispatch'' supported Moulton, the Liberal candidate, who ultimately won the election:&lt;blockquote&gt;

Though a successful lawyer, Mr. Moulton is much more than that. He is a thorough and independent student of political science, who may be trusted to do good service to the Liberal cause with brain as well as with tongue. It will be matter for hearty congratulation if he defeats the Hon. Algernon Henry Bourke, who is a dashing and unscrupulous young Tory, and a nephew of the well-known politician with the same surname.&lt;ref&gt;&quot;The Political Campaign in London. VI. — The South-West Divisions.&quot; ''Weekly Dispatch'' (London) 15 November 1885, Sunday: 9 [of 16], Col. 3c [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003358/18851115/069/0009. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

On Saturday 21 November 1885 the ''South London Press'' reported on posters for Bourke's candidacy:&lt;blockquote&gt;

The Hon. Algernon Bourke, Conservative candidate for Clapham, has a very industrious billsticker, who pastes up his patron’s bills in every possible place where they can be seen to advantage. It is unfortunate, however, that choosing the flank wall of an auctioneer’s the modern &quot;Sam Slap&quot; has produced some curious combinations, such as — &quot;Vote for Bourke,&quot; &quot;Now on View;&quot; &quot;Electors of Clapham, Vote for Mr. Bourke, and&quot; &quot;Be Sold Without Reserve;&quot; &quot;Mr, Bourke will&quot; &quot;Advance Money to&quot; &quot;the Electors of Clapham;&quot; &quot;Great Conservative Meeting. The British Constitution will be&quot; &quot;Offered for Sale this Evening,&quot; &amp;c.&lt;ref&gt;&quot;Pick-up Notes.&quot; ''South London Press'' 21 November 1885, Saturday: 10 [of 16], Col. 1b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18851121/155/0010. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

'''1885 November 3, Tuesday, 11:00 a.m.''', Algernon Bourke attended the [[Social Victorians/Mayo-Ponsonby Wedding 1885-11-03|wedding of his brother, Dermot, 7th  Earl of Mayo and Geraldine Ponsonby]]. He gave them 2 Sheraton secretaires.

'''1886 January 5, Tuesday, late''', the Hon. Algernon Bourke attended the [[Social Victorians/Timeline/1886#Twelfth Night|Twelfth Night celebration at the Drury Lane theatre]].

'''1886 March 13, Saturday evening''', an Hon. Mr. Bourke attended a [[Social Victorians/1886-03-13 Reception at the French Embassy|reception at the French Embassy]], possibly Algernon Bourke or possibly [[Social Victorians/People/Mayo|one of his brothers]].

'''1886 July 10, Saturday''', Hon. Algernon Bourke was invited to a [[Social Victorians/Timeline/1886#Garden Party at Marlborough House Given to the Queen|garden party at Marlborough House given to the Queen]]. Gwendolen Sloane Stanley is not mentioned but Mr. and Mrs. Hans Sloane Stanley are, as are Mr. and Mrs. F. Sloane Stanley.&lt;p&gt;

'''1886 July 21, Wednesday''', Algernon Bourke was invited to the [[Social Victorians/1886-07-21 Marlborough House Ball|Ball at Marlborough House]], as were a [[Social Victorians/People/Bourke#The Sloane-Stanleys 2|Mr. and Mrs. F. Sloane-Stanley]], possibly the parents of Gwendolen Sloane-Stanley (if the &quot;F&quot; is a mistake), who married Bourke on 15 December 1887. Gwendolen is not mentioned as having been invited.

'''1886 July 27, Tuesday''', Algernon Bourke attended a service honoring a memorial at St. Paul's for his father, who had been assassinated.&lt;ref&gt;&quot;Memorial to the Late Earl of Mayo.&quot; ''Northern Whig'' 28 July 1886, Wednesday: 6 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000434/18860728/143/0006. Print p. 6.&lt;/ref&gt;

'''1886 September 2, Thursday''', Mr. Algernon Bourke was part of a group of mostly aristocratic men taking part in [[Social Victorians/Timeline/1886#Augustus Harris's A Run of Luck|a &quot;trial-rehearsal&quot; as part of Augustus Harris's production]] ''A Run of Luck'', about sports.

'''1886 October 2, Saturday''', the Duke of Beaufort and the Hon. Algernon Bourke arrived in Yougal: &quot;His grace has taken a residence at Lismore for a few weeks, to enjoy some salmon fishing on the Blackwater before the close of the season.&quot;&lt;ref&gt;&quot;Chippenham.&quot; ''Wilts and Gloucestershire Standard'' 02 October 1886, Saturday: 8 [of 8], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001955/18861002/142/0008. Print p. 8.&lt;/ref&gt;

'''1886 October 11, Monday''', Algernon Bourke may have been taking part in a [[Social Victorians/Timeline/1886#Performance of Run of Luck|performance of ''Run of Luck'' at the Drury Lane]].

'''1886 October 23, Saturday''', Algernon Bourke was [[Social Victorians/Timeline/1886#Party at Wemyss Castle, Fife|staying at Wemyss Castle, Fife]].

'''1886 December 30, Thursday''', Algernon Bourke was back in London and attending the [[Social Victorians/Timeline/1886#Augustus Harris's The Forty Thieves|&quot;Forty Thieves&quot; pantomime at the Drury Lane Theatre]].

'''1887 January 5, Wednesday''', the Hon. Algernon Bourke was one of the chief mourners at the [[Social Victorians/Timeline/1887#Funeral of Lady Margaret Harriett Bourke|funeral of Lady Margaret Harriett Bourke]].

'''1887 March 1, 2:00 p.m.''', Algernon Bourke is listed among the Messieurs attending the [[Social Victorians/Timeline/1887#Queen's Levee at St. James's Palace|Queen's Levee at St. James's Palace]].&lt;p&gt;

'''1887 May''', a &quot;signalling incident&quot; in 1907 [[Social Victorians/Timeline/1887#May 1887|caused the Waterford ''Evening News'' to recall a similar event]] that had occurred 20 years earlier, in which Algernon Bourke, as special correspondent for the ''Times'', caused the incident to be publicized:&lt;blockquote&gt;During the manoeuvres in connection with the 1887 Jubilee of Queen Victoria a signal was observed going up from [[Social Victorians/People/Beresford|Lord Charles [Beresford]]]'s ship. It was a message to his wife, Lady Beresford, to the effect that, as he should be late for dinner, she was not to wait. Beyond the hilarity this domestic signal evoked, nothing more would have been heard of it, but Mr. Algernon Bourke (Lord Mayo's brother) was acting as special correspondent for the &quot;Times,&quot; and that paper the next morning contained a full and humorous report of the incident. Then there was trouble.&lt;ref&gt;&quot;Signalling Incident.&quot; ''Evening News'' (Waterford) 13 November 1907, Wednesday: 1 [of 4], Col. 6c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004557/19071113/021/0001.&lt;/ref&gt;&lt;/blockquote&gt;

'''1887 June 15, Wednesday''', the Hon. Algernon Bourke attended a [[Social Victorians Foreign Office Reception 1887-06-15|reception at the Foreign Office in honor of Queen Victoria's Golden Jubilee]].

'''1887 July 6, Wednesday''', Algernon Bourke was invited to and, presumably, attended the State Ball at Buckingham Palace.&lt;ref&gt;&quot;The State Ball at Buckingham Palace.&quot; ''Morning Post'' 08 July 1887, Friday: 3 [of 8], Col. 5a–6c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18870708/013/0003. Same print title and p.&lt;/ref&gt; (Col. 1c)

'''1887 August 6, Saturday''', the ''Brighton Gazette'' says that the &quot;Hon. Mrs and Mr Algernon Bourke&quot; were staying at the Royal Crescent Hotel in Brighton, but they didn't marry until 15 December 1887.&lt;ref&gt;&quot;Royal Crescent Hotel.&quot; ''Brighton Gazette'' 6 August 1887, Saturday: 3 [of 8], Col. 5c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000938/18870806/047/0003. Print title ''Brighton Gazette and Sussex Telegraph'', p. 3.&lt;/ref&gt; Perhaps an elder relative, because she is mentioned first?

'''1887 November 9, Wednesday''', the ''Hampshire Advertiser County Newspaper'' announced that&lt;blockquote&gt;A marriage is arranged, and will take place early in January, between Mr. Algernon Bourke, third son of the late Earl of Mayo, and Miss Guendolen Sloane Stanley, only daughter of Mr. Hans Sloane Stanley, of Paultons.&lt;ref&gt;&quot;Romsey, Nov. 9.&quot; ''Hampshire Advertiser'' 9 November 1887, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18871109/034/0003. Print title ''Hampshire Advertiser County Newspaper'', p. 3.&lt;/ref&gt;&lt;/blockquote&gt;Shortly after, the papers announced that the wedding would not take place.

'''1887 December 15, Thursday''', Hon. [[Social Victorians/Timeline/1887#Wedding of Algernon Bourke and Gwendolen Sloane Stanley|Algernon Bourke and Gwendolen Stanley were married at St. Paul's]], Knightsbridge, by Bourke's uncle the Hon. and Rev. George Bourke. Only family members attended because of &quot;the recent death of a near relative of the bride.&quot;&lt;ref&gt;&quot;Court Circular.&quot; ''Morning Post'' 16 December 1887, Friday: 5 [of 8], Col. 7c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18871216/066/0005.&lt;/ref&gt; Who the &quot;near relative of the bride&quot; was not in her nuclear family, and perhaps that explains the cancellation of the wedding and then the changing of the wedding date and not some problem in the couple.

'''1888 – 1899 January 1''', the Hon. Algernon Bourke was &quot;proprietor&quot; of [[Social Victorians/London Clubs#White's|White's Club, St. James's Street]].&lt;ref name=&quot;:9&quot;&gt;&quot;The Hon. Algernon Bourke's Affairs.&quot; ''Eastern Morning News'' 19 October 1899, Thursday: 6 [of 8], Col. 7c [of7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001152/18991019/139/0006. Print p. 6.&lt;/ref&gt;

'''1888 January 21, Saturday''', Gwendolen Bourke attended the wedding of [[Social Victorians/Timeline/1888#Hamilton-Ewart Wedding|Florence Ewart and Henry Hamilton]].

'''1888 March 7, Wednesday''', assuming that this date is not a week after the actual date, [[Social Victorians/People/Beresford|Lady Charles Beresford]] held a [[Social Victorians/Timeline/1888#1888 March 7, Wednesday|notable and well-attended &quot;at home&quot;]] that Gwendolen Bourke attended, reported for being dressed in white and being among the beautiful women present.

'''6 April 1888, Friday''', Algernon and Gwendolen Bourke attended the [[Social Victorians/Timeline/1888#6 April 1888, Friday|New Forest United Hunt ball at the New Forest Hall, Lyndhurst]].

'''1888 May 2, Wednesday''', Algernon and Gwendolen Bourke attended the [[Social Victorians/Timeline/1888#The Marchioness of Salisbury's Reception|Marchioness of Salisbury's reception]] at the Salisbury home on Arlington-street.

'''1888 May 22, Tuesday''', the Dowager Countess of Mayo presented Gwendolen Bourke at the [[Social Victorians/Timeline/1888#Queen's Drawing Room|Queen's drawing-room]] hosted by the Princess of Wales. This is Gwendolen Bourke's dress:&lt;blockquote&gt;Empire robe de cour of white satin duchesse, lined with rich pink silk, sufficiently bright to give a beautiful shell-like tint through the satin; tulle underdress, with upper skirt, embroidered with pearl, and caught up in Greek folds with large pink Tosca roses; white satin bodice, with Josephine pink sash tied at side, Headdress, veil and plumes; ornaments, diamonds.&lt;ref&gt;&quot;Dresses at the Drawing-Room.&quot; ''Epsom Journal'' 22 May 1888, Tuesday: 3 [of 6], Col. 5b–c [of 6]. ''British Newspapers Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004837/18880522/034/0003. Print: title ''Local Journal'', p. 3.&lt;/ref&gt;&lt;/blockquote&gt;

Another description:&lt;blockquote&gt;Mrs. Algernon Bourke's train was of white satin lined with pink, which showed through with charmingly shell-like effect. The dress, fashioned after those of the Empire period, was of white satin embroidered with pearls. A very broad sash of pink satin made the waist seem quaintly short, a trying thing to any but the young and tall, both of which qualifications Mrs. Bourke most happily possesses. She carried a lovely posy of La France roses.&lt;ref&gt;&quot;Gossip on Dress.&quot; ''Boston Spa News'' 25 May 1888, Friday: 2 [of 8], Col. 1b–2b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003395/18880525/014/0002. Print title The News, n.p.&lt;/ref&gt; (Col. 1c)&lt;/blockquote&gt;'''1888 June 8, Friday''', Hon. Algernon and Mrs. Bourke attended a [[Social Victorians/Timeline/1888#Dinner and Dance Hosted by Lord and Lady Wimborne at Hamilton House|dinner and dance Hosted by Lord and Lady Wimborne at Hamilton House]] featuring Prince and Princess Christian of Schleswig-Holstein, and for the ball, the King of Sweden and Norway and the Prince and Princess of Wales and their daughters were present.

'''1888 June 19, Tuesday''', Gwendolen Bourke was one of the principal guests at the wedding of [[Social Victorians/Timeline/1888#19 June 1888, Tuesday|Captain Philip Green and Miss Mabel Emilie Scott]].

'''1888 July 26''', [[Social Victorians/People/Montrose|Caroline Graham Stirling-Crawford]] (known as Mr. Manton for her horse-breeding and -racing operations) and Marcus Henry Milner married.&lt;ref name=&quot;:12&quot;&gt;&quot;Hon. Caroline Agnes Horsley-Beresford.&quot; {{Cite web|url=https://thepeerage.com/p6863.htm#i68622|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt; According to the ''Nottingham Evening Post'' of 31 July 1888,&lt;blockquote&gt;LONDON GOSSIP.

(From the ''World''.)

The marriage of &quot;Mr. Manton&quot; was the surprise as well the sensation of last week. Although some wise people noticed a certain amount of youthful ardour in the attentions paid by Mr. Marcus Henry Milner to Caroline Duchess of Montrose at '''Mrs. Oppenheim's ball''', nobody was prepared for the sudden ''dénouement''; '''and it''' were not for the accidental and unseen presence [[Social Victorians/People/Mildmay|a well-known musical amateur]] who had received permission to practice on the organ, the ceremony performed at half-past nine on Thursday morning at St. Andrew's, Fulham, by the Rev. Mr. Propert, would possibly have remained a secret for some time to come. Although the evergreen Duchess attains this year the limit of age prescribed the Psalmist, the bridegroom was only born in 1864. Mr. &quot;Harry&quot; Milner (familiarly known in the City as &quot;Millions&quot;) was one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys, and Mr. Algernon Bourke, the head of the house (who, of course, takes a fatherly interest in the match) went down to Fulham to give away the Duchess. The ceremony was followed by a ''partie carrée'' luncheon at the Bristol, and the honeymoon began with a visit to the Jockey Club box at Sandown. Mr. Milner and the Duchess of Montrose have now gone to Newmarket. The marriage causes a curious reshuffling of the cards of affinity. Mr. Milner is now the stepfather of the [[Social Victorians/People/Montrose|Duke of Montrose]], his senior by twelve years; he is also the father-in-law of [[Social Victorians/People/Lady Violet Greville|Lord Greville]], Mr. Murray of Polnaise, and [[Social Victorians/People/Breadalbane|Lord Breadalbane]].&lt;ref name=&quot;:8&quot; /&gt;&lt;/blockquote&gt;

'''1888 December 1st week''', according to &quot;Society Gossip&quot; from the ''World'', the Hon. Algernon Bourke was suffering from malaria, presumably which he caught when he was in South Africa:&lt;blockquote&gt;I am sorry to hear that Mr. Algernon Bourke, who married Miss Sloane-Stanley a short time ago, has been very dangerously ill. Certain complications followed an attack of malarian fever, and last week his mother, the Dowager Lady Mayo, and his brother, Lord Mayo, were hastily summoned to Brighton. Since then a change for the better has taken place, and he is now out of danger.&lt;ref&gt;&quot;Society Gossip. What the ''World'' Says.&quot; ''Hampshire Advertiser'' 08 December 1888, Saturday: 2 [of 8], Col. 5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18881208/037/0002. Print title: ''The Hampshire Advertiser County Newspaper''; print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;

'''1888 December 20, Thursday''', the Sloane-Stanley family, including Gwendolen Bourke, attended the [[Social Victorians/Timeline/1888#20 December 1888, Thursday|funeral of Hans Sloane Stanley]]. Algernon Bourke did not attend because he was still too ill.

'''1889 January 22, 2:30 p.m., Tuesday''', Algernon and Gwendolen Bourke sent a gift for the [[Social Victorians/Cecil Lambton Wedding 1889 January 22|wedding of Lady Eleanor Lambton and Lord Robert]] Cecil, a pair of antique mirrors.

'''1889 May 18, Saturday''', Algernon Bourke attended the [[Social Victorians/Timeline/1889#18 May 1889, Saturday|opening of the Italian Opera season at Covent Garden]].

'''1889 May 27, Monday, 11 p.m.''', the dancing commenced at [[Social Victorians/Timeline/1889#The Queen's State Ball at Buckingham Palace|the Queen's State Ball at Buckingham Palace]], with both the Hon. Algernon and the Hon. Gwendolen Bourke present.

'''1889 June 8, Saturday''', the Hon. Algernon Bourke contributed some art he owned to the collection of the Royal Institute of Painters in Water-Colours' [[Social Victorians/Timeline/1889#8 June 1889, Saturday|exhibition of &quot;the works of the 'English Humourists in Art.'&quot;]]

'''1889 July 2, Tuesday''', Gwendolen and Algernon Bourke sat in the Muriettas' box at a [[Social Victorians/Timeline/1889#The Shah at a Covent Garden Opera Performance|gala performance at Covent Garden also attended by the Prince and Princess of Wales, a number of other royals and the Shah]].&lt;p&gt;

'''1889 27 July, Saturday''', Gwendolen and Algernon Bourke attended a [[Social Victorians/Timeline/1889#Garden Party Hosted by Mr. and Mrs. Augustus Harris|garden party hosted by Mr. and Mrs. Augustus Harris]], which was attended by a people from the theatre and arts worlds.&lt;p&gt;

'''1889 December 2, Monday''', Gwendolen Bourk's mother, Emilie Sloane-Stanley, married James Shelly Bontein:&lt;blockquote&gt;&lt;p&gt;

BONTEIN—STANLEY — December 2, at St. George's, Hanover Square, London, by the Rev. G. S. de Sansmarez, James Shelly, only son of the late James Bontein, Gentleman Usher and Clerk of the Robes to the Queen, to Emilie Josephine, widow of Hans Sloane Stanley, of Paultons.&lt;ref name=&quot;:18&quot; /&gt;&lt;/blockquote&gt;'''1889 December 17, Tuesday''', Hon. Algernon and Mrs. Bourke gave a gift to [[Dangan-Neville Wedding|Lady Violet Nevill for her wedding to Henry Wellesley, Viscount Dangan]] and so were probably in attendance.

=== 1890s ===
'''1890 January 9, Thursday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1890#The York Hunt Ball|fancy-dress Hunt Ball in York]]. She&lt;blockquote&gt;looked a picture in a Gainsborough gown. The white satin skirt was flounced with sable and veiled with ''chiffon'', the setuage of which was left to show without being hemmed up. There was a broad sash of rose-pink silk and each buttonhole was filled round with crimped lisse.&lt;ref&gt;&quot;Our London Letter.&quot; ''Irish Society'' (Dublin) 11 January 1890, Saturday: 17 [of 24], Col. 2a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001939/18900111/042/0017. Same print title, p. 29.&lt;/ref&gt;&lt;/blockquote&gt;'''1890 February''' '''12, Wednesday''', Hon. Algernon and Mrs. Bourke attended [[Social Victorians/Timeline/1890#Lady Constance Leslie's Reception|Lady Constance Leslie's reception]] at her house in Stratford-place.

'''1890 April 9, Wednesday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1890#The New Forest United Hunt Ball|the New Forest United Hunt Ball]].

'''1890 June 3, Tuesday''', Gwendolen Bourke attended the 2:30 p.m. [[Social Victorians/Timeline/1890#Münster-Hay Wedding|wedding of Count Alexander Münster and Lady Muriel Henrietta Constance Hay]]. She is also listed as having attended a [[Social Victorians/Timeline/1890#Dinner and Concert Hosted by Mrs. Arthur Williams and Ball by Mrs. Menzies|ball hosted by Mrs. J. Menzies (daughter of Mrs. Arthur Wilson)]] that Prince Eddie, the Duke of Clarence and Avondale, also attended, that night.  

'''1890 July 4, Friday, 11 p.m.''', the Hon. Algernon and Gwendolen Bourke attended [[Social Victorians/Timeline/1890#The Queen's State Ball at Buckingham Palace|the Queen's State Ball at Buckingham Palace]]. The dancing commenced shortly after 11:00. 

'''1890 July 15, Tuesday''', Hon. Algernon and Mrs. Bourke were invited to a [[Social Victorians/Timeline/1890#Garden Party at Marlborough House to Meet the Queen|garden party at Marlborough House to meet the Queen]]. 

'''1890 July 19, Saturday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1890#Wedding of James Francis Harry St. Clair-Erskine and Violet Aline Vyner|wedding of James Francis Harry St. Clair-Erskine and Violet Aline Vyner]], the two of them giving &quot;four small silver dessert dishes&quot; and Gwendolen giving an &quot;enamel and diamond pin.&quot;&lt;ref&gt;&quot;Marriage of Lord Loughborough with Miss Vyner.&quot; ''Fife Free Press'' 26 July 1890, Saturday: 2 [of 8], Col. 1a–2b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001110/18900726/015/0002. Same print title and p.&lt;/ref&gt; (Col. 2b)

'''1890 July 24, Thursday''', Algernon and Gwendolen Bourke attended a [[Social Victorians/Timeline/1890#Dinner and Dance Hosted by Lord Alington|dance hosted by Lord Alington]] attended also by the Prince and Princess of Wales and Princesses Victoria and Maud.

'''1890 September 6, Saturday''', the ''Country Gentleman'' (as it was called at the time) reported that &quot;Muckross, the only deer forest in Ireland, it may be said, has this year been rented by Mr. Algernon Bourke, who will next week be joined there for the stalking season by his brother, Lord Mayo.&quot;&lt;ref&gt;&quot;Shooting. Moors, Forests, and Fishings.&quot; ''Sporting Gazette'' 06 September 1890, Saturday: 11 [of 38], Col. 1c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002525/18900906/065/0011. Print: ''Country Gentleman'', p. 1251.&lt;/ref&gt; On 11 October 1890 the ''St. James's Gazette'' says,&lt;blockquote&gt;The Earl of Durham has been staying at Muchross, county Kerry, on a visit to the Hon. A. Bourke, who has rented the celebrated shootings and fishings on that estate for the autumn.&lt;ref&gt;&quot;Court and Society.&quot; ''St James's Gazette'' 11 October 1890, Saturday: 12 [of 16], Col. 1b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/18901011/064/0012. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;'''1890 October 25, Saturday''', the Hon. Algernon and Mrs. Bourke gave a gold-mounted box to [[Social Victorians/Loder De Vere Beauclerk Wedding|Lady Louise De Vere Beauclerk on her wedding to Gerald Loder, M.P.]], so they were probably present at the wedding, or at least the reception. Mrs. Bontein [sic Bontine], Gwendolen's mother, gave a silver box, suggesting the relationship was through the women.

'''1890 November 29, 11:30 Saturday morning''', Algernon Bourke's gift for the [[Social Victorians/Dudley-Beckwith Wedding 1890-11-29|wedding of the Hon. Francis Dudley and Miss Forbes Beckwith]] was some cases of a Bordeaux wine: &quot;three dozen Cantenac, 1875 vintage.&quot;&lt;ref&gt;&quot;Marriage of Lord Leigh's Heir. Descriptive Sketch of the Ceremony, and Full List of Guests and Presents.&quot; ''Leamington Spa Courier'' 6 December 1890, Saturday: 6 [of 10], Cols. 1a–4a. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0000319/18901206/021/0006. Same print title and p.&lt;/ref&gt;{{rp|Col. 3b}} Gwendolen Bourke is not listed as having been invited to the reception, but this list from the ''Leamington Spa Courier'' has some gaps.

'''1890 December 4, Thursday''', Gwendolen and Algernon Bourke attended the [[Mure-Portal Wedding 1890-12-04|wedding of Miss Mure and Mr. S. J. Portal]]. Their gift is not recorded.

'''1891 January''', Algernon Bourke took party in a [[Social Victorians/Timeline/1891#Shooting Party in Kallarnet, Totton|shooting party in Kallarnet, Totton]].

'''1891 June 24, Wednesday''', the Hon. Algernon and Mrs. Bourke attended a [[Social Victorians/Timeline/1891#Dinner and Ball Hosted by Lord and Lady Wimborne|dinner and ball Hosted by Lord and Lady Wimborne]] featuring Princess Mary Adelaide, the Duke of Teck, and Princess Victoria.

'''1891 July 9, Thursday''', Algernon and Gwendolen Bourke were invited to a [[Social Victorians/1891-07-09 Garden Party|large Garden Party at Marlborough House]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]] in honor of Queen Victoria and the German Emperor and Empress. The more than 3,000 people invited also included a number of people from the [[Social Victorians/People/Mayo|family of the Earl of Mayo]].

'''1891 July 22, Wednesday''', Gwendolen Bourke attended a [[Social Victorians/Timeline/1891#Dinner and Dance at Alington House|dance at the Earl and Countess Alington]]'s that also included the Prince and Princess of Wales.

'''1891 October 22, Thursday''', Hon. and Mrs. Bourke attended at least the reception of the [[Social Victorians/Timeline/1891#Le Strange Astley Wedding|Le Strange—Astley Wedding]], although perhaps the couple is not the Algernon Bourkes.

'''1891 November 22, Sunday''', the London ''Weekly Dispatch'' reports a performance by American &quot;Lady Magnet&quot; Mrs. Abbott, who claimed to be able to lift anybody using only her magnetic properties. An enthusiastic &quot;committee of some fifteen gentlemen presented a written and signed testimonial&quot; supporting Mrs. Abbott, &quot;the Hon. Algernon Bourke, Professor Atkinson, Dr. Hides, and three other doctors who prefer to remain incog., being among the signatories. All the medical gentlemen concerned assured the ''Evening News and Post'' reporter of their complete and unconditional surrender. One of them went so far as to say that he had come with the full determination of disbelieving, but had been quite able to act up to his resolve.&quot;&lt;ref&gt;&quot;The Lady Magnet. Draws Crowds of People Who Divide in Opinion about Her.&quot; ''Weekly Dispatch'' (London) 22 November 1891, Sunday: 16 [of 16], Cols. 3a–4b [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003358/18911122/203/0016. Print: same title and p.&lt;/ref&gt;

'''1892''', the Hon. Algernon Bourke privately published his ''The History of White's'', the exclusive gentleman's club.

'''1892 January 27, Saturday''', Algernon and Gwendolen Bourke attended the very fashionable [[Social Victorians/Timeline/1892#The Wedding of Lord Henry Cavendish Bentinck, M.P., and Lady Olivia Taylour|wedding of Lord Henry Cavendish Bentinck, M.P., and Lady Olivia Taylour]]. Their gift was not noted in the list.

'''1892 February''' '''10, Wednesday''', Gwendolen Bourke attended the [[Social Victorians/1892-02-10 Alington Leigh Wedding|very fashionable wedding of Henry, Lord Alington and Evelyn Henriette Leigh]] [[Social Victorians/1892-02-10 Alington Leigh Wedding|in St. Paul's, Knightsbridge]]

'''1892 April''' '''10, Wednesday, about 2:30 p.m.''', Gwendolen Bourke attended [[Social Victorians/1892-02-10 Alington Leigh Wedding|the very fashionable wedding between Henry Sturt, Lord Alington and Evelyn Leigh]]. Her gift was a &quot;tortoiseshell and gold heart-shaped tray.&quot;&lt;ref name=&quot;:02&quot;&gt;&quot;Lord Alington to Miss Leigh.&quot; ''Gentlewoman'' 20 February 1892, Saturday: 21 [of 46], Cols. 1a–3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18920220/092/0021. Same print title, p. 237.&lt;/ref&gt; (Col. 3a) 

'''1892 June 25, Saturday''', the ''Gentlewoman''&lt;nowiki/&gt;'s &quot;Overheard by the Little Bird&quot; says &quot;That pretty Mrs. Algernon Bourke has been staying here, but returned to England in time for Ascot.&quot;&lt;ref&gt;Little Bird, The. &quot;Overheard by the Little Bird.&quot; ''Gentlewoman'' 25 June 1892, Saturday: 32 [of 60], Col. 3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18920625/157/0032. Same print title, p. 860.&lt;/ref&gt; 

'''1892 December 13, Tuesday''', the ''Gentlewoman'' says Gwendolen Bourke is lovely in its coverage of [[Social Victorians/Timeline/1892#Wedding of Miss Eleanor M. Ewart and Captain Guy Withington|Eleanor M. Ewart and Captain Guy Withington's wedding]]. 

'''1892 December 22, Thursday''', Algernon Bourke attended the [[Social Victorians/Timeline/1892#22 December 1892, Thursday|monthly meeting of the Zoological Society in Hanover-square]].&lt;p&gt;

'''1893 February 11, Tuesday''', Algernon Bourke opened Willis's Restaurant:&lt;blockquote&gt;Mr. Algernon Bourke has in his time done many things, and has generally done them well. His recently published history of White's Club is now a standard work. White's Club itself was a few years ago in its agony when Mr. Bourke stepped in and gave it a renewed lease of life. Under Mr. Bourke's auspices &quot;Willis's Restaurant&quot; opened its doors to the public on Tuesday last in a portion of the premises formerly so well known as Willis's Rooms. This new venture is to rival the Amphitryon in the matter of cuisine and wines; but it is not, like the Amphitryon, a club, but open to the public generally. Besides the restaurant proper, there are several ''cabinets particuliers'', and these are decorated with the very best of taste, and contain some fine portraits of the Georges.&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Letter from the Linkman.&quot; ''Truth'' 20 April 1893, Thursday: 25 [of 56], Col. 1a [of 2]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025# https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025]. Print p. 855.&lt;/ref&gt;&lt;/blockquote&gt;

'''1893 February 7, Tuesday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1893#1893 February 7, Tuesday|the reception after Lady Emily Cadogan's wedding]].

'''1893 February 20, Monday''', the Hon. Algernon Bourke is listed as having attended the [[Social Victorians/Timeline/1893#Queen's Levee at St. James's Palace|Queen's Levee at St. James's Palace]] held by the Prince of Wales; because wives generally are not listed, it seems likely Gwendolen Bourke attended as well.

'''1893 February 28, Tuesday, 3:00 p.m.''', Gwendolen Bourke attended a [[Social Victorians/Queens Drawing Room 1893-02-28|Queen's Drawing Room at Buckingham Palace]].&lt;p&gt;

'''1893 March 22, Wednesday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1893#22 March 1893, Wednesday|Lady Wimborne's reception]].

'''1893 April 1, Saturday''', Algernon Bourke published a letter to the editor of the ''Times'', reprinted in the ''Kildare Observer'', arguing against Gladstone's Home Rule bill on the grounds that Ireland would not be able to take out a loan on its own behalf because of its obligations to the U.K., including what was called its share of the national debt.&lt;ref&gt;&quot;Irish Unionist Alliance.&quot; ''Kildare Observer and Eastern Counties Advertiser'' 01 April 1893, Saturday: 6 [of 8], Col. 4c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001870/18930401/062/0006. Print: The ''Kildare Observer'', n.p.&lt;/ref&gt;

'''1893 May 13, Saturday''', Algernon Bourke was seen at [[Social Victorians/Timeline/1893#13 May 1893, Saturday|exhibitions of art and furniture for sale by Christie's and on display by Lord Clifden]].

'''1893 July 13, Thursday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1893#The Countess of Listowel's Garden Party|Countess of Listowel's Garden Party]] [[Social Victorians/Timeline/1893#The Countess of Listowel's Garden Party|at her residence, Kingston House, Princes-gate]], accompanied by Miss Adeane.

'''1893 July 14, Friday''', Gwendolen Bourke attended [[Social Victorians/Sandown Races 1893-07-14|the races at Sandown]] wearing a dark-blue-and-white outfit and black hat that got described in the newspaper.

'''1893 August 1, Tuesday – August 4, Friday''', Gwendolen Bourke, at least, was at [[Social Victorians/Timeline/1893#1 August 1893, Tuesday – 4 August 1893, Friday|the Goodwood races]], mentioned in the ''Gentlewoman'' for her beauty, although none of the dresses were noted.

'''1893 November 4–11, Wednesday–Saturday''', Gwendolen Bourke was at a [[Social Victorians/Timeline/1893#Ralph and Mary Sneyd Hosted a Shooting Party|shooting party at Keele Hall hosted by Ralph and Mary Sneyd]].

'''1893 November 30, Thursday''', with Sir Walter Gilbey the Hon. Algernon Bourke &quot;assisted&quot; in &quot;forming [a] collection&quot; of engravings by George Morland that was exhibited at Messrs. J. and W. Vokins’s, Great Portland-street.&lt;ref&gt;&quot;The George Morland Exhibition at Vokins's.&quot; ''Sporting Life'' 30 November 1893, Thursday: 4 [of 4], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000893/18931130/058/0004.&lt;/ref&gt;

'''1893 December 14, Thursday, afternoon''', Gwendolen Bourke attended the [[Social Victorians/1893-12-14 Wedding Adele Grant and George, 7th Earl of Essex|wedding of American Adele Grant and George, 7th Earl of Essex]] and gave a &quot;pearl and gold box.&quot;&lt;ref name=&quot;:22&quot;&gt;&quot;Wedding of the Earl of Essex.&quot; ''Herts Advertiser'' 16 December 1893, Saturday; 8 [of 8], Col. 1a–4b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000415/18931216/125/0008. Print title: ''The Herts Advertiser and St Albans Times'', p. 8.&lt;/ref&gt;{{rp|Col. 3c}} Mr. and Mrs. Shelley Bontein also attended, and Mrs. Bontein gave a &quot;green leather bag and purse, with coronet and monogram in gold.&quot;&lt;ref name=&quot;:22&quot; /&gt;{{rp|3b}}

'''1894 January 27, Saturday''', Psyche in &quot;The Social Peepshow&quot; in the ''Gentlewoman'' reported on a [[Social Victorians/Timeline/1894#27 January 1894, Saturday|ball hosted by Lord and Lady Dunraven at Adare Manor]] that Gwendolen Bourke attended.

'''1894 January 31, Wednesday''', Algernon and Gwendolen Bourke, who was dressed more stylishly than most, attended the [[Social Victorians/Timeline/1894#Also 31 January 1894, Wednesday|Kildare Hunt Ball]] hosted by Dermot, [[Social Victorians/People/Mayo|Earl of Mayo]] and Geraldine, Countess of Mayo.

'''1894 February 24, Saturday''', ''The Field'' reported on a series of tennis matches; Algernon Bourke attended the one played at the Prince's Club.&lt;ref&gt;&quot;Tennis.&quot; ''Field'' 24 February 1894, Saturday: 39 [of 72], Col. 1c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002446/18940224/349/0039. Print title ''The Field, The Country Gentleman's Newspaper'', p. 249.&lt;/ref&gt;

'''1894 March 31, Saturday''', Psyche, in the &quot;Social Peepshow&quot; column in the ''Gentlewoman'', says that &quot;Mr. Algernon Bourke has still further embellished Willis's restaurant hard by [the St. James's Theatre], by the addition of some valuable old tapestry that lately came to the hammer at Christie's.&quot;&lt;ref&gt;Psyche. &quot;The Social Peepshow.&quot; ''Gentlewoman'' 31 March 1894, Saturday: 16 [of 56], Col. 2b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18940331/081/0016. Same print title, p. 408.&lt;/ref&gt;

'''1894 April 13, Friday''', Gwendolen Bourke set sail on the [[Social Victorians/Timeline/1894#P. and O. Line S.S. Rome for Gibraltar|P. and O. Line ''S.S. Rome'' for Gibraltar]] along with her stepfather, Mr. Shelley Bontein, and her brother, Mr. Sloane Stanley.

'''31 May 1894, Thursday''', the Hon. Algernon and Mrs. Bourke attended the [[Social Victorians/Timeline/1894#Reception at Devonshire House|Duchess of Devonshire's reception at Devonshire House]].&lt;p&gt;

'''1894 June 18, Monday''', the London ''Echo'' reported that Algernon Bourke was [[Social Victorians/London Clubs#Brooks'|writing a history of Brooks' Club]].&lt;p&gt;

'''1894 June 20, Wednesday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1894#Princess Louise, Marchioness of Lorne Opened the Annual Sale of the Scottish Home Industries|Annual Sale of the Scottish Home Industries]]; her outfit was described in the article in ''Lady's Pictorial''.

'''1894 August 2, Thursday''', the column &quot;Overheard by the Little Bird&quot; says, &quot;At Willis' [restaurant] — 'What a smart cotillon Mr. and Mrs. Algernon Bourke gave on Thursday evening.&quot;&lt;ref&gt;Bird, The Little. &quot;Overheard by the Little Bird.&quot; ''Gentlewoman'' 04 August 1894, Saturday: 30 [of 56], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18940804/148/0030. Print title same, p. 144.&lt;/ref&gt; Willis's Restaurant, King-street, St. James's, was a restaurant Algernon Bourke opened in 1893.&lt;p&gt;

'''1894 September 7, Saturday''', Algernon and Gwendolen Bourke were at a [[Social Victorians/Timeline/1894#7 September 1894, Saturday|shooting party at Witley]], which had been loaned to one of his brothers by William Ward, 2nd Earl of Dudley.&lt;p&gt;

'''1894 October 22, Thursday''', Algernon and Gwendolen Bourke attended the [[Social Victorians/Timeline/1894#Wedding of Lord Connemara and Mrs. Coleman|luncheon after the wedding of Lord Connemara and Mrs. Coleman]].

'''1894 November 3, Saturday''', Psyche, in &quot;The Social Peepshow&quot; for the Gentlewoman, reported that Gwendolen Bourke had been [[Social Victorians/Timeline/1894#3 November 1894, Saturday|seen shopping in London]].

'''1895 January 5, Saturday, 2:00 p.m.''', Algernon and Gwendolen Bourke gave an old mother-of-pearl workbox to [[Wolverton-Ward Wedding 1895-01-05|Lady Edith Ward for her wedding to Frederick Glyn, Lord Wolverton]] and presumably attended the wedding and reception afterwards.&lt;p&gt;

'''1895 February 23, Saturday''', the Hon. Algernon Bourke attended the [[Social Victorians/Timeline/1895#23 February 1895, Saturday|fashionable wedding of Laurence Currie and Edith Sibyl Mary Finch]]. Gwendolen Bourke is not listed as having attended, but she is not noted as absent, either. Daphne Bourke was born on 5 April 1895, probably explaining Gwendolen's absence.

'''1895 March 24, Sunday – 30 March, Saturday''', Algernon Bourke was [[Social Victorians/Timeline/1895#24, Sunday – 30 March 1895, Saturday|enjoying the sunny weather in Brighton]].

'''1895 April 27, Saturday''', Algernon Bourke attended the [[Social Victorians/Timeline/1895#1895 April 27, Saturday|wedding of Norah Bourke and Henry E. A. Lindsay]]. Again, Gwendolen Bourke is not listed as having attended. Daphne Bourke was born on 5 April 1895, and Psyche, writing the &quot;Social Peepshow&quot; column in the Gentlewoman, says,&lt;blockquote&gt;

I regret to hear of the serious illness of Mrs. Algernon Bourke, whose first child was born a fortnight ago. It is feared that the attack is of the nature of typhoid, but happily the patient's strength keeps up. Mrs. Bourke is at her mother's house in Clarges-street.&lt;ref&gt;Psyche. &quot;The Social Peepshow.&quot; ''Gentlewoman'' 27 April 1895, Saturday: 28 [of 84], Col. 2c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18950427/147/0028. Same print title, p. 506.&lt;/ref&gt;&lt;/blockquote&gt;

'''1895 July 13, Saturday''', Algernon Bourke donated 10s. to the ''Daily Telegraph'' National Shilling Testimonial to W. G. Grace.&lt;ref&gt;&quot;''Daily Telegraph'' National Shilling Testimonial to W. G. Grace.&quot; ''Daily Telegraph &amp; Courier'' (London) 13 July 1895, Saturday: 7 [of 12], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18950713/079/0007. Print: ''Daily Telegraph'', p. 7.&lt;/ref&gt;

'''1895 August 24, Saturday''', &quot;Marmaduke&quot; in the ''Graphic'' says that Algernon Bourke &quot;opened a cyclists' club in Chelsea.&quot;&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Court and Club.&quot; The ''Graphic'' 24 August 1895, Saturday: 11 [of 32], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18950824/017/0011. Print p. 223.&lt;/ref&gt;

'''1895 October''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#24 October 1902, Friday|opened the Prince's ice-skating rink for the]] season.if the newspapers were right that 1902 was the 7th season. He also was planning a bicycling club for Kensington Gardens to open the following season.&lt;ref&gt;Mackenzie, Ethel Morell (Miss). &quot;Pins and Needles.&quot; ''Hull Daily News'' 12 October 1895, Saturday: 24 [of 40], Col. 1a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003443/18951012/024/0024. Print title: ''Hull News Supplement'', p. 1[6? 8?].&lt;/ref&gt;

'''1895 October 7, Monday''', the Hon. Algernon and Mrs. Bourke attended the [[Social Victorians/Timeline/1895#Adeane-Cator Wedding|Maud Adeane–John Cator wedding]].

'''1895 December 11, Wednesday''', Gwendolen and Algernon Bourke attended a [[Social Victorians/Timeline/1895#Sneyd Party to Meet the Duke of Coburg|shooting party at the Sneyds' to meet the Duke of Coburg]].

'''1895 December 18, Wednesday''', Algernon and Gwendolen Bourke attended the [[Social Victorians/Timeline/1895#Wedding of Lady Albreda Fitzwilliam and the Hon. Charles Bourke|wedding of Lady Albreda Fitzwilliam and the Hon. Charles Bourke]]. Their gift is not noted in the newspaper account.

'''1896 March 17, Tuesday''', Algernon Bourke attended the [[Social Victorians/Timeline/1896#17 March 1896, Tuesday|annual dinner of the Cymmrodorion, or the Honourable Society of Cymmrodorion]], a society for Welsh culture and history.

'''1896 April 21, Monday''', Mr. and Mrs. A. Bourke sent a gift — a &quot;box for miniature&quot; — for [[Social Victorians/Timeline/1896#Monday, 1896 April 27|the wedding of Lady Angela St. Clair Erskine and James Stewart Forbes]].

'''1896 May 21, Thursday''', the Hon. and Mrs. Algernon Bourke attended [[Social Victorians/Timeline/1896#Mrs. C. H. Wilson's Ball|Mrs. C. H. Wilson's ball in Grosvenor-square, London]].

'''1896 May 26, Tuesday,  through 28 May, Thursday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1896#Coming of Age of Mr Sloane Stanley|3-day celebration in honor of the coming of age of her brother, Cyril Sloane Stanley]].

'''1896 June 15, Monday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1896#Dinner and Dance Hosted by the Countess of Huntingdon|dance hosted by the Earl and Countess of Huntingdon]] after their dinner party.

'''1896 July 13, Monday''', Algernon Bourke (listed among the &quot;Honourables&quot;) and Mrs. A. Bourke (Listed among the &quot;Honourable Ladies&quot;) were invited to the [[Social Victorians/Timeline/1896#Queen's Garden Party at Buckingham Palace|Queen's Garden Party at Buckingham Palace]].

'''1896 June 29, Monday''', the Hon. Mrs. Algernon Bourke attended the [[Social Victorians/Cadogan-Scott Wedding 1896-06-29|wedding and reception of Lady Sophie Cadogan and Sir Samuel Scott]]. Algernon Bourke published a letter to the editor of the ''Daily Telegraph'' about White's Club — and thus Bourke's — &quot;[[Social Victorians/London Clubs#Summer Club|Summer Club]]&quot; in Kensington Park, the subject of a little controversy.

'''1896 July 21, Tuesday''', the Hon. Algernon and Mrs. Bourke attended a [[Social Victorians/Timeline/1896#Dinner Hosted by Sir Horace and Lady Farquhar|dinner hosted by Sir Horace and Lady Farquhar in Grosvenor-square]].

'''1896 August 5, Wednesday''', Algernon and Gwendolen Bourke attended at the [[Social Victorians/Timeline/1896#5 August 1896|wedding of the Hon. Terence Bourke and Miss Eveline Haines]] and gave the bride an &quot;enamel muff chain.&quot;&lt;p&gt;

'''1896 August 10, Monday''', the Morning Leader reported that the Hon. Algernon Bourke, for the Foreign Office, received Li Hung Chang at St. Paul's:&lt;blockquote&gt;At St. Paul's Li Hung was received by Field-Marshal Simmons, Colonel Lane, the Hon. Algernon Bourke, of the Foreign Office (who made the necessary arrangements for the visit) and Canon Newbolt, on behalf of the Dean and Chapter. A crowd greeted Li with a cheer as he drove up in Lord Lonsdale’s striking equipage, and his Excellency was carried up the steps in an invalid chair by two stalwart constables. He walked through the centre door with his suite, and was immediately conducted by Canon Newbolt to General Gordon’s tomb in the north aisle, where a detachment of boys from the Gordon Home received him as a guard of honor.

Li inspected the monument with marked interest, and drew the attention of his suite to the remarkable likeness to the dead hero. He laid a handsome wreath of royal purple asters, lilies, maidenhair fern, and laurel, tied with a broad band of purple silk, on the tomb.

The visit was not one of inspection of the building, but on passing the middle aisle the interpreter called the attention of His Excellency to the exquisite architecture and decoration of the chancel. Li shook hands in hearty English fashion with Canon Newbolt and the other gentlemen who had received him, and, assisted by his two sons, walked down the steps to his carriage. He returned with his suite to Carlton House-terrace by way of St. Paul’s Churchyard, Cannon-st., Queen Victoria-st., and the Embankment.&lt;ref&gt;&quot;At St. Paul's.&quot; ''Morning Leader'' 10 August 1896, Monday: 7 [of 12], Col. 2b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18960810/134/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1896 August 19, Wednesday''', the ''Edinburgh Evening News'' reported on the catering that White's Club and Mr Algernon Bourke arranged for the visiting Li Hung Chang:&lt;blockquote&gt;It is probably not generally known (says the &quot;Chef&quot;) that Mr Algernon Bourke, manager of White's Club, London, has undertaken to the whole of the catering for our illustrious visitor front the Flowery Land. Li Hung Chang has five native cooks in his retinue, and the greatest good fellowship exists between them and their English ''confreres'', although considerable difficulty is experienced in conversation in understanding one another's meaning. There are between 40 and and 50 to cater for daily, besides a staff about 30; that Mr Lemaire finds his time fully occupied. The dishes for his Excellency are varied and miscellaneous, and from 14 to 20 courses are served at each meal. The bills of fare contain such items as bird's-nest soup, pigs' kidneys stewed in cream, boiled ducks and green ginger, sharks' fins, shrimps and prawns stewed with leeks and muscatel grapes, fat pork saute with peas and kidney beans. The meal usually winds with fruit and sponge cake, and freshly-picked green tea as liqueur.&lt;ref&gt;&quot;Li Hung Chang's Diet.&quot; ''Edinburgh Evening News'' 19 August 1896, Wednesday: 3 [of 4], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000452/18960819/057/0003.&lt;/ref&gt;&lt;/blockquote&gt;

'''1896 November 6, Friday''', both Algernon and Gwendolen Bourke were on the committee for the [[Social Victorians/London Clubs#Prince's Skating Club|Prince's Club ice-skating rink]], which [[Social Victorians/Timeline/1896#Opening of the Prince's Club Skating Rink|opened on this day]].

'''1896 November 22, week of''', Mrs. Algernon Bourke was part of a [[Social Victorians/Timeline/1896#Shooting Party at the Charles Wilsons' Warter Priory, Yorkshire|shooting party at the Charles Wilsons' Warter Priory, Yorkshire]].&lt;p&gt;

'''1896 November 25, Wednesday''', Mr. and Mrs. Algernon Bouke attended [[Social Victorians/Timeline/1896#Lord and Lady Burton Hosted a Party for Derby Day|Lord and Lady Burton's party for Derby Day]].&lt;p&gt;

'''1896 December 4, Friday''', the Orleans Club at Brighton was robbed:&lt;blockquote&gt;The old building of the Orleans Club at Brighton, which opens its new club house at 33, Brunswick-terrace to-day, was the scene of a very ingenious burglary during the small hours of yesterday morning. The greater portion of the club property had already been removed to the new premises, but Mr Algernon Bourke, his private secretary, and some of the officials of the club, still occupied bed-rooms at the house in the King’s-road. The corner shop of the street front is occupied by Mr. Marx, a jeweller in a large way of business, and upon his manager arriving at nine o'clock he discovered that the place had been entered through hole in the ceiling, and a great part of a very valuable stock of jewelry extracted. An examination of the morning rooms of the club, which runs over Mr. Marx's establishment reveal a singularly neat  specimen of the burglar's art. A piece of the flooring about 15in square had been removed by a series of holes bored side by side with a centre-bit, at a spot where access to the lofty shop was rendered easy by a tall showcase which stood convemently near. A massive iron girder had been avoided by a quarter of an inch, and this circumstance and the general finish of the operation point to an artist in his profession, who had acquired an intimate knowledge of the premises. The club doors were all found locked yesterday morning, and the means of egress adopted by the thief are at present a mystery.&lt;ref&gt;&quot;Burglary at Brighton.&quot; ''Daily Telegraph &amp; Courier'' (London) 05 December 1896, Saturday: 5 [of 12], Col. 7a [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18961205/090/0005. Print title: ''Daily Telegraph''; p. 5.&lt;/ref&gt;&lt;/blockquote&gt;

'''1896 December 10, Thursday''', Gwendolen Bourke was present to help staff a stall at the [[Social Victorians/Timeline/1896#10 December 1896, Thursday|Irish Industries Exhibition and Sale, Brighton]].

'''1896 December 31, Thursday''', Gwendolen Bourke hosted a New Year's Eve dance:&lt;blockquote&gt;Mrs. Algernon Bourke gave a highly satisfactory and enjoyable dance on Thursday night, when the old year was danced out and the new one danced in. Most of the silver gilters at present in to len were to the fore.&lt;ref&gt;&quot;The Man about Town.&quot; ''Sporting Gazette'' 02 January 1897, Saturday: 7 [of 34], Col. 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002525/18970102/041/0007. Print title ''The County Gentleman'', p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1897 January 9, Saturday''', Psyche in &quot;The Social Peepshow&quot; says that Algernon Bourke's &quot;cheerful countenance was quite in keeping with the [Christmas] season,&quot; seen in London.&lt;ref&gt;Psyche. &quot;The Social Peepshow.&quot; ''Gentlewoman'' 9 January 1897, Saturday: 22 [of 56], Col. 2a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970109/097/0022. Same print title, p. 40.&lt;/ref&gt; 

'''1897 January 13, Wednesday – 18, Monday''', Algernon and Gwendolen Bourke were guests of the [[Social Victorians/Timeline/1897#The Warwickshire Hunt Club Ball|house party associated with the Warwickshire Hunt Ball]] at [[Social Victorians/People/Warwick|Warwick Castle]].

'''1897 January 30, Saturday''', Gwendolen Bourke was reported to have been out shopping in London: &quot;Another charming figure was that of Mrs. Algernon Bourke all in chinchilla, with something of pale blue in a smart toque.&quot;&lt;ref&gt;Psyche. &quot;The Social Peepshow.&quot; ''Gentlewoman'' 30 January 1897, Saturday: 20 [of 59]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970130/107/0020. Same print title, p. 134.&lt;/ref&gt;

'''1897 May 31, Monday''', Hon. Algernon and Mrs. Bourke were present at a [[Social Victorians/Timeline/1897#House Party at Warwick Castle|House Party at Warwick Castle]] hosted by the Earl and Countess of Warwick.

'''1897 June 2, Wednesday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1897#Reception at the Foreign Office|reception at the Foreign Office]].

'''1897 June 12, Saturday''', the ''Gentlewoman'' reported on Gwendolen Bourke's dress and hat at the [[Social Victorians/Timeline/1897#The Duchess of Albany's Bazaar at the Imperial Institute|Duchess of Albany's Bazaar at the Imperial Institute]]. 

'''1897 June 19, Saturday''', Psyche in &quot;The Social Peepshow&quot; column in the ''Gentlewoman'' writes that Gwendolen Bourke was seen driving in London, &quot;in blue, ... looking as usual very handsome.&quot;&lt;ref&gt;Psyche. &quot;The Social Peepshow.&quot; ''Gentlewoman'' 19 June 1897, Saturday: 28 [of 108], Col. 2b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970619/159/0028. Same print title, p. 848.&lt;/ref&gt;

'''1897 June 28, Monday''', Algernon and Gwendolen Bourke were invited to the [[Social Victorians/Diamond Jubilee Garden Party|Garden Party at Buckingham Palace]], the final official event of the London Diamond Jubilee celebrations. Members of the family of the [[Social Victorians/People/Mayo|Earl of Mayo]] were also among the 5,000–6,000 people invited.

'''1897 July 2, Friday''', the Hon. A. and Mrs. A. Bourke and Mr. and Mrs. Bourke attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House.

'''1897 July 8, Thursday, 11:00 p.m.''', Hon. Algernon and Gwendolen Bourke were present at [[Social Victorians/Timeline/1890#Queen's State Ball at Buckingham Palace|the Queen's State Ball at Buckingham Palace]]. The dancing commenced shortly after 11:00 p.m.

'''1897 July 11–16, week of''', a dog of Gwendolen Bourke's won a prize at the [[Social Victorians/Timeline/1897#The Ladies' Kennel Association show in the Royal Botanic Gardens in Regent's Park|Ladies' Kennel Association show in the Royal Botanic Gardens in Regent's Park]]. 

'''1897 July 23, Friday''', both the Hon. Algernon Bourke and Gwendolen Bourke attended the [[Social Victorians/Timeline/1897#Bourke-Curzon Cricket Match at the Queen's Club|Bourke-Curzon cricket match at the Queen's Club]], which Algernon Bourke's team lost. 

'''1897 July 23 — or July 30, Friday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1897#Lady Burton's party at Chesterfield House|Lady Burton's party at Chesterfield House]]. &lt;blockquote&gt;Far the prettiest women in the room were Lady Henry Bentinck (who looked perfectly lovely in pale yellow, with a Iong blue sash; and Mrs. Algernon Bourke, who was as smart as possible in pink, with pink and white ruchings on her sleeves and a tall pink feather in her hair.&lt;ref&gt;&quot;Lady Burton's Party at Chesterfield House.&quot; ''Belper &amp; Alfreton Chronicle'' 30 July 1897, Friday: 7 [of 8], Col. 1c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004151/18970730/162/0007. Print title: ''Belper and Alfreton Chronicle''; n.p.&lt;/ref&gt;&lt;/blockquote&gt;

'''1897 August 2, Monday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1897#Warwick House Party for the Easton Lodge Cricket Week Games|Earl and Countess of Warwick's house party for Easton Lodge cricket week]].

'''1897 August 2, Monday''', Mrs. Algernon Bourke was listed as among [[Social Victorians/Timeline/1897#The Most Beautiful Women in England|the most beautiful women in England]] in an article from ''Vanity Fair'' that was reprinted elsewhere.

'''1897 September 25, Saturday''', according to the ''Pall Mall Gazette'',&lt;blockquote&gt;The [[Social Victorians/People/Mayo|Dowager-Countess of Mayo]] is staying with her son, the Hon. Algernon Bourke, at Bramnber, near Brighton.&lt;ref&gt;&quot;Pall Mall Gazette Office.&quot; ''Pall Mall Gazette'' 25 September 1897, Saturday: 8 [of 10], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18970925/023/0008. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;'''1897 October 2, Saturday''', &quot;Yenatrix&quot; in &quot;Kennel Column&quot; in the ''Gentlewoman'' reported that Gwendolen Bourke had joined the Ladies' Kennel Association.&lt;ref&gt;Yenatrix. &quot;Kennel Column.&quot; ''Gentlewoman'' 02 October 1897, Saturday: 39 [of 61], Col. 2a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18971002/182/0039. Same print title, p. 434.&lt;/ref&gt;

'''1897 October 9, Saturday''', Algernon and Gwendolen Bourke were at [[Social Victorians/Timeline/1897#Harrogate|Harrogate, presumably taking the waters and baths]]. Lady May was on her way to visit Algernon Bourke in Brighton:&lt;blockquote&gt;The Earl of Mayo is expected to return from Sweden on Saturday next. Lady Mayo leaves Bournemouth on Sarurday for Brighton, where she will pay a two days' visit to her brother-in-law, the [[Social Victorians/People/Bourke|Hon. Algernon Bourke]]. The Earl and Countess will then return to Palmerstown, their seat in County Kildare.&lt;ref&gt;&quot;Pall Mall Gazette Office.&quot; ''Pall Mall Gazette'' 7 October 1897, Thursday: 8 [of 12], Col. 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18971007/022/0008. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;&lt;p&gt;

'''1897 October 30, Saturday''', ''Black and White'' published '''J.P.B.'''&lt;nowiki/&gt;'s &quot;The Case of Mrs. Elliott,&quot;&lt;ref name=&quot;:13&quot;&gt;J.P.B. &quot;The Case of Mrs. Elliott.&quot; ''Black &amp; White'' 30 October 1897, Saturday: 12 [of 34], Cols. 1a–2b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004617/18971030/036/0012. Print title ''Black and White'', p. 542.&lt;/ref&gt; an odd short short story in which the Honourable Algernon Bourke Herriott is &quot;rude to Mrs. Elliott,&quot;&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2b}} presumably having proposed sexual relations while her husband is out. J.P.B. links to the biographical Algernon Bourke's career in the stock market in the description of Mrs. Christine Elliott not even simulating interest in her husband's bicycling: &quot;a soul is a grievous burthen for a stockbroker's wife,&quot;&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2a}} suggesting that Mr. Elliott rather than Algernon Bourke Herriott is the stockbroker. The Hon. Algy&lt;blockquote&gt;was a senior member of several junior clubs. A woman had dubbed him once &quot;a rip with a taste for verses.&quot; The description was severe, but not unwarranted. His was a pretty pagan sensualism, though, singing from a wine palate to Church music. For the rest, he had just imagination enough to despise mediocrity.&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2a}}&lt;/blockquote&gt;

'''1897 November 25–26, Thursday–Friday''', Gwendolen Bourke was in Brighton, helping the Countess of Mayo at the [[Social Victorians/Timeline/1897#The Irish Industries' Association Annual Exhibition|bazaar of the Irish Industries' Association]].

'''1897 December 7, Tuesday''', Algernon Bourke attended the [[Social Victorians/Timeline/1897#7 December 1897, Tuesday|7th annual dinner for the Actors' Benevolent Fund]].

'''1897 December 30''', Algernon and Gwendolen Bourke attended a [[Social Victorians/Timeline/1897#Blenheim Palace Party with Amateur Theatricals|party at Blenheim Palace in which people performed tableaux vivants]] that got reported on, many of whom wearing the costumes from the Duchess of Devonshire's ball. The ''Irish Independent'' said Algernon Bourke was &quot;mainly responsible for the living pictures.&quot;&lt;ref&gt;&quot;Mr Algernon Bourke ....&quot; ''Irish Independent'' 05 January 1898, Wednesday: 6 [of 8], Col. 2c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001985/18980105/115/0006.&lt;/ref&gt;

'''1898''', Algernon Bourke called a meeting at White's Club about attempting to [[Social Victorians/Timeline/1900s#The Thames Salmon Experiment|restock the Thames with salmon]]. In 1899 he was on a [[Social Victorians/People/Bourke#Committees|committee led by the Lord Mayor about this topic]] as well.

'''1898 February 3, Thursday''',  Algernon Bourke was among [[Social Victorians/Timeline/1898#The Dundee Evening Telegraph Report on People at Monte Carlo|those visiting Monte Carlo according to the Dundee ''Evening Telegraph'']].

'''1898 March 12, Saturday''', ''The World'' reported on Algernon Bourke's upgrading of the Orleans Club at Brighton:&lt;blockquote&gt;

The Orleans Club at Brighton is flourishing exceedingly, and the new buildings which Mr. Algernon Bourke has just had erected at the back of the comfortable mansion at the corner of Lansdowne-place now provide all that was wanting to make the present habitat of the club all that its members desire. The new billiard-room is rapidly approaching completion, and the coffee-room, excellent and spacious now, was open on Saturday night, when every table was occupied by club diners and their guests, all of whom were enthusiastic over the excellence of this latest addition to the comfort of the house. All interested may be congratulated on what is practically new lease of life to the Orleans Club, than which there is no more comfortable place stay within the four seas.&lt;ref&gt;&quot;From '''The World''.'&quot; ''East &amp; South Devon Advertiser'' 12 March 1898, Saturday: 6 pop 8], Col. 2b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001639/18980312/132/0006. Print title ''The East and South Devon Advertiser'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;

'''1898 March 30, Wednesday''', Algernon Bourke was charged with assaulting a Mr. Potter, but it is not clear from this account what exactly happened:&lt;blockquote&gt;The Hon. Algernon H. Bourke, of Bramber, was summoned, at the instance of Mr. Walter John Potter, clerk to Mr. G. A. Flowers, solicitor, of Steyning, for assault, on the 30th March. — Mr. J. Edward Dell supported the case, and Mr. J. C. Buckwell defended, and pleaded not guilty. — The evidence was to the effect that Mr. Potter had occasion go to defendant's house on Wednesday last to serve a writ. He was going to drop the letter into [Col. 5c–6a] defendant's pocket when he turned and struck him a violent blow on the chest, making witness stagger backwards. Witness put up his hands to keep his balance, and defendant then struck him violently across the head with a weeding spud. — Richard Reed, who was at work for Mr. Bourke on the date named, and was working in garden at the time of the alleged assault, gave corroborative evidence. — Defendant, in the witness box, made a similar statement. — The magistrates differed as to whether the assault was committed, and dismissed the case.&lt;ref&gt;&quot;Steyning.&quot; ''Sussex Express'' 9 April 1898, Saturday: 2 [of 12], Col. 5c–6a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000654/18980409/036/0002. Print: ''The Sussex Express, Surrey Standard, Weald of the Kent Mail, Hants and County Advertiser'', p. 2.&lt;/ref&gt;&lt;/blockquote&gt;'''1898 April 12, Tuesday''', Algernon Bourke was among [[Social Victorians/Timeline/1898#1898 April 12, Tuesday|those visiting Monte Carlo according to the ''Gentlewoman'']].

'''1898 May 25, Wednesday''', Gwendolen Bourke wore pink to [[Social Victorians/1898-05-25 Savoy Dinner Dance Hwfa|Mrs. Hwfa Williams' dinner-dance at the Savoy]].

'''1898 June 7, Tuesday''', the Hon. Algernon and Mrs. A. Bourke were invited to and probably attended the [[Social Victorians/Timeline/1898#7 June 1898, Tuesday|State Ball at Buckingham Palace hosted by the Prince and Princess of Wales]].

'''1898 July 4, Thursday afternoon''', the Hon. Algernon and Mrs. Bourke were invited to and probably attended the [[Social Victorians/Timeline/1898#Garden Party at Marlborough House|Garden Party at Marlborough House given to the Queen and Shah of Persia]].

'''1898 October 29, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1898#Tennis Championship Game at Prince's Club, Knightsbridge|tennis match at Prince's Club, Knightsbridge]].

'''1898 November 22, Tuesday''', Algernon Bourke was present at a [[Social Victorians/Timeline/1898#Shooting Party Hosted by William James|shooting party hosted by Mr. William James]].

'''1898 December 3, Saturday''', Hon. Algernon and Mrs. A. Bourke attended the [[Social Victorians/Timeline/1898#The Funeral of Lady Connemara|funeral of Lady Connemara in Christ Church]], Down street, Piccadilly.&lt;p&gt;

'''1899 January 10, Tuesday''', the Brighton Championship Dog Show opened:&lt;blockquote&gt;Princess of Wales a Winner at the Ladies’ Kennel Club Show.

[Exclusive to &quot;The Leader.&quot;)

The Brighton Championship Dog Show opened in the Dome and Corn Exchange yesterday, and was very well patronised by visitors and exhibitors. Among the latter was H.R.H. the Princess of Wales, who did very well; and others included Princess Sophie Duleep Singh, Countess De Grey, Sir Edgar Boehm, the Hon Mrs. Algernon Bourke, Lady Cathcart, Lady Reid, Mr. Shirley (chairman of the Kennel Club), and the Rev. Hans Hamiiton (president of the Kennel Club).

The entry of bloodhounds is one of the best seen for some time; the Great Danes are another strong lot; deerhounds are a fine entry, all good dogs, and most of the best kennels represented; borzois are another very stylish lot. The bigger dogs are, as usual, in the Corn Exchange and the &quot;toy&quot; dogs in the Dome. To everyone's satsfaction the Princess of Wales carried off two first prizes with Alex in the borzois class.&lt;ref&gt;&quot;Dogs at Brighton.&quot; ''Morning Leader'' 11 January 1899, Wednesday: 8 [of 12], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18990111/142/0008. Print p. 8.&lt;/ref&gt;&lt;/blockquote&gt;

'''1899 January 11, Wednesday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1899#11 January 1899, Wednesday|a luncheon at Stanfield-hall, home of Mr. and Mrs. Basil Montogomery, for Princess Henry of Battenberg]], that also included the Countess of Dudley (sister of Mrs. Montgomery), General Oliphant, and the Mayor and Mayoress of Romsey.

'''1899 January 17–18, Tuesday and Wednesday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1899#Ladies' Kennel Association in Brighton|Ladies' Kennel Association in Brighton]], where she showed an Italian greyhound named Brenda.

'''1899 February 7, Tuesday''', Gwendolen Bourke was a member of the very high-ranking committee organizing the [[Social Victorians/Timeline/1899#Gordon Memorial College Ball|Gordon Memorial College Ball at the Hotel Cecil on 7 February 1899]]. The committee had been planning for the ball, of course, for at least 3 weeks before.

'''1899 February 22, Wednesday – April''', Gwendolen Bourke was part of [[Social Victorians/Timeline/1899#Society in St. Moritz|Society in St. Moritz]]. 1899 March 29, Wednesday, the ''Dundee Advertiser'' says that [[Social Victorians/Timeline/1899#29 March 1899, Wednesday|Cyril Sloane-Stanley was spending part of the winter in St. Moritz]] with his sister Gwendolen Bourke.

'''1899 April 7, Friday, probably''', oddly, Algernon and Gwendolen Bourke are not reported to have attended the [[Social Victorians/Timeline/1899#Funeral of the Hon. Charles Bourke, C.B.|Funeral of the Hon. Charles Bourke, C.B.]] or even to have sent flowers.

'''1899 April 8, Saturday''', the ''Gentlewoman'' reported that Gwendolen Bourke had gone to [[Social Victorians/Timeline/1899#8 April 1899, Saturday|St. Moritz with her brother, Mr. Stanley, who had gotten engaged to Lady Cairns]].

'''1899 April 26, Wednesday''', according to &quot;Local and District News&quot; for Totton, Gwendolen Bourke was &quot;ill with influenza in Paris, and Mrs. Shelley Bontein, her mother, has gone out to nurse her.&quot;&lt;ref&gt;&quot;Local and District News. Totton.&quot; ''Hampshire Advertiser'' 26 April 1899, Wednesday: 4 [of 4], Col. 2b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18990426/037/0004. Print title ''Hampshire Advertiser County Newspaper'', p. 4.&lt;/ref&gt;

'''1899 June 1, Thursday, or 2, Friday''', the Hon. Algernon and Gwendolen Bourke attended the [[Social Victorians/Timeline/1899#Wedding of Roger Cyril Sloane Stanley and Olivia, Countess Cairns|wedding of her brother, Sloane Stanley and Olivia Countess Cairns]] at Holy Trinity Church, Brompton.

'''1899 June 8, Thursday''', Algernon Bourke's money troubles:&lt;blockquote&gt;The Hon. Algernon Bourke, son of the Earl of Mayo, has been appearing before the official receivers in connection with a winding-up order made against Willis’ Restaurant, Limited. The companyf [sic] was formed to acquire the well known restaurant from the Hon. H. A. Bourke. The chairman reminded the creditors that on the last occasion the meeting was adjourned because Mr. Bourke said he thought he would be able in the course of a fortnight to obtain an offer for a sum sufficient to satisfy the creditors and debenture holders. He had received a letter from Mr. Bourke to the effect that he had been unable to complete arrangements. Having looked into the affairs of the company more closely, it appeared to him that Mr. Bourke was legally liable to repay the sum of £5,000 which was advanced to White's Club, and the question would arise whether Mr. Bourke was not also liable to repay the sum of £4,000.&lt;ref&gt;&quot;Mr. Bourke Must Pay.&quot; ''Irish Independent'' 8 June 1899, Thursday: 4 [of 8], Col. 8c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001985/18990608/118/0004. Print title: ''The Irish Weekly Independent'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;'''1899 July 1, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1899#1 July 1899, Saturday|meeting in London at the Duke of Westminster's Grosvenor House]] about preserving Killarney as part of the National Trust and seems to have been acting for someone who wanted to purchase the Muckross Estate.

'''1899 July 5, Wednesday''', Gwendolen Bourke attended a [[Social Victorians/Timeline/1899#Dinner and Dance at Devonshire House|dance at Devonshire House hosted by the Duke and Duchess of Devonshire]].

'''1899 July 6, Thursday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1899#Joan Wilson and Guy Fairfax's Wedding|wedding of Joan Wilson and Guy Fairfax in St. Mark's, near Grosvenor Square]].

'''1899 July 14, Friday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1899#14 July 1899, Friday|Ernest Beckett's dinner party]].

'''1899 July 18, Tuesday''', Gwendolen Bourke attended a [[Social Victorians/Timeline/1899#Ludovici Lecture on Impressionism|lecture on Impressionism by Ludovici hosted by the Countess of Mayo]].

'''1899 July 28, Friday''', [[Social Victorians/London Clubs#White's|White's Club]] was no longer under Algernon Bourke's management and was reconstituting itself after the possibility that it would have to close.

'''1889 July 31, Wednesday''', the Hon. Algernon and Mrs. Bourke attended a [[Social Victorians/Timeline/1889#Fete of the Uxbridge Habitation of the Primrose League|Fete of the Uxbridge Habitation of the Primrose League]] at Hillingdon Court and hosted by the Hon. Algernon and Lady Mary Mills.

'''1899 September 9, Saturday''', the ''Eastern Morning News'' includes Algernon Bourke (&quot;St. James's-street, London, club proprietor&quot;) in a list of men &quot;Receiving Orders,&quot; which it is reprinting from the ''London Gazette''.&lt;ref&gt;&quot;Receiving Orders.&quot; ''Eastern Morning'' News 9 September 1899, Saturday: 5 [of 8], Col. 3c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001152/18990909/074/0005. Same print title and p.&lt;/ref&gt;&lt;p&gt;

'''1899 October 19, Thursday''', the Hon. Algernon Bourke had a bankruptcy hearing:&lt;blockquote&gt;The public examination of the Hon. Algernon Bourke was held before Mr Registrar Giffard yesterday, at the London Bankruptcy Court. The debtor, described as proprietor of a St. James's-street club, furnished a statement of affairs showing unsecured debts £13,694 and debts fully secured £12,800, with assets which are estimated at £4,489 [?]. He stated, in reply to the Official Receiver, that he was formerly a member of the Stock Exchange, but had nothing to do with the firm of which he was a member during the last ten years. He severed his connection with the firm in May last, and believed he was indebted to them to the extent of £2,000 or £3,000. He repudiated a claim which they now made for £37,300. In 1889 he became proprietor of White's Club, St. James's-street, and carried it on until January 1st last, when he transferred it to a company called Recreations, Limited. One of the objects of the company was to raise money on debentures. The examination was formally adjourned.&lt;ref name=&quot;:9&quot; /&gt;&lt;/blockquote&gt;

'''1899 October 20, Friday''', the ''Morning Leader'' mentions Bourke's bankruptcy:&lt;blockquote&gt;Mr. Algernon Bourke, whose bankruptcy is much talked about, has been connected with numerous enterprises in clubland. He raised White's from the slough into which it had sunk after the secession of the Prince of Wales. He started the Willis Restaurant, put fresh life into the Orleans Club at Brighton, arranged a big restaurant for the bicyclists in the time of the bicycle parade, and was concerned at first in the smart and short-lived Trafalgar Bicycle Club. At one time his name spelt success. Latterly his luck has left him. He is a brother of Lord Mayo, a son of the peer who was assassinated at the post of duty, and is one of the best known men about town of the day.&lt;ref&gt;&quot;Club, Stage, and Salon.&quot; ''Morning Leader'' 20 October 1899, Friday: 6 [of 12], Col. 5b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18991020/085/0006. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;'''1899 November 8, Wednesday''', the Hon. Algernon Bourke's bankruptcy case came up again:&lt;blockquote&gt;At Bankruptcy Court, yesterday, the case the Hon. Algernon Bourke again came on for hearing before Mr. Registrar Giffard, and the examination was concluded. The debtor has at various times been proprietor of White’s Club, St. James’s-street, and the Orleans’ Club, Brighton, and also of Willis's Restaurant, King-street, St. James's. He attributed his failure to losses sustained by the conversion of White’s Club and the Orleans' Club into limited companies, to the payment of excessive Interest on borrowed money, and other causes. The liabilities amount to £26,590, of which £13,694 are stated to be unsecured, and assets £4,409.&lt;ref&gt;&quot;Affairs of the Hon. A. Bourke.&quot; ''Globe'' 09 November 1899, Thursday: 2 [of 8], Col. 1c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001652/18991109/020/0002. Print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;

'''1899 December 23, Saturday''', &quot;Mr. Algernon Bourke has departed for a tour in Africa, being at present the guest of his brother in Tunis.&quot;&lt;ref&gt;&quot;The Society Pages.&quot; ''Walsall Advertiser'' 23 December 1899, Saturday: 7 [of 8], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001028/18991223/143/0007. Print p. 7.&lt;/ref&gt;

'''1899 December 29, Friday''', Gwendolen Bourke was at the [[Social Victorians/Timeline/1899#Christmas Party Hosted by the Duke and Duchess of Marlborough|Christmas Party Hosted by the Duke and Duchess of Marlborough]].&lt;p&gt;

'''1899 December 31''', the San Francisco newspaper ''The Wave'' wrote the following about London society:&lt;blockquote&gt;The most prominent untitled people in London may be said to be Mr. and Mrs. [[Social Victorians/People/Williams|Hwfa Williams]], Mr. and Mrs. [[Social Victorians/People/Grenfell|Willie Grenfell]] and Mr. Algy Bourke. That they are passing rich, goes without saying, and that they entertain lavishly, understood — for to be untitled, prominent and successful, argues wealth, hospitality and cleverness.&lt;ref&gt;&quot;London.&quot; The (San Francisco) ''Wave'' 14 January 1899 (Vol. XIX, No. 2): 14. ''The Internet Archive'' https://archive.org/details/wave19unse/page/n20/mode/1up.&lt;/ref&gt;&lt;/blockquote&gt;

=== 1900s ===

'''1900 February 15, Thursday''', Daphne Bourke, the four-year-old daughter of the Hon. Algernon and Mrs. Bourke was a bridesmaid in the [[Social Victorians/Wilson Chesterfield Wedding 1900-02-15|wedding of Enid Wilson and the Earl of Chesterfield]].&lt;ref&gt;&quot;London Day by Day.&quot; ''Daily Telegraph'' 15 February 1900, Thursday: 8 [of 12], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/19000215/175/0008. Name in British Newspaper Archive: ''Daily Telegraph &amp; Courier'' (London). Print p. 8.&lt;/ref&gt; Gwendolen Bourke, &quot;who was in grey, wore a chinchilla toque with violets.&quot;&lt;ref&gt;&quot;Society. Entertainments, Balls, &amp;c.&quot; ''The Queen'' 24 February 1900, Saturday: 40 [of 76], Col. 1a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19000224/235/0040. Print: ''The Queen, The Lady's Newspaper'', p. 308.&lt;/ref&gt;

'''1900 March 10, Saturday''', the ''Weekly Irish Times'' reprinted society gossip from ''The World'':&lt;blockquote&gt;Mrs. Algernon Bourke, who has been staying with her husband's uncle, old Connemara, during Mr. Algernon Bourke's absence abroad, has taken a new house near Portman square, and will be settling there before Easter.&lt;ref&gt;&quot;Society Gossip.&quot; ''Weekly Irish Times'' 10 March 1900, Saturday: 17 [of 20], Col. 1b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001684/19000310/116/0017. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;'''1900 July''' '''17, Tuesday''', Gwendolen Bourke took part in the [[Social Victorians/Timeline/1900s#17 July 1900, Tuesday|Children's Fete in support of the National Society for the Prevention of Cruelty to Children]] on the grounds of the Royal Botanic Society. Daphe was 5 at this time, so it seems logical that she would have been there, too.

'''1900 July 30, Monday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1900s#Barber of Seville at Covent Garden|''The Barber of Seville'' at Covent Garden]].

'''1890 August 6, Friday''', &quot;[[Social Victorians/Timeline/1890#Beautiful Women|Beautiful Women]],&quot; an article in ''Vanity Fair'' that was reprinted elsewhere, mentions Gwendolen Bourke (&quot;Lady Algernon Bourke&quot;) as one of the most beautiful women in England.

'''1900 August 11, Saturday''', Gwendolen Bourke got&lt;blockquote&gt;the pretty little Yorkshire String, an especially tiny mite, weighing only 2&lt;sup&gt;1&lt;/sup&gt;/&lt;sub&gt;2&lt;/sub&gt;lb, and carrying a very promising coat, ... at the Aquarium Show.&lt;ref&gt;&quot;The Witchampton Kennel.&quot; &quot;Ladies Kennels.&quot; ''Ladies' Field'' 11 August 1900, Saturday: 16 [of 60], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0006043/19000811/043/0016. Print title same, p. 390.&lt;/ref&gt;&lt;/blockquote&gt;&lt;p&gt;

'''1900 September 16''', the Hon. Algernon Bourke became the heir presumptive to the Earldom of Mayo when his older brother Captain Hon. Sir Maurice Archibald Bourke died.&lt;p&gt;

'''1900 October 06, Saturday''', the ''Weekly Irish Times'' says that Mr. Algernon Bourke, now heir presumptive to the earldom of Mayo, &quot;has been for some months lately staying with Mr. Terence Bourke in Morocco.&quot;&lt;ref&gt;&quot;Society Gossip.&quot; ''Weekly Irish Times'' 06 October 1900, Saturday: 14 [of 20], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001684/19001006/121/0014. Print p. 14.&lt;/ref&gt;&lt;p&gt;

'''1901 May 30, Thursday''', the Hon. Mrs. Algernon Bourke attended the fashionable [[Social Victorians/Timeline/1900s#1901 May 30, Thursday|Ladies' Kennel Association Dog Show at the Botanic Garden]].

'''1901 July 2, Tuesday''', Gwendolen Bourke — &quot;pretty Mrs. Algernon Bourke, in a mauve gown and and purple tulle toque&quot; — attended a children's party at the Botanic Gardens hosted by the Earl and Countess of Kilmorey.&lt;ref&gt;&quot;The Earl of Kilmorey, K.P.&quot; ''Gentlewoman'' 13 July 1901: Saturday, 50 [of 84], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010713/237/0050. Print: title the same, p. 60.&lt;/ref&gt;

'''1901 July 4, Thursday''', Gwendolen Bourke — dressed &quot;in pale grey, with her pretty little girl,&quot; 6-year-old Daphne — attended a [[Social Victorians/Timeline/1900s#The Countess of Yarborough's Children's Party|children's party hosted by the Countess of Yarborough]].&lt;ref&gt;&quot;The Countess of Yarborough ....&quot; ''Gentlewoman'' 13 July 1901, Saturday: 76 [of 84], Col. 2b, 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010713/381/0076. Print p. xxxvi.&lt;/ref&gt;{{rp|Col. 3a}}

'''1901 July 4–6, Thursday–Saturday''', Gwendolen Bourke helped staff the Perthshire stall&lt;ref&gt;&quot;The Great County Sale.&quot; ''Gentlewoman'' 29 June 1901, Saturday: 43 [of 72], Col. 3a [of 3]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010629/223/0043# https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010629/223/0043]. Same print title, pp. 679.&lt;/ref&gt; at the [[Social Victorians/Timeline/1900s#The Great County Sale|Great County Sale in the Imperial Gardens of the Earl's Court Exhibition]].

'''1901 July 20, Saturday''', the ''Gentlewoman'' published the Hon. Mrs. Algernon Bourke's portrait (identified with &quot;Perthshire&quot;) in its 3rd series of &quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot;&lt;ref&gt;&quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot; ''Gentlewoman'' 20 July 1901, Saturday: 31 [of 60], Col. 4b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010720/141/0031. Print n.p.&lt;/ref&gt; Their daughter Daphne appears in the portrait as well.

'''1901 July 23, Tuesday''', an &quot;Hon. Mrs. Bourke&quot; was in the [[Social Victorians/Timeline/1900s#Lord and Lady Algernon Gordon Lennox|party &quot;entertained by Lord and Lady Algernon Gordon Lennox]].&quot;&lt;p&gt;

'''1901 September 12, Thursday''', Mrs. Gwendolen Bourke wanted her name listed as Mrs. Algernon Bourke in the Electoral Register, apparently a frequent complaint:&lt;blockquote&gt;Mr. Underhill, the Conservative agent, mentioned to the Revising Barrister (Mr. William F. Webster) that the name of the Hon. Mrs. Gwendolen Bourke was on the list in respect of the house, 75, Gloucester-place. The lady had written to him to say that she was the Hon. Mrs. Algernon Bourke and that she wished that name to appear on the register. In reply to the Revising Barrister, Mr. Underhill said that “Algernon” was the name of the lady’s husband.

Mr. Cooke, the rate-collector, said that Mrs. Bourke had asked to be addressed Mrs. Algernon Bourke, but that the Town Clerk thought the address was not a correct one. The lady signed her cheques Gwendolen.”

Mr. Underhill said the agents frequently had indignant letters from ladies because they were not addressed by their husband’s Christian name.

The Revising Barrister — lf a lady gave me the name of Mrs. John Smith I should say I had not got the voter’s name. The name Gwendolen must remain.&lt;ref name=&quot;:15&quot;&gt;&quot;Ladies’ Names.&quot; ''Morning Post'' 12 September 1901, Thursday: 7 [of 10], Col. 3a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19010912/130/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1901 October 26, Friday''', Algernon Bourke was on the Men's Committee of the [[Social Victorians/London Clubs#Prince's Club Ice-skating Rink|Prince's Club Ice-skating Rink]], which had [[Social Victorians/Timeline/1900s#The Prince's Club Ice-skating Rink Opening|its official opening on his day]]. 

'''1902 January''', Algernon Bourke is mentioned in [[Social Victorians/Schools#&quot;More of My Contemporaries at School.&quot;|reminiscences of Eton written by the &quot;Earl of X&quot;]] as being among those in the &quot;world of letters,&quot; and whose brother, later the Earl of Mayo, the Earl of X did not like. 

'''1902 January 25, Saturday''', Mrs. Algernon Bourke gave a box to Lady Helen Stewart-Vane-Tempest in honor of [[Social Victorians/Stewart-Stavordale Wedding 1902-01-25|Lady Helen's wedding to Giles Fox-Strangways, Lord Stavordale]]. 

'''1902 April 26, Saturday''', Mrs. A. Bourke is listed as being at the Norfolk Hotel in Brighton.&lt;ref&gt;&quot;Guide to Visitors at Hotels and Boarding Houses.&quot; ''Brighton Gazette'' 26 April 1902, Saturday: 3 [of 8], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000938/19020426/116/0003. Same print title and p.&lt;/ref&gt; 

'''1902 May, End of''', Gwendolen Bourke attended a [[Social Victorians/Timeline/1900s#End of May 1902|party at Blenheim Palace hosted by the Duke and Duchess of Marlborough]]. 

'''1902 June 11, Monday''', the Hon. Mrs. Algernon Bourke had a dog entered in the [[Social Victorians/Timeline/1900s#Ladies' Kennel Association Show|Ladies' Kennel Association competitions in the Botanic Gardens]]. 

'''1902 September 4, Thursday''', the ''Daily Express'' reported that &quot;Mrs. Algernon Bourke is staying with Lord and Lady Alington at Scarborough.&quot;&lt;ref&gt;&quot;Onlooker.&quot; &quot;My Social Diary.&quot; &quot;Where People Are.&quot; ''Daily Express'' 04 September 1902, Thursday: 5 [of 8], Col. 1b? [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020904/099/0005. Print p. 4, Col. 7b [of 7].&lt;/ref&gt;

'''1902 September 22, Monday''', Gwendolen Bourke was a guest at the [[Social Victorians/Timeline/1900s#Earl and Countess of Mar and Kellie's House Party|large house party hosted by the Earl and Countess of Mar and Kellie]].

'''1902 October 24, Friday''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#Annual Opening of the Prince's Ice-skating Rink|opened the Prince's ice-skating rink for the season]], which he had been doing since 1895.

'''1902 October 25, Saturday''', Algernon Bourke was bequeathed £500 by his uncle [[Social Victorians/People/Mayo|Robert Bourke]], who had died 3 September 1902.&lt;ref&gt;&quot;Will of Lord Connemara.&quot; ''Kildare Observer and Eastern Counties Advertiser'' 25 October 1902, Saturday: 2 [of 8], Col. 4b–c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001870/19021025/037/0002. Print title the ''Kildare Observer'', n.p.&lt;/ref&gt;&lt;p&gt;

'''1902 October 31, Friday''', the [[Social Victorians/Timeline/1900s#Annual Opening of the Prince's Ice-skating Rink|7th opening of the Prince's Skating Club]]. Guendoline Bourke was on the Women's Committee and Algernon Bourke was on the Men's.&lt;p&gt;

'''1902 November 8, Friday, beginning, perhaps''', Gwendolen Bourke was part of the [[Social Victorians/Timeline/1900s#8 November 1902, Saturday|Earl and Countess of Warwick's shooting party at Easton Lodge]].&lt;p&gt;

'''1902 December 9, Tuesday''', Gwendolen Bourke attended [[Social Victorians/Timeline/1900s#9 December 1902, Tuesday|Lady Eva Wyndham-Quin's &quot;at home,&quot; held at the Welch Industrial depot]] for the sale Welsh-made Christmas gifts and cards. Bourke wore &quot;a fur coat and a black picture hat.&quot;&lt;ref&gt;&quot;A Lady Correspondent.&quot; &quot;Society in London.&quot; ''South Wales Daily News'' 11 December 1902, Thursday: 4 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000919/19021211/082/0004. Print p. 4.&lt;/ref&gt;

'''1903 February 6, Friday''', Hon. Mrs A. Bourke was present at a [[Social Victorians/Timeline/1900s#Dinner Party Hosted by Lord Lieutenant of Ireland and the Countess of Dudley|dinner party Hosted by Lord Lieutenant of Ireland and the Countess of Dudley]]. &lt;p&gt;

'''1903 February 9, Monday''', Gwendolen Bourke was present at a [[Social Victorians/Timeline/1900s#Dinner Party Hosted by Lord Lieutenant of Ireland and the Countess of Dudley|house party at Dublin Castle hosted by the Lord Lieutenant and Countess of Dudley that began the Viceregal season]].

'''1903 March 17, Tuesday''', Gwendolen Bourke staffed a booth at a [[Social Victorians/Timeline/1900s#1903 March 17, Tuesday|sale of the Irish Industries Association]] on St. Patrick's Day with [[Social Victorians/People/Mayo|Lady Mayo]], [[Social Victorians/People/Dudley|Georgina Lady Dudley]] and [[Social Victorians/People/Beresford|Miss Beresford]]. A number of other aristocratic women were also present at the sale in other booths, including [[Social Victorians/People/Londonderry|Lady Londonderry]] and [[Social Victorians/People/Lucan|Lady Lucan]].

'''1903 June 19, Friday''', Gwendolen Bourke was invited to the [[Social Victorians/Timeline/1900s#Grand Ball in the Waterloo Chamber at Windsor Castle|grand ball at Windsor Castle]], the end of the Ascot-week festivities.

'''1903 June 23, Tuesday''', Gwendolen and Daphne Bourke were invited to a [[Social Victorians/Timeline/1900s#1903 June 23, Tuesday|children's party at Buckingham Palace for Prince Eddie's birthday]].

'''1903 July 10, Friday, or so''', Gwendolen Bourke attended a [[Social Victorians/Timeline/1900s#Party Hosted by the Duke and Duchess of Marlborough|party hosted by the Duke and Duchess of Marlborough]].

'''1904 May 17, Tuesday''', Gwendolen Bourke had agreed to let Daphne appear in the tableaux vivants arranged by Sir Philip Burne-Jones for the [[Social Victorians/Timeline/1900s#Countess Cadogan's Great Bazaar|Countess of Cadogan's great bazaar]]. Some mothers had had to decline because of the outbreaks of measles and chicken pox.&lt;p&gt;

'''1904 June 30, Thursday''', Gwendolen and Daphne Bourke attended another birthday party for Prince Eddie at Buckingham Palace, and the ''Gentlewoman'' says, &quot;No prettier little girl was to be seen that day than little Miss Daphne Bourke, the daughter of the Hon. Mrs. Algernon Bourke, with her wonderful Irish eyes and colouring, her pretty white frock being relieved with a rose pink sash.&quot;&lt;ref&gt;&quot;Prince Eddie's Birthday.&quot; ''Gentlewoman'' 02 July 1904, Saturday: 68 [of 92]. Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19040702/360/0068. Print: title the same, p. 42.&lt;/ref&gt;&lt;p&gt;

'''1904 September 15, Thursday''', according to what was at the time called the ''Irish Daily Independent and Nation'', Algernon Bourke was living in Venice and not in the UK at this point:&lt;blockquote&gt;Algernon Bourke, who usually lives in Venice, has spent some time in England during the present summer, and has now gone on a fishing expedition to Sweden, accompanied by his brother, Lord Mayo. Lady Mayo has been staying meanwhile in Ireland, and has had a visit from her mother, Lady Maria Ponsonby, who is a sister of Lend Obventry.&lt;ref name=&quot;:10&quot;&gt;&quot;Society Notes.&quot; ''Irish Independent'' 15 September 1904, Thursday: 4 [of 8], Col. 5b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001986/19040915/131/0004. Print title: ''Irish Daily Independent and Nation'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

'''1904 October 22, Saturday''', the ''Gentlewoman'' reported that &quot;Mrs. Algernon Bourke is paying a visit to Venice, which Mr. Bourke has made his headquarters for several years past, as he is connected with some very artistic stone and marble works situated near the Grand Canal.&quot;&lt;ref&gt;&quot;The Social Peepshow.&quot; ''Gentlewoman'' 22 October 1904, Saturday: 24 [of 6ths 8], Col. 2c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19041022/112/0024. Print title same, p. 672.&lt;/ref&gt;

'''1905 February 17, Friday''', the Dundee ''Evening Post'' reported that Algernon Bourke &quot;set up a shop in Venice for the sale of art treasures and old furniture.&quot;&lt;ref&gt;&quot;Social News.&quot; Dundee ''Evening Post'' 17 February 1905, Friday: 6 [of 6], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000582/19050217/105/0006. Print p. 6.&lt;/ref&gt;

'''1905 April 26, Wednesday''', Gwendolen Bourke attended the [[Social Victorians/Timeline/1900s#New Forest United Hunt Ball|New Forest United Hunt Ball]], as did her brother Captain R. C. H. Sloane Stanley and his wife Olivia Countess Cairns.&lt;p&gt;

'''1905 June 5, Monday''', Algernon Bourke wrote to the ''Times'' from Venice that &quot;The Venetian wits have suggested a motto for Admiral Togo, Togo Tenga Tutto (Togo takes the lot).&quot;&lt;ref&gt;&quot;Mr. Algernon Bourke.&quot; ''Hull Daily Mail'' 08 June 1905, Thursday: 2 [of 6], Col. 6a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000324/19050608/008/0002. Print title ''Daily Mail'', p. 6.&lt;/ref&gt;&lt;p&gt;

'''1905, last week of July''', Gwendolen Bourke and daughter Daphne Bourke — who was 10 years old — attended [[Social Victorians/Timeline/1900s#Last week of July, 1905|Lady Cadogan's children's party at Chelsea House]]. Daphne was &quot;One of loveliest little girls present.&quot;&lt;ref&gt;&quot;Court and Social News.&quot; ''Belfast News-Letter'' 01 August 1905, Tuesday: 7 [of 10], Col. 6b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/19050801/157/0007. Print p. 7.&lt;/ref&gt;&lt;p&gt;

'''1906 March 9, Friday''', Gwendolen Bourke was a reference for Mr. Frances Burgess, who taught piano, singing, voice production, organ and music theory. Burgess was &quot;Organist and Choirmaster of St. Columbs', North Kensington, Director of the Plainsong and Medieval Music Society's Choir, etc., etc.&quot;&lt;ref name=&quot;:21&quot;&gt;&quot;Mr. Francis Burgess.&quot; ''Kilburn Times'' 9 March 1906, Friday: 3 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001813/19060309/086/0003. Print title: ''Kilburn Times Hampstead and North-western Press'', p. 3.&lt;/ref&gt;&lt;p&gt;

'''1906 December 10, Monday''', Gwendolen Bourke was seen in the tea room, possibly with Lady Grosvenor, at [[Social Victorians/Timeline/1900s#1906 December 10, Monday|Lady Dudley's sale of Irish needlework]].&lt;p&gt;

'''1907 May''', a &quot;naval signalling incident&quot; [[Social Victorians/Timeline/1887#May 1887|caused the Waterford ''Evening News'' to recall a similar event]] that had occurred 20 years earlier, in which Algernon Bourke, as special correspondent for the ''Times'', publicized [[Social Victorians/People/Beresford|Lord Charles Beresford]]'s use of his ship's signalling capabilities to send a message to his wife about being late for dinner:&lt;blockquote&gt;

The naval signalling incident is still in the air. It is expected that the matter will not be threshed out until Emperor William leaves England. A story of a former signalling incident in which [[Social Victorians/People/Beresford|Lord Charles Beresford]] was concerned is going the rounds at the moment.&lt;/blockquote&gt;

'''1907 August 24, Saturday''', Algernon Bourke was present at [[Social Victorians/Timeline/1900s#Polo Week at Eaton Hall, Duke and Duchess of Westminster|Polo Week at Eaton Hall, hosted by the Duke and Duchess of Westminster]].

'''1908 July 30, Thursday''', Gwendolen Bourke was at [[Social Victorians/Timeline/1900s#Glorious Goodwood. Cup Day and Dresses.|Cup Day at the Goodwood races]], wearing salmon-pink with a matching hat.

'''1909 April 20, Tuesday''', Lady Rosemary Cairns — daughter of Olivia Sloan-Stanley, Countess Cairns and Cyril Sloane-Stanley — and Wyndham Portal were [[Social Victorians/Timeline/1900s#20 April 1909, Tuesday|married in St. Margaret's, Westminster]]. Lavender and Diane Sloane-Stanley were bridesmaids.&lt;p&gt;

'''1909 May 22, Saturday''', Algernon Bourke appears to have been living in Pisa. A columnist for the ''Queen'' reported on the Royal School of Art Needlework:&lt;blockquote&gt;Lady Leconfield [?] was there, also her sister-in-law, the [[Social Victorians/People/Mayo|Dowager Lady Mayo]], only just back from her winter on the Continent, when she spent most of the time at Pisa, where her son Mr Algernon Bourke has also been staying. The latter is a great connoisseur as regards [art?] notably in what is really good in the way of old Italian sculpture and carving. He and his handsome wife have a place near to Putney, and this winter again Mr Bourke, as the result of his Italian travels, has been sending home such relics of the old Italian palace gardens as as stone and marble carved vases, garden seats, and what-not of the kind — not all for himself and his own gardens by any means, I fancy; but his friends, relying on his knowledge in such matters, get him when abroad to choose for [them?] the adornment of their English terraces and gardens.&lt;ref&gt;&quot;My Social Diary.&quot; The ''Queen'' 22 May 1909, Saturday: 31 [of 86], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19090522/203/0031. Print p. 871.&lt;/ref&gt;&lt;/blockquote&gt;'''1909 September''', the Hon. Algernon Bourke was among the [[Social Victorians/Timeline/1900s#Visitors in Venice from the U.K.|many visitors from &quot;England&quot; in Venice]] in September.

=== 1910s ===
'''1910 April 20, Wednesday''', the ''Tatler'' printed an &quot;open letter&quot; to Geraldine, Countess of Mayo, as part of its &quot;The Searchlight in Society&quot; series and mentioned Algernon Bourke, saying he had been keeping &quot;a curiosity shop at Venice&quot;:&lt;blockquote&gt;The Bourkes have brains, and a good example is afforded by Mr. Algernon Bourke, next brother to Lord Mayo and heir-presumptive to the title. He is a good-looking man who used to be known as Buttons Bourke, and he married well, as his wife was the rich and pretty Miss Guendolen Sloane Stanley. He may be described as a &quot;Jack of all trades,&quot; but it is not I who will say that he is a master of none. He was once in the Stock Exchange, then he took White's Club in hand and restored it to much of its former prestige. After that he dabbled in smart hotels and restaurants, and the last thing I heard of him was that he kept a curiosity shop at Venice.&lt;ref&gt;Candida. &quot;The Searchlight in Society. Our Open Letter. No. CII. The Countess of Mayo.&quot; The ''Tatler'' 20 April 1910, Wednesday: 18 [of 42], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001852/19100420/023/0018. Print title same, p. 72.&lt;/ref&gt;&lt;/blockquote&gt;

'''1911 November 21, Tuesday''', Gwendolen Bourke assisted the [[Social Victorians/Timeline/1910s#21 November 1911, Tuesday|Duchess of Marlborough at her at-home]] that included a sale of work by the wives of prisoners.&lt;p&gt;

'''1912 September 27, Friday''', Gwendolen and Daphne Bourke were visiting Mr. and Mrs. Shelley Bontein, her mother and stepfather.&lt;ref&gt;&quot;From 'The World.'&quot; ''Berks and Oxon Advertiser'' 27 September 1912, Friday: 2 [of 8], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002298/19120927/014/0002. Same print title, n.p.&lt;/ref&gt;&lt;p&gt;

'''1913 April 23, Wednesday''', the Irish Independent reported that Gwendolen and Daphne Bourke had arrived in London for the season:&lt;blockquote&gt;&lt;p&gt;

The Hon. Mrs. Algernon Bourke and Miss Bourke have arrived for the season at 75 Gloucester place, Portman square, London.&lt;ref&gt;&quot;Social and Personal.&quot; ''Irish Independent'' 23 April 1913, Wednesday: 4 [of 10], Col. 5b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001715/19130423/081/0004. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;&lt;p&gt;

'''1913 May 7, Wednesday''', Gwendolen Bourke presented her daughter Daphne Bourke at court:&lt;blockquote&gt;Mrs. Algernon Bourke presented her daughter, and wore blue and gold broché with a gold lace train.&lt;ref&gt;&quot;Social and Personal.&quot; London ''Daily Chronicle'' 08 May 1913, Thursday: 6 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/19130508/120/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

The ''Pall Mall Gazette'' has a description of Daphne Bourke's dress, but what exactly &quot;chiffon [[Social Victorians/Terminology#Hoops|paniers]]&quot; means in 1913 is not clear:&lt;blockquote&gt;Court dressmakers appear to have surpassed all previous records in their efforts to make the dresses for to-night’s Court as beautiful as possible. Noticeable among these is the dainty presentation gown to be worn by Miss Bourke, who will be presented by her mother, the Hon. Mrs. Algernon Bourke. This has a skirt of soft white satin draped with chiffon [[Social Victorians/Terminology#Hoops|paniers]] and a bodice veiled with chiffon and trimmed with diamanté and crystal embroidery. Miss Bourke’s train, gracefully hung from the shoulders, is of white satin lined with pale rose pink chiffon and embroidered with crystal and diamanté.&lt;ref&gt;&quot;Fashion Day by Day. Lovely Gowns for To-night's Court.&quot; ''Pall Mall Gazette'' 07 May 1913, Wednesday: 13 [of 18], Col. 1a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/19130507/199/0013. Print n.p.&lt;/ref&gt;&lt;/blockquote&gt;The ''London Evening Standard'' describes Gwendolen and Daphne Bourke the same way except with differences in editing:&lt;blockquote&gt;Miss Bourke: Presented by her mother, the Hon. Mrs. Algernon Bourke. Dainty presentation gown of white satin, the skirt draped with chiffon paniers, bodice veiled chiffon and trimmed with diamanté and crystal embroidery. Train gracefully hung from shoulder of white satin embroidered with crystal and diamanté, lined with pale rose pink chiffon.&lt;ref&gt;&quot;Some of the Dresses.&quot; &quot;The King and Queen. Third Court. Most Brilliant of the Year.&quot; ''London Evening Standard'' 08 May 1913, Thursday: 11 [of 18], Col. 4b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/19130508/237/0011. Print title ''The Standard'', p. 11.&lt;/ref&gt;&lt;/blockquote&gt;

According to the ''Lady's Pictorial'', Daphne Bourke's dress was designed and constructed by [[Social Victorians/People/Dressmakers and Costumiers#Messrs Russell and Allen|Messrs. Russell and Allen]], Old Bond-street, W., and the description is identical (except for a couple of commas).&lt;ref&gt;&quot;Their Majesties' Court.&quot; ''Lady's Pictorial'' 17 May 1913, Saturday: 35 [of 64], Col. 2c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005980/19130517/296/0035. Same print title, p. 787.&lt;/ref&gt;

'''1914 May 11, Monday''', Gwendolen and Daphne Bourke attended a [[Social Victorians/Timeline/1910s#Dance at the Ritz Hosted by Mrs. George Marjoribanks|dance at the Ritz hosted by Mrs. George Marjoribanks]].

'''1915 January 1, Friday''', Algernon Bourke is listed as being on the Executive Committee of the [[Social Victorians/Timeline/1910s#1915 January 1, Friday|National Food Fund, publicized by the ''Conservative and Unionist Women's Franchise Review'']].

'''1916 August 25, Friday''', Daphne Bourke's and John Fortescue's engagement was announced:&lt;blockquote&gt;A most attractive prospective bride (says the &quot;Star&quot;) is Mr. and Mrs. Algernon Bourke's only daughter, Miss Daphne Bourke, whose engagement has just taken place to Mr. Fortescue, of the Coldstream Guards. Miss Bourke is tall, dark, and very beautiful; and Mr. Fortescue is one of the family of Boconoc, Cornwall, and Dropmore, Maidenhead. At the latter place the two families have been neighbours, for Mr. and Mrs. Algernon Bourke have a charming country residence at Taplow, while Dropmore is famous for its magnificent gardens.&lt;ref&gt;&quot;Personalia.&quot; ''Uxbridge &amp; W. Drayton Gazette'' 25 August 1916, Friday: 4 [of 8], Col. 5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002285/19160825/043/0004. Print title ''The Advertiser'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;&lt;p&gt;'''1917 June 7, Thursday''', Daphne Bourke and John Grenville Fortescue [[Social Victorians/Timeline/1910s#7 June 1917, Thursday|married in the Coldstream Guards' chapel]].

== Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball ==
According to both the ''Morning Post'' and the ''Times'', the Hon. Algernon Bourke was among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]] at the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]].&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt; Based on the people they were dressed as, Gwendolen Bourke was probably in this procession but it seems unlikely that Algernone Bourke was.

[[File:Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.jpg|thumb|alt=Black-and-white photograph of a standing woman richly dressed in an historical costume with a headdress and a very large fan|Hon. '''Guendoline''' Bourke as Salammbô. ©National Portrait Gallery, London.]]
=== Hon. Guendoline Bourke ===
[[File:Alfons Mucha - 1896 - Salammbô.jpg|thumb|left|alt=Highly stylized orange-and-yellow painting of a bare-chested woman with a man playing a harp at her feet|Alfons Mucha's 1896 ''Salammbô''.]]
Lafayette's portrait (right) of &quot;Guendoline Irene Emily Bourke (née Sloane-Stanley) as Salammbô&quot; in costume is photogravure #128 in the '''Album''' presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot;&gt;&quot;Devonshire House Fancy Dress Ball (1897): photogravures by Walker &amp; Boutall after various photographers.&quot; 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.&lt;/ref&gt; The printing on the portrait says, &quot;The Hon. Mrs. Algernon Bourke as Salammbo.&quot;&lt;ref name=&quot;:23&quot;&gt;&quot;Mrs. Algernon Bourke as Salammbo.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158491/Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.&lt;/ref&gt;

The Lafayette Archive has 2 additional poses from the same session on 5 July 1897 as the one chosen for the Album:

* Same image as the Album photograph but higher resolution than the one the National Portrait Gallery, London, gives permission to post (Neg. No. GP [L] ).
* Standing with fan behind head, includes close-up of skirt fabric and left hand (Neg. No. GP [L] [http://lafayette.org.uk/bou1368-444.html 1368-444]).
* Reclining on pillows and furs, includes close-up of face and headdress (Neg. No. GP [L] [http://lafayette.org.uk/bou1368-442.html 1368-442]).

==== Newspaper Accounts ====
The Hon. Mrs. A. Bourke was dressed as Salambo in the Oriental procession&lt;ref name=&quot;:2&quot; /&gt;&lt;ref name=&quot;:3&quot; /&gt; in a costume made by [[Social Victorians/People/Dressmakers and Costumiers#Mrs. Mason|Mrs. Mason]].

Besides the two that mention her — the ''Morning Post'' and the ''Times'' — only two describe her costume, the London ''Evening Standard'' and the ''Gentlewoman'':
* &quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}

==== Commentary ====

*

==== Salammbô ====
Salammbô is the fictitious protagonist in Gustave Flaubert's 1862 novel ''Salammbô'', set during the Roman war against Carthage.&lt;ref name=&quot;:5&quot;&gt;{{Cite journal|date=2024-04-29|title=Salammbô|url=https://en.wikipedia.org/w/index.php?title=Salammb%C3%B4&amp;oldid=1221352216|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Salammb%C3%B4.&lt;/ref&gt; Salammbô is a Carthaginian priestess of the lunar goddess Tanit. Matho, a Roman mercenary, breaks into Tanit's temple and steals her sacred veil — the spiritual guardian of Carthage. Salammbô sneaks into the enemy encampment to steal the veil back. She meets Matho in his tent, and &quot;believing each other to be divine apparitions,&quot; they make love,&lt;ref name=&quot;:5&quot; /&gt; although it is also a defilement. Salammbô succceds in getting the veil back, but Matho is tortured and executed, which causes her to die of shock, the effect of both having touched the veil. The plot of the opera is not identical to that of the novel.

What Gwendolen Bourke saw as representative of herself in Salammbo is difficult to discern, unless her costume contains references to particular images or productions. Translations and illustrated editions of Flaubert's novel came out steadily beginning in the 1880s. A production of Ernest Reyer's opera ''Salammbô'', based on Flaubert's novel and published in Paris in 1890, opened at the Paris Opéra on 16 May 1892,&lt;ref&gt;{{Cite journal|date=2024-04-11|title=Ernest Reyer|url=https://en.wikipedia.org/w/index.php?title=Ernest_Reyer&amp;oldid=1218353215|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Ernest_Reyer.&lt;/ref&gt; starring Madame Rose Caron, with Mademoiselle Lucienne Bréval performing when Caron was on vacation.&lt;ref&gt;Jullienn, Adolphe. &quot;Mademoiselle Lucienne Bréval de L'Académie Nationale de Musique [or de l'Opéra in the Table of Contents].&quot; ''Le Théatre'' April 1898 (No. 4). Google Books https://www.google.com/books/edition/_/_oxRAQAAMAAJ. Pp. 8–10.&lt;/ref&gt; (8, Col. 2c) This production was widely reviewed and discussed in the papers in the UK, and its production design was notable, especially Caron's costumes, the sets and the very scale of the production. So Bourke or her costumier may have seen the opera, images of the performers or its posters, influencing the design of her costume.

* Rose Caron in her Salammbo costume is here: https://www.gettyimages.com/detail/news-photo/rose-caron-french-soprano-in-costume-in-the-title-role-of-news-photo/1439485238.
* A headshot of Bréval in costume is here: https://books.google.com/books/content?id=_oxRAQAAMAAJ&amp;pg=RA3-PP7&amp;img=1&amp;zoom=3&amp;hl=en&amp;bul=1&amp;sig=ACfU3U2Gv8Os_rEmx2gM9SakJkYLJ9hW7g&amp;ci=6%2C1%2C988%2C1371&amp;edge=0.)
* &quot;Salammbo's hair [was] powdered with a violet dust when she first appeared before the eyes of Matho.&quot;&lt;ref&gt;&quot;Salome.&quot; ''Pall Mall Gazette'' 27 February 1893, Monday: 3 [of 8]. Col. 2b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18930227/010/0003. Same print title and p.&lt;/ref&gt;

Salammbo figured in paintings, sculptures and illustrations of editions of Flaubert's novel before Ernest Reyer's 1890 opera. She is often depicted as nude and highly sexual or sexualized (kissing a huge snake, for example, that she holds aloft).

Gwendolen Bourke's costume and her social life as reported in the newspapers do not suggest that she was a big risk-taker like, for example, the eccentric la Comtesse de Castiglione, who appeared at a ball in a Salammbo costume in 1886, 4 years after Flaubert's novel was first published. In 1889 the ''Edinburgh Evening News'' exaggerates her nudity and doesn't describe the rush in the ballroom to see her but does address the lingering memory:&lt;blockquote&gt;The late Countess Castiglione, whose death in Paris is recorded yesterday, made her first appearance at the Imperial Court in 1866, where her extraordinary beauty made a great impression on Napoleon III., and eventually led to the Empress Eugenie’s undertaking an unexpected and much-talked-of visit to Scotland. The Countess had a face and complexion which would have enchanted Rubens, and her lovely golden hair touched her feet. Even at the present day Paris has not forgotten her costume, or rather absence of costume as Salammbo, in which character she figured at a certain memorable ball at the Tuileries, wearing her hair, her jewels, and very little else. The Empress Eugenie, when she was presented to her thus lightly arrayed, declared that she must be cold, and insisted upon her there and then donning a mantle. Mme. de Castiglione was never again invited to an entertainment over which the Empress Eugenie presided.&lt;ref&gt;&quot;A Countess’ Queer Ball Costume.&quot; ''Edinburgh Evening News'' 2 December 1899, Saturday: 2 [of 6], Col. 7b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000452/18991202/024/0002. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;Given how widely this incident was discussed at the time of the death of la Comtesse in 1889, Gwendolen Bourke might easily have known about it. But she was developing relationships with people like the Princess of Wales, and what Countess Castigiolone did does not sound at all like her. 

===== Scale of the Production of ''Salammbo'' =====

* &quot;In Reyer's opera of 'Salammbo,' lately produced at the Grand Opera in Paris, there were 1,400 persons on the stage in the last act.&quot;&lt;ref&gt;&quot;Facts and Fancies.&quot; ''Louth and North Lincolnshire Advertiser'' 9 July 1892, Saturday: 3 [of 8], Col. 6c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000313/18920709/038/0003. Same print title and p.&lt;/ref&gt;
* &quot;the battle scene in [''Salammbo''] requires no less than 3000 square yards of 'decorative surface' [probably canvas]. This establishes a record, the next largest surface being that of the salles des fetes in 'Don Giovanni.'&quot;&lt;ref&gt;&quot;A French paper gives interesting details....&quot; ''Sevenoaks Chronicle and Kentish Advertiser'' 26 August 1892, Friday: 2 [of 8], Col. 3c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001067/18920826/032/0002. Same print title, n.p.

&lt;/ref&gt;

===== Influence of the Production of ''Salammbo'' =====
Rose Caron's productions were influential, including for the costumes she wore. The 1892 ''Lohengrin'' she starred in was the source of the costumes worn by [[Social Victorians/People/Stonor#Julia Caroline Stonor, Marquise of Hautpoul|Julia Stonor, Marquise of Hautpoul]] and her brother, [[Social Victorians/People/Stonor#Hon. Harry Stonor|Hon. Harry Stonor]].

Women's clothing was influenced by the costumes in the opera, particularly those worn by Rose Caron. One color of intense red was called Salammbo. A bonnet was named the Salammbô:&lt;blockquote&gt;About the smartest thing in bonnets for ordinary complimentary mourning is called the Salammbô, and is copied from a head-dress worn by a leading artiste at one of the Paris theatres. It is made of jet, and has a rose on each side of the front from the centres of which rise two black ospreys.&lt;ref&gt;Mantalini, Miss. &quot;The Shows in the London Shops. With Mems. about Millinery.&quot; ''Pall Mall Budget'' 29 December 1892, Thursday: 22 [of 40], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005967/18921229/092/0022. Same print title, p. 1928.&lt;/ref&gt;&lt;/blockquote&gt;In a long illustrated article describing the wedding of Princess Marie of Edinburgh, the ''Lady's Pictorial'' provides a sketch of &quot;a very pretty [hat] (No. 4) of brown mirror velvet trimmed with mink and a brown velvet bow in front with Salammbo '''fantaisie''&lt;nowiki/&gt;'&quot; that is among the bride's millinery.&lt;ref&gt;&quot;The Marriage of H.R.H. Princess Marie of Edinburgh and H.R.H. Ferdinand Crown Prince of Roumania.&quot; ''Lady's Pictorial'' 14 January 1893, Saturday: 40 [of 76], Col. 3c [of 3]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0005980/18930114/064/0040. Same print title, p. 56.&lt;/ref&gt;&lt;p&gt;

Shoes appeared:&lt;blockquote&gt;At Mrs Merritt's, Savile-street, the stock is particularly attractive, there being so many new styles in shoes this season. One of the latest designs is the Salammbo Shoe, glace kid, with one strap, a jet buckle, and very low French heels. This shoe is especially designed for tender feet, as it is very light in weight.&lt;ref&gt;&quot;House and Home. Local Letter for Women Reader [sic], (By Our Lady Contributor).&quot; ''Hull Daily Mail'' 22 July 1897, Thursday: 5 [of 6], Col. 1b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000324/18970722/069/0005. Same print title, n.p.&lt;/ref&gt;&lt;/blockquote&gt;Patterns for making the Tunique Romaine and Corsage Salammbo were for sale just a few months after the opening:&lt;blockquote&gt;Some of the leading fashionable novelties described in ''Le Follet de Paris'' are almost ahead of the season, but they look so well that it will not be long before our provincial dressmakers have them. A revival and modification of the ancient tunic is one item which is transforming the modern gowns of tailor-built tweeds into long clinging draperies, of simple cut but ineffable grace. We have had the Russian blouse with us now for the last couple of months. Now the reign of Tunique Romaine and Corsage Salambo is upon us.

...

A very successful novelty is the ''corsage'' “Salammbo.” In reality, it is more of a blouse and short tunic than a ''corsage'', as there is no attempt at shaping to the figure. In [sic] consists, indeed, of two straight pieces of material cut round on the shoulders, where the back and front are fastened together by clasps. There is no arm-hole, and the two pieces meet at the waist under the arm, and then hang open on to the skirt. There being no dart, the waist is as wide as the shoulders; the fullness is drawn to the centre under a ''ceinture Russe'', or of oxydised silver. The outlines are trimmed with ''galon'' or some similar garniture. The &quot;Salammbo” ''guimpe'' or ''corsage'' are made of flannel or ''mousseline de laine'' of bright colour, and are worn with fitting bodices or skirts of serge, or woollen of dark colour. They are very effective, and nothing can be easier to make, while their addition to a frock constitutes a separate costume.

The fitting bodices worn under the ''guimpes'' or ''robes'' &quot;Salammbo&quot; are very simply made; being round-waisted, they are without side pieces, and only require a seam under each arm; one in the centre of the back, and one or two darts in front, according to the figure. The skirt is mounted on a round waistband, and the ''ceinture'' worn over this gives the bodice and skirt the effect of a princess dress.&lt;ref&gt;&quot;A Womans Ceilidh.&quot; ''Oban Times and Argyllshire Advertiser'' 3 September 1892, Saturday: 3 [of 8], Col. 6a–b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000462/18920903/078/0003. Print title: ''The Oban Times'', p. 3.&lt;/ref&gt;&lt;/blockquote&gt;Stationery even before the opera opened in Paris:&lt;blockquote&gt;The last fad in fancy stationery is the carte Salammbo, a delightfully smooth surface for writing upon, the envelopes are very small, square, and of the wallet make; the paper folds over once to fit. The newest shades are rose pink, pale English blue, apple green, and the evergreen heliotrope.&lt;ref&gt;&quot;Fashions of the Month.&quot; ''Nottinghamshire Guardian'' 27 February 1892, Saturday: 7 [of 8], Col. 2b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000176/18920227/059/0007. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;Both Modest Mussorgsky and Sergei Rachmaninoff had attempted but not completed operas based on the novel as well.&lt;ref name=&quot;:5&quot; /&gt; Alfons Mucha's 1896 lithograph of Salammbô (above left) was published the year before the ball.

Reyer's opera was first produced in 1890 in Brussels. 

[[File:Algernon Henry Bourke Vanity Fair 20 January 1898.jpg|thumb|alt=Old colored drawing of an elegant elderly man dressed in a 19th-century tuxedo with a cloak, top hat and formal pointed shoes with bows, standing facing 1/4 to his right|''Algy'' — Algernon Henry Bourke — by &quot;Spy,&quot; ''Vanity Fair'' 20 January 1898]]

=== Hon. Algernon Bourke ===
[[File:Hon-Algernon-Henry-Bourke-as-Izaak-Walton.jpg|thumb|left|alt=Black-and-white photograph of a man richly dressed in an historical costume sitting in a fireplace that does not have a fire and holding a tankard|Hon. Algernon Henry Bourke as Izaak Walton. ©National Portrait Gallery, London.]]
'''Lafayette's portrait''' (left) of &quot;Hon. Algernon Henry Bourke as Izaak Walton&quot; in costume is photogravure #129 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot; /&gt; The printing on the portrait says, &quot;The Hon. Algernon Bourke as Izaak Walton.&quot;&lt;ref&gt;&quot;Hon. Algernon Bourke as Izaak Walton.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158492/Hon-Algernon-Henry-Bourke-as-Izaak-Walton.&lt;/ref&gt;

This portrait is amazing and unusual: Algernon Bourke is not using a photographer's set with theatrical flats and props, certainly not one used by anyone else at the ball itself. Isaak Walton (baptised 21 September 1593 – 15 December 1683) wrote ''The Compleat Angler''.&lt;ref&gt;{{Cite journal|date=2021-09-15|title=Izaak Walton|url=https://en.wikipedia.org/w/index.php?title=Izaak_Walton&amp;oldid=1044447858|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Izaak_Walton.&lt;/ref&gt; A cottage Walton lived in and willed to the people of Stafford was photographed in 1888, suggesting that its relationship to Walton was known in 1897, raising a question about whether Bourke could have used the fireplace in the cottage for his portrait. (This same cottage still exists, as the [https://www.staffordbc.gov.uk/izaak-waltons-cottage Isaak Walton Cottage] museum.)

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

=== Mr. and Mrs. Bourke ===
The ''Times'' made a distinction between the Hon. Mr. and Mrs. A. Bourke and Mr. and Mrs. Bourke, including both in the article.&lt;ref name=&quot;:3&quot; /&gt; Occasionally this same article mentions the same people more than once in different contexts and parts of the article, so they may be the same couple. (See [[Social Victorians/People/Bourke#Notes and Question|Notes and Question]] #2, below.)

== Demographics ==

=== The Bourkes ===
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;

==== Residences ====
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1888–1891: 33 Cadogan Terrace, S.W., Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1904: Algernon Bourke was &quot;usually liv[ing] in Venice&quot;&lt;ref name=&quot;:10&quot; /&gt;
*1906: 75, Gloucester-place, W.&lt;ref name=&quot;:21&quot; /&gt;
*Gwendolen Bourke
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

=== The Sloane-Stanleys ===

==== Residences ====

* 1871: Chester Street, St George Hanover Square (Census), with 5 servants, including a cook and a footman.&lt;ref name=&quot;:16&quot;&gt;The National Archives; Kew, London, England; ''1871 England Census''; Class: ''RG10''; Piece: ''104''; Folio: ''21''; Page: ''37''; GSU roll: ''838763''. Ancestry.com. ''1871 England Census'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations Inc, 2004.&lt;/ref&gt;
* 1881–1885&lt;ref&gt;''UK, City and County Directories, 1600s-1900s''. Ancestry.com. ''UK, City and County Directories, 1766 - 1946'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2013.&lt;/ref&gt; [at least]: 14 Halkin Street, W., St. Georges, 14 servants, including a governess, a house steward, an under butler, a footman and a cook.&lt;ref&gt;''Census Returns of England and Wales, 1881''. Kew, Surrey, England: The National Archives of the UK (TNA): Public Record Office (PRO), 1881. Class: ''RG11''; Piece: ''98''; Folio: ''66''; Page: ''37''; GSU roll: ''1341022''. Ancestry.com and The Church of Jesus Christ of Latter-day Saints. ''1881 England Census'' [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2004.&lt;/ref&gt;
* 1888: 49, Cadogan-square, St. Luke, Chelsea&lt;ref&gt;Ancestry.com. ''London, England, Overseer Returns, 1863-1894'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2013.&lt;/ref&gt;
* 1899, Roger Cyril Sloane-Stanley: 4 Down St., St George, Hanover Square&lt;ref&gt;London Metropolitan Archives; London, England; ''Electoral Registers''. Ancestry.com. ''London, England, Electoral Registers, 1832-1965'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt;
* 1911, Roger Cyril Sloane-Stanley: Paultons, Ower, Romsey

== Family ==
*Hon. Algernon Henry Bourke (31 December 1854 – 7 April 1922)&lt;ref&gt;&quot;Hon. Algernon Henry Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p29657.htm#i296561|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
*Gwendolen Irene Emily Sloane-Stanley Bourke (c. 1869 – 30 December 1967)&lt;ref name=&quot;:1&quot;&gt;&quot;Guendoline Irene Emily Stanley.&quot; {{Cite web|url=https://www.thepeerage.com/p51525.htm#i515247|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
#Daphne Marjory Bourke (5 April 1895 – 22 May 1962)

=== Relations ===
*Hon. Algernon Henry Bourke (the 3rd son of the [[Social Victorians/People/Mayo|6th Earl of Mayo]]) was the older brother of Lady Florence Bourke.&lt;ref name=&quot;:0&quot; /&gt;
*Wilfred Blunt was a cousin of Algernon Bourke: his mother's &quot;mother was one of the Blunts of Crabbet Park, Sussex, which makes them kinswomen of Mr. Alfred Scawen Blunt, poet, Egyptophil and counsel for Arabi Pasha in his trial.&quot;&lt;ref&gt;&quot;From ''Truth''.&quot; ''Mid-Lothian Journal'' 23 August 1912, Friday: 8 [of 8], 2c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002721/19120823/147/0008. Print title and p. same.&lt;/ref&gt;

==== Other Bourkes ====
*Hubert Edward Madden Bourke (after 1925, Bourke-Borrowes)&lt;ref&gt;&quot;Hubert Edward Madden Bourke-Borrowes.&quot; {{Cite web|url=https://www.thepeerage.com/p52401.htm#i524004|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p52401.htm#i524004.&lt;/ref&gt;
*Lady Eva Constance Aline Bourke, who married [[Social Victorians/People/Dunraven|Windham Henry Wyndham-Quin]] on 7 July 1885;&lt;ref&gt;&quot;Lady Eva Constance Aline Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p2575.htm#i25747|title=Person Page|website=www.thepeerage.com|access-date=2020-12-02}} https://www.thepeerage.com/p2575.htm#i25747.&lt;/ref&gt; he became 5th Earl of Dunraven and Mount-Earl on 14 June 1926.

=== The Sloane-Stanleys ===
* Emilie Josephine S Stanley ( 21 December 1848 [baptism]&lt;ref&gt;London Metropolitan Archives; &quot;London, England, UK&quot; ; ''London Church of England Parish Registers''; Reference Number: ''P87/Tri/001''. Ancestry.com. ''London, England, Church of England Births and Baptisms, 1813-1923'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt;  – October 1945)
* Hans T Sloane Stanley (11 May 1840 [baptism]&lt;ref&gt;Ancestry.com. ''England, Select Births and Christenings, 1538-1975'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2014.&lt;/ref&gt; – 15 December 1888&lt;ref&gt;Ancestry.com. ''UK and Ireland, Find a Grave® Index, 1300s-Current'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2012.&lt;/ref&gt;)
* James Shell[e?]y Bontein ()
*# Gwendoline&lt;ref name=&quot;:14&quot; /&gt; Irene Emily G Stanley (c. 1870&lt;ref name=&quot;:16&quot; /&gt; – )
*# '''Roger Cyril Hans Sloane Stanley''' (29 April 1875&lt;ref&gt;The National Archives; Kew, Surrey, England; ''WO 42 War Office: Officers' Birth Certificates, Wills and Personal Papers 1755-1908''; Reference: ''WO 42/72''. Ancestry.com. ''UK, Officers' Birth Certificates, Wills and Personal Papers, 1755-1908'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2023.&lt;/ref&gt; – 18 November 1944&lt;ref&gt;''Find a Grave''. Find a Grave®. http://www.findagrave.com/cgi-bin/fg.cgi. Ancestry.com. ''UK and Ireland, Find a Grave® Index, 1300s-Current'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2012.&lt;/ref&gt;)


* Olivia Elizabeth Berens, Countess Cairns&lt;ref&gt;The National Archives of the UK (TNA); Kew, Surrey, England; ''Census Returns of England and Wales, 1911''. Ancestry.com. ''1911 England Census'' [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2011.&lt;/ref&gt; (c. 1871 – 20 June 1951&lt;ref&gt;&quot;Olivia Elizabeth Berens.&quot; Person Page 3908; person #39077. ''The Peerage: A Genealogical Survey of the Peerage of Britain as well as the Royal Families of Europe''. https://www.thepeerage.com/p3908.htm#i39077.

&lt;/ref&gt;)
* Arthur William Cairns, 2nd Earl Cairns (21 December 1861 – 14 January 1890)&lt;ref name=&quot;:20&quot;&gt;&quot;Arthur William Cairns, 2nd Earl Cairns.&quot; Person Page 3908; Person #39076. ''The Peerage: A Genealogical Survey of the Peerage of Britain as well as the Royal Families of Europe''. https://www.thepeerage.com/p3908.htm#i39076.&lt;/ref&gt;
*# Lady Louise Rosemary Kathleen Virginia Cairns (10 March 1889 – 17 May 1962)&lt;ref name=&quot;:20&quot; /&gt;
* Roger Cyril Hans Sloane Stanley (1875 – 18 November 1944)
*# Lavender Elizabeth (20 May 1900 [baptism]&lt;ref&gt;Hampshire Archives and Local Studies; Winchester, England, UK; ''Anglican Parish Registers''; Reference: ''35M76/PR3''. Ancestry.com. ''Hampshire, England, Church of England Baptisms, 1813-1921''[database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2023.&lt;/ref&gt; – )
*# Diane Sloane Stanley (c. 1905 – )


* Lavender Elizabeth (20 May 1900 [baptism] – )
* John Everett ()


* Diane Sloane Stanley (c. 1905 – )
* Elwyn Villiers Rhys ()

== Writings, Memoirs, Biographies, Papers ==

=== Writings ===
* Bourke, the Hon. Algernon. ''The History of White's''. London: Algernon Bourke [privately published], 1892.
* Bourke, the Hon. Algernon, ed., &quot;with a brief Memoir.&quot; ''Correspondence of Mr Joseph Jekyll with His Sister-in-Law, Lady Gertrude Sloane Stanley, 1818–1838''. John Murray, 1893.
* Bourke, the Hon. Algernon, ed. ''Correspondence of Mr Joseph Jekyll''. John Murray, 1894.

=== Papers ===
* Where are the papers for the Earl of Mayo family? Are Algernon and Gwendolen Bourke's papers with them?

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
#Hans Stanley-Sloane's estate was £33,704 7s. 5d. in the final probate in December 1889,&lt;ref&gt;Principal Probate Registry; London, England; ''Calendar of the Grants of Probate and Letters of Administration made in the Probate Registries of the High Court of Justice in England''. Ancestry.com. ''England &amp; Wales, National Probate Calendar (Index of Wills and Administrations), 1858-1995'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt; which might lead his widow to consider remarrying.
== Footnotes ==
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      <text bytes="177658" sha1="11ziqz428cw1am876b2dquapkad4fqo" xml:space="preserve">[[Social Victorians/Timeline/1840s|1840s]]  [[Social Victorians/Timeline/1850s |1850s]] [[Social Victorians/Timeline/1860s | 1860s]] [[Social Victorians/Timeline/1870s | 1870s]] [[Social Victorians/Timeline/1880s | 1880s]] [[Social Victorians/Timeline/1890s | 1890s]] 1900s [[Social Victorians/Timeline/1910s | 1910s]] [[Social Victorians/Timeline/1920s-30s|1920s–1930s]]

==1900==
1900, early, [[Social Victorians/People/Mathers|MacGregor and Moina Mathers]] were living at 87 Rue Mozart, Paris (Howe 203).
===January 1900===
====1 January 1900, Monday, New Year's Day====
====13 January 1900, Tuesday====
&lt;blockquote&gt;THE HOUSEHOLD TROOPS. ENTERTAINMENT AT HER MAJESTY'S.

The Prince and Princess of Wales, accompanied by Princess Victoria and Prince Charles of Denmark, attended the entertainment to aid the widows and orphans of her Majesty's Household Troops, organised by Mrs. Arthur Paget and presented under the direction of Mr. H. Beerbohm Tree at Her Majesty's Theatre last night.

... [The major part of this story is the program of the entertainment, in which [[Social Victorians/People/Muriel Wilson|Muriel Wilson]], among others, played an important part.]

Among those present at the entertainment were: The Prince and Princess of Wales, Princess Victoria of Wales, and Prince Charles of Denmark, the French Ambassador, the Russian Ambassador, the Portuguese Minister, Count Mensdorff, the Austrian Embassy, Prince and Princess Demidoff, Prince and Princess Hatzfeldt, Prince and Princess Alexis Dolgorouki, Count and Countess Roman Potocki, Count and Countess Alexander Münister, the Duke and Duchess of Devonshire, the Marquis of Downshire, the Earl and Countess of Cork, the Earl and Countess of Westmorland, the Earl and Countess of Gosford, the Earl of Lathom, the Countess of Ancaster, the Countess of Wilton, the Countess of Yarborough, the Countess of Huntingdon, Viscount Curzon, Lord and Lady Farquhar, Lord and Lady Savile, Lord Rowton, Lord Westbury, Baroness d'Erlanger, Count and Countess Seilern, Lord and Lady Ribblesdale, Lord and Lady Hothfield, Lord and Lady Raincliffe, Lord Wandsworth, Lord Charles Montagu, Lady Cunard, Sir Edgar and Lady Helen Vincent, Lady Kathleen and Mr. Pilkington, Lady Violet Brassey, Lady Grey Egerton, the Hon. Humphry and Lady Feodorowna Sturt, Lady Ripley, Lady Katherine Coke, Lady Agneta Montagu, Lady Tatton Sykes, Lady Templemore, Lady Florence Grant, Lady Garrick, Lady Pearson, Lady Constance Haddon, Sir F. Burdett, the Hon. M. Charteris, Sir A. de la Rue, Sir Frederick and Lady Milner, the Hon. E. Stonor, Sir Edward and Lady Sassoon, Mrs. Joseph Chamberlain, the Hon. Mrs. Lawrence, the Hon. Mrs. Napier, Sir Charles Forbes, Mrs. Bradley Martin, Mrs. Cornwallis West, Mr. Arnold Morley, Mr. L. Neumann, Madame Vagliano, Mr. Gillett, Mrs. Godfrey Samuelson, Mrs. Reginald Ward, Mr. and Mrs. Arthur Wilson, Mr. Menzies, Mr. Dreyfous [sic], Mrs. George Coats, Mr. Hartmann, Mrs. Rube, Mrs. Neumann, Mr. Lukach, Mrs. Candy, Mr. Bargrave Deane, Mr. L. V. Harcourt, Mrs. Oppenheim, Mrs. Lionel Phillips, Mr. King. Mr. James Finch, Mrs. Clayton Glyn, Miss Van Wart, Mr. Hall Walker, Mr. Drexell, Mrs. Van Raalte, Mr. Alfred Beit, Mr. Douglas Uzielli, Mrs. Alfred Harmsworth, Mr. Munday, Mrs. William James, Mrs. Newhouse, Mrs. Max Waechter, Mr. G. Prentis, Mrs. M'Calmont, Mr. Blacklock, Mrs. Ausell, Captain Holford (Equerry to the Prince of Wales), Mr. De Nino, Mrs. Keyser, Mrs. Fleming, Mrs. Breitmeyer, Mrs. Wernher, Mrs. Armour, Mr. Van Alan, Mrs. Ewart, Mrs. Carl Meyer, Mrs. Powell, Mr. Hambro, Colonel Charles Allen, Colonel Cunningham, Mrs.Hutchinson, Mrs. Schumacher, Colonel Kennard, Mrs. Fludyer, Mrs. Williamson, Mr. Thellusson, Mr. Sackville West, Captain M'Neil, Mrs. Dalrymple Hamilton, Mrs. Penn Curzon, Mrs. Hamar Bass, Mrs. Kuhliug, General Stracey, Mrs. Jeffcock, Colonel Thynne.&lt;ref&gt;&quot;The Household Troops. Entertainment at Her Majesty's.&quot; ''Morning Post'' 14 February 1900, Wednesday: 3 [of 10], Col. 1a–2b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19000214/014/0003 (accessed February 2020).&lt;/ref&gt;&lt;/blockquote&gt;

====17 January 1900, Saturday====

1900 February 17, Lady Greville writes about the amateur theatricals Muriel Wilson is involved in: &lt;blockquote&gt;The most notable social event of the week was the amateur performance of tableaux at Her Majesty's Theatre. One is accustomed to the amateurs under every aspect, leaping in where angels fear to tread, essaying the most difficult parts, dabbling in the arts of music and literature, but so full and rich and interesting a performance has rarely been given before. To begin with, there was a masque, modelled on the Elizabethan lines, with song and dance, and special music composed for the occasion by Mr. Hamish McCunn, dresses statuesque and graceful, and a bevy of pretty women to carry out the idea.

One original feature there was, too, which certainly did not present itself before our Virgin Queen, and that was the graceful fencing of Miss Lowther, who looked an ideal young champion in her russet suit and jaunty little cap. A very young debutante appeared in the person of Miss Viola Tree, who, dressed in the nest diaphanous garments, acted with a grace and lightness that promises well for her future career. Mrs. Crutchly, as &quot;Glory,&quot; appeared amid a din of thunder and a rosy glare of limelight, and clashed her cymbals in truly determined fashion. An element of wildness suited to the character, distinguished her agreeable posturing, and her high spiked crown gave distinct individuality to the representation. Mrs. Martineau, Hebe-like in a white robe and a large crown of roses, as if she had just stepped out of a picture by Leighton, then danced and took the palm for poetry and suppleness of movement; Miss [[Social Victorians/People/Muriel Wilson|Muriel Wilson]], meanwhile, having daringly shot up through a trap-door in scarlet robes with a flaming torch, announced herself as &quot;War,&quot; and beckoned to Glory, Victory, and Prosperity, when they finished their performance, to sit beside her on her throne. &quot;Rumour,&quot; alias Mr. Gervase Cary Elwes, sang an excellent topical song, attired in a quaint garb covered with interrogations, and carrying an electric telegraph-post in her hand. Lady Maud Warrender, as &quot;Pity,&quot; advanced from a barge that had just arrived, and sang a doleful ditty which made one wish &quot;Pity&quot; might combine a sense of gaiety. But as Mrs. Willie James, in the part of &quot;Mercy,&quot; dressed as a nurse, recited some bright lines anent Tommy, to the accompaniment of distant fifes and drums, the audience decided to take this as a satisfactory compensation.

All being now harmoniously arranged, &quot;War&quot; performed a sleight-of-hand feat, divested herself of her red dress, her headgear of flaming serpents, and her glistening breastpiece, and appeared in virgin white, crowned with roses, as “Peace,&quot; surrounded by “Music&quot; in a gorgeous gown of gold tissue, by “Painting,&quot; “Science,&quot; and “Literature.&quot; A pleasant finaleof gay music brought the Masque to a close, and left a decidedly agreeable and novel impression behind it.

Tableaux then followed, all more or less well grouped by well-known artists, and represented by beautiful women of Society. Among the familiar faces were Lady St. Oswald, Lady Mary Sackville, Miss Agatha Thynne, Mrs. Fitz Ponsonby, Lady Maitland, Madame von André, &amp;c., but neither Lady Helen Vincent, Lady De Grey, Lady Cynthia Graham, the Duchess of Portland, nor many other well-known and lovely ladies took part in the performance.

Finally, came the Patriotic Tableau, which had evidently engaged all the energies of the organisers of the fête. On a high throne, with a most realistic lion, open-mouthed and fierce-looking, beside her, sat Lady Westmoreland as &quot;Great Britain,&quot; a stately and dignified figure in white satin, draped in a red cloak and crowned with a large wreath of laurel. The stage on each side was lined by genuine stalwart Guardsmen, and to the sound of lively martial music, composed and conducted by Sir Arthur Sullivan, slowly advanced a procession of Great Britain's dependencies, figured by ladies magnificently costumed, their long jewelled trains borne by two little pages in cloth of gold brocade coats, with black silk legs. Very beautiful were the blendings of the colours in this tableau, artistically designed by Mr. Percy Anderson. Lady Claude Hamilton, as &quot;British Columbia,&quot; moved with stately gait in a robe of palest green; Lady Feo Sturt glittered barbarically with jewels; her headdress and her bosom were covered with gems. As the typical representative of &quot;India,&quot; she was dressed in apricot colour and bore branches of hibiscus in her hands. Mrs. Hwfa Williams, in blazing red, carried a parrot and some red flowers. The Hon. Barbara Lister looked lovely and picturesque in her violet robes under a massive wreath of wisteria blossoms; Lady Raincliffe, wearing a curious high head-dress, was dressed in white to represent &quot;Canada.&quot; &quot;Rhodesia&quot; made one of the prettiest figures in her khaki gown and cloak, with the coquettish hat and feathers and the red trimming associated with the Colonial Volunteers. &quot;Natal&quot; appeared appropriately clad all in black, while little &quot;Nigeria,&quot; for the nonce, wore spotless white robes. /

Miss Muriel Wilson spoke an ode, and looked striking in apricot and white, with a high diamond crown and a long standing-up white feather. None of the ladies suffered from shyness; they showed thorough acquaintance with the stage, and moved easily thereon. In fact, costumes, arrangements, music, and the glorious feast of beauty left nothing to be desired.

The final impression in one's mind was that the stage produces strange effects. It idealises some faces, hardens others, and alters many. The large wreaths, almost grotesque in size, proved eminently becoming, and the Grecian draperies carried away the palm for beauty. After them our modern dress seems stiff, angular, and inartistic. The whole performance was one to be commended, and will no doubt be as successful financially as it was from the aesthetic and spectacular point of view.

Mrs. James Stuart Wortley, who died last week, will be regretted by every class of society. This lady, a beauty in her youth, devoted the latter part of her life entirely to works of charity. She founded the East London Nursing Society, to the tender and skilful ministrations of which many a poor woman owes her return to health, and in every philanthropic scheme, emigration, the befriending of young servants, and the education of youth, she took a lively interest. Her clear sense, her logical grasp of subjects and her immense activity were of infinite service in everything she undertook, and her memory will smell sweet in the hearts of the many who loved and depended on her.

I really wonder at the patience of the British taxpayer. During the snow of this week Belgravia, Eaton, and other fashionable squares, remained a morass of slush, ice, and half-melted snow. The pavements as slippery as glass had not been cleansed, and only at the risk of one's life one made one's way from street to street.&lt;ref&gt;Greville, Lady Violet. &quot;Place aux Dames.&quot; ''The Graphic'' 17 February 1900, Saturday: 7 [of 40], Col.1a–2a, 2c [of 3]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0000057/19000217/008/0007 (accessed July 2019). [Col. 2c only for the last 2 paragraphs, not really relevant to Muriel Wilson]&lt;/ref&gt;{{rp|Col. 1a-2a}}&lt;/blockquote&gt;

'''25 January 1900, Thursday'''

David Lindsay, [[Social Victorians/People/Crawford and Balcarres|Lord Balcarres]] and Constance Lilian Pelly married:
&lt;blockquote&gt;
MARRIAGE OF LORD BALCARRES.

The marriage of Lord Balcarres, M.P. for North Lancashire, eldest son of the Earl of Crawford of Balcarres House, Fife, and Haigh Hall, Wigan, to Miss Pelly, daughter of the late Sir H. Peily, Bart., and granddaughter of the Earl of Wemyss, was solemnised yesterday (Thursday) at St Margaret's Church, Westminster, in the presence of a large gathering of friends.

Among the invited guests were the Earl and Countess of Crawford, the Dowager Countess of Crawford, the Earl of Wemyss, Lord and Lady Elcho, the Hon. E. Lindsay, the Hon. Lionel Lindsay, the Hon. Ronald Lindsay, Lord and Lady Cowper, Mr. A. J. Balfour, the Hon. L. Greville, and many othsrs. The service was fully choral, and was conducted by the Bishop of Stepney, assisted by the the Rev. Canon Gore. Mr Yorke, the stepfather of the bride, gave her away. She wore a dress of white velvet, draped with old Brussels lace, the gift of the Dowager Countess of Crawford: chiffon veil and wreath of natural orange blossoms. Her only ornament was a Maltese cross of diamonds, also the gift of the Dowager Countess of Crawford.

There were nine bridesmaids. Miss Pelly, sister of the bride) [sic], the Hon. Mary Vasey, the Hon. Cynthia Charteris, Miss Brodrick, Miss Sybil Brodrick, Miss Benita Pelly, the Hon. Aline Menjendie, Miss Daisy Benson, and Miss Madeline Bourke. They were attired alike in costumes of white de chine, with lace insertions, with blue chiffon hat, trimmed with plumes of white and blue ostrich feathers. They carried bouquets of violets, and wore red enamel brooches with diamond centres and pearl drops, the gifts of the bridegroom. The Hon E. Lindsay supported his brother as best man.

At the conclusion of the ceremony the guests drove to the town residence of the bride's mother in Queen Anne's Gate, where the wedding reception was held. Later in the day the newly-married couple left town for Wrest Park, Ampthill, kindly lent them for the honeymoon by Earl and Countess Cowper. Princess Louise (the Marchioness of Lorne) sent the bride a handsome silver basket as a wedding present.&lt;ref&gt;&quot;Marriage of Lord Balcarres.&quot; ''Dundee Courier'' 26 January 1900 Friday: 4 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000164/19000126/105/0004.&lt;/ref&gt;
&lt;/blockquote&gt;

===February===
1900, February, a brief account of the Matherses' Isis ceremony appeared in &quot;the New York periodical the ''Humanist'', February 1900&quot; (Howe 201).

==== 15 February 1900, Thursday ====
[[Social Victorians/Wilson Chesterfield Wedding 1900-02-15|Enid Wilson and the Earl of Chesterfield Wedding]]
==== 27 February, 1900, Tuesday ====
Mardi Gras

===April 1900===

==== 8 April 1900, Sunday ====
Palm Sunday

====14 April 1900, Saturday====
Wynn Westcott assumed W. A. Ayton was on, as he wrote, &quot;the Committee to investigate the G. D. which contains Yeats, Bullock and I suppose Ayton&quot; (Howe 217).

====20 April 1900, Friday====
The R.R. et A.C. was code named Research and Archaeological Association (Howe 226)

====21 April 1900, Saturday====
The Inner Order of the Golden Dawn met at 116 Netherwood Road, West Kensington (Howe 227).

==== 27 April 1900 ====

===== The Thames Salmon Experiment =====
&lt;blockquote&gt;The fact that they were taking part in what may in after years be considered an historical event was no doubt the cause of the little crowd which gathered round Teddington Weir on Shakespeare's day. It is getting on for half a century since Stephen Ponder and Frank Dockland hatched out some thousands of salmon eggs, at Kingston-on-Thames and South Kensington respectively, and turned the resulting fry into the Thames. In the light of our present knowledge the failure of their experiments was a foregone conclusion; but that no salmon were found ascending the river in after years was very generally considered a sufficient proof that the Thames was for various reasons no longer capable of becoming a salmon river. In the sixties the art of rearing healthy fry was only beginning to be understood, and the fearful mortality which takes place among infant Salmonidæ both in stew and river was by no means appreciated. It is the A B C of modern fish culture that even if some thousands of ordinary brown trout fry are turned into a suitable stream successful results cannot be, as a rule, expected. The yearling form is invariably recommended. Our greatest experts now hold the opinion that, if salmon rivers are to be stocked by means of fry, the little fish must be placed in large quantities in the head-waters, and by large quantities is meant not thousands or even hundreds of thousands, but millions. The Thames, however, is not in its characteristics an ordinary salmon river. For many years coarse fish have been preserved in the interests of the angler; thus pike, perch, chub, and barbel, all fish of cannibalistic habits, are so numerous that if fry were placed in the headwaters they would have to run the gauntlet through considerably over a hundred miles of current in which voracious fish are plentiful. Dangers of pollution above London can be put out of the reckoning, for, owing to the water supply being largely taken from the river, the duty has been placed upon the Thames Conservancy of stopping pollution of all kinds above the intake of the metropolitan water companies. The river below London, however, still presents many dangers to fish owing to pollution from manufactories, gas and chemical works, though the London County Council have done much towards improving matters. The tideway is in appearance infinitely cleaner now than it has been for many years, and the fact that smelts can push their way up through portions of the river which it was believed would prove fatal to fish, while not being conclusive proof, certainly gives fair grounds for hope that the young salmon may descend to the sea in safety.

Though the tideway has much improved in one respect, it has, in another, seriously deteriorated, for, owing to imperfect dredging, the channels have silted up. At certain states of the tide even steamers of light draught churn up the foul deposits at the bottom, and the water becomes charged with matter of a very offensive and possibly, from the salmon's point of view, dangerous character. The Royal Commission which is now inquiring into the matter may lead ultimately to the formation of a new authority for the port of London with power and funds to deepen the river. Should this body be brought into existence, and extensive dredging be carried out, the chances of salmon running up the Thames will be materially increased. Had it been decided to place fry by the million in the headwaters of the Thames, there would still have remained the almost insurmountable difficulty of getting a sufficient number of eggs. Now that salmon have become so scarce, local fishery authorities are most reluctant to allow ova to bo taken from their districts, and until we have a fishery department with a river providing a supply of spawning fish and a hatchery of its own, it is hardly likely that an adequate supply of salmon eggs will ever be forthcoming for the purpose of restocking any of our large rivers. The Thames Salmon Association unquestionably had a most difficult problem to grapple with, and the committee's decision to place no fry in the river was undoubtedly a wise one under all the circumstances. The system adopted by the association is to rear the fry until they put on smolt livery, and then turn them into the upper portions of the Thames tideway; they thus largely escape danger from pike and other predatory fish. It is only [Col. 1c–2a] reasonable to assume that one smolt placed in the tideway is worth some thousands of fry turned in higher up. We may here remind our readers that the association was formed in 1899, and in July of that year the subject was discussed at a public meeting held at the Mansion House under the support of the Lord Mayor. In the previous year there had been a meeting of a few persons interested in the question, called together by the [[Social Victorians/People/Bourke|Hon. Algernon Bourke]], at White's Club; but the leading spirit of the present association is Mr W. H. Grenfell, M.P. What success has been obtained is largely owing to him and to the enthusiasm and liberality of Mr W. Crosbie Gilbey, who has devoted the whole of his trout hatchery at Denham, on the Misbourn, a tributary of the Colne, to hatching salmon for the association, Mrs Goodlake, his neighbour, rendering very valuable assistance. It is an interesting fact that the great majority of the little fish which were turned into the Thames on Tuesday were Irish, having been presented to the association by Mr W. L. Moore from his Boyle and Bank fishery. A smaller number were obtained from Scotland.

The result of the first year's hatching and rearing is about 8000 samlets. Of these, only the 600 which were turned into the Thames had assumed, or partially assumed, smolt livery, and there are hopes of turning in some additional hundreds this year; but the bulk of the 8000 will have to be retained until their second year at Denham, when we may expect most of them to put on the silver vesture which, with a certain restlessness, may be considered a decisive indication that they are ready to descend to the sea. How many of the 600 will return? It is difficult even to make a surmise on the point, the element of chance being so very considerable. As the little fish descend the great estuary of the Thames they may be met by the sudden outpour of a manufactory's destructive refuse; but, on the other hand, they may escape all dangers and reach the sea in safety. When there they have, of course, many natural enemies to meet, and at the best we could only reasonably expect a small percentage to return to their river of adoption. Those who are well acquainted with fish culture will perhaps say that the scale upon which the Thames Association is working is not likely to restock the Thames with salmon, but the actual restocking of the river is not the immediate object of the committee. It is well to understand that what is now being done is merely in the nature of an experiment to test the question whether salmon can exist in the Thames, passing down the estuary as smelts, finding their river again, and returning to fresh water as mature fish. If a few salmon are sooner or later seen in the river then the experimental stage will be probably considered at an end and the question of how to stock the Thames on an efficient scale will have to be considered. When that time arrives there will no doubt be questions arising as to the interests of those for whom coarse fish have been so long preserved; for it is not unnatural to suppose that, should the Thames become again an important salmon river, fishery rights which now lie dormant will be asserted, and pike and other coarse fish will not be viewed with favour. Meanwhile the Association will be turning out its few thousand smelts annually for the next three or four years, and questions of conflicting interests are not likely to arise yet awhile, though if, by happy fortune, a single returning grilse were to be taken in the Thames on its return from the sea before the end of the coming summer, the public interest would be instantly aroused and events would march rapidly.&lt;ref&gt;&quot;The Thames Salmon Experiment.&quot; ''Field'' 27 April 1901, Saturday: 28 [of 76], Col. 1b–2b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002446/19010427/266/0028. Print title: ''The Field, The Country Gentleman's Newspaper'', p. 562.&lt;/ref&gt;&lt;/blockquote&gt;

===May 1900===
====26 May 1900, Saturday====
Arthur Sullivan is visited by &quot;Sir George Martin, the organist at St. Paul's Cathedral, and Colonel Arthur Collins, one of the royal equerries&quot; to get him to write a Te Deum thanking God for the end of the Boer War (Ainger, Michael. Gilbert and Sullivan: a Dual Biography. P. 381.).

====30 May 1900, Wednesday====
Derby Day.

According to the Morning Post, &lt;quote&gt;The Derby Day. / The Archbishops of Canterbury and York hold a Reception of Colonial and Missionary Church Workers in the Great Hall of the Church House, 4.30 to 6.30. / ... May Fair and Bazaar, St. George's Drill Hall, Davies-street, Berkeley-square, opened by Lady Edward Spencer Churchill, 2.30.&lt;/quote&gt; (&quot;Arrangements for This Day.&quot; The Morning Post Wednesday, 30 May 1900: p. 7 [of 12], Col. 6C)

===June 1900===
Summer 1900: WBY summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

==== 3 June 1900, Sunday ====
Whit Sunday (Pentecost)

Whitsun party at Sandringham House, described by Lord Knutsford in his letters and summarized by Anita Leslie, whose parent's generation remembered some of these people Knutsford mentions as present:

* The Prince and Princess of Wales
* Princess Victoria
* Other daughters of the Prince and Princess of Wales
* Lord Knutsford
* [[Social Victorians/People/Ripon|Lord and Lady Gladys de Grey]]
* Luís De Soveral
* Tosti
* [[Social Victorians/People/Durham|Hon. George Lambton]]
* [[Social Victorians/People/Churchill|Lady Randolph Churchill]]
* [[Social Victorians/People/Holford|Holford]]
* Lady Musgrave

Leslie's summary of Knutsford's letters:&lt;blockquote&gt;The Whitsun party that year included Lord and Lady de Grey, De Soveral, whose caustic wit always lightened Edward's humour, Tosti, the famous baritone-songwriter (Alexandra and her daughters were so musical — strumming away ''à quatre mains'' while Totti's voice made chandeliers vibrate in after-dinner songs), the Hon. George Lambton (racing trainer), and Lady Randolph Churchill, &quot;just back from her hospital ship which had been a boon in South Africa, but fractiously insisting she is going to marry George Cornwallis-West.&quot;

Lord Knutsford describes the chattering guests travelling in that special train coach from St. Pancras to Wolverton Station where the house party was met by royal carriages with officious flunkeys in red livery who dealt with the luggage — and ''such'' luggage! Big trunks had to be brought for a few days' stay so that the correct attire could be produced for every meal and outing.

How exciting to drive through a forest of rhododendrons and to disembark in front of Sandringham House. The royal host and hostess stood in the hall to welcome their guests. After handshakes Queen Alexandra sat down to pour tea. Dinner was at 9 &lt;small&gt;P&lt;/small&gt;.&lt;small&gt;M&lt;/small&gt;. (at Sandringham all clocks were kept half an hour ahead of time). Footmen informed the gentlemen what waistcoats were to be worn. Ladies' maids scurried to the ironing rooms. At nine, having assembled in the drawing room, each man was told whom he must escort into dinner and where to sit. This saved hesitation and embarrassment. On this occasion Knutsford describes the Prince giving his arm to Lady de Grey, while Alexandra walked beside De Soveral and Lord de Grey escorted the unmarried Princess Victoria. There were, of course, no cocktails, but exquisite wines accompanied each course. The Prince never drank more than a glass or so of claret at dinner and a brandy after the last course.

When the ladies left the dining room cigarettes and cigars were brought by footmen. Heavy drinking was never encouraged, and / after half an hour the gentlemen moved to the drawing room to chat with the ladies, until Alexandra rose and they retired to their bedrooms where the ladies' maids would be waiting to unlace them from their gorgeous satin and velvet gowns. Hard as the existence of a servant might be, they were perhaps consoled by the colossal meals offered in recompense for late hours. A five-course breakfast could be consumed by every scullery maid if she so desired, and many a working-class mother strove to &quot;get her daughter's knees under a good table.&quot;

When the ladies had disappeared upstairs the men went to the billiards room, where the Prince, who idolised his dogs, would roar with laughter when his black bulldog nipped the legs of players. No one could go to bed before Edward, but at twelve-thirty he would certainly retire. There was no thought of any hanky-panky after hours at Sandringham. That would have been considered bad taste and an insult to the royal hostess.

On Sunday morning the breakfast gong sounded at 10 &lt;small&gt;A&lt;/small&gt;.&lt;small&gt;M&lt;/small&gt;. Then came church and a stroll in the garden until lunch at one-thirty. After a fairly heavy meal the ladies went upstairs to change into walking skirts and strong boots. The whole party then underwent a slow three-hour walk to the kennels and stables and farm. Talk was almost entirely about animals — dogs, pedigree cattle and, of course, race horses. Knutsford noticed Alexandra's &quot;touching girl-like love&quot; for every stone and corner of Sandrringham. She reminded him of &quot;a bird escaped from a cage.&quot;

Certainly the royal pair were never so happy as in this big Norfolk house, which they regarded as home, but guests grew weary of trying to do the right thing. Knutsford found dinner very wearing, with the conversation in mingled English and French: &quot;they drop from one to another in the same sentence.&quot;

Then came the local Whitsunday sports. Off drove the house party — Lady de Grey and Holford in the first carriage with Edward. Knutsford found himself in the second carriage with Princess Victoria and Lady Randolph Churchill and Lady Musgrave. The ladies wore coloured blouses and contrasting skirts and jackets over their blouses, white gloves and feather boas. A brisk wind nearly blew off their huge hats. Lady Musgrave in particular had difficulty with her concoction. &quot;Send it to the bazaar!&quot; cried Alexandra, and everyone roared with laughter.

Sandringham parties were called &quot;informal,&quot; but what a relief, nevertheless, when they all got back to the station in those regal carriages followed by the four horse-drawn vans of luggage.

In this spring of 1900 the visitors departed to their homes full to / the brim of food and anecdote. Jennie, who had been argumentative all weekend, would almost immediately marry her young George. Gladys de Grey would get on her newly installed phone to admirer number one, the Hon. Reginald Listen, or if he was not available to admirer number two, Sir John Listen-Kaye. Ladies were now able to ring the men up and guardedly converse instead of sending dangerous notes. Servants might overhear but there would be nothing ''on paper''.&lt;ref&gt;Leslie, Anita. ''The Marlborough House Set''. Doubleday, 1973.&lt;/ref&gt;{{rp|195–197}}&lt;/blockquote&gt;

====26 June 1900, Tuesday====
There was apparently a regular celebration of Arthur Collins' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902.

==== 28 June 1900, Thursday ====
Lady Randolph Churchill and George Cornwallis-West married at St. Paul's, Knightsbridge.&lt;ref&gt;Martin, Ralph G. ''Lady Randolph Churchill : A Biography''. Cardinal, 1974. Internet Archive: https://archive.org/details/ladyrandolphchur0002mart_w8p2/.&lt;/ref&gt;{{rp|220–223}}

===July 1900===

==== 17 July 1900, Tuesday ====
A number of Society women took part in the Children's Fete in support of the National Society for the Prevention of Cruelty to Children:
&lt;blockquote&gt;
&lt;p&gt;In the grounds of the Royal Botanic Society yesterday afternoon a very delightful Children's Fete was organised by the Countess of Ancaster in aid of the National Society for the Prevention of Cruelty to Children. The good work of the society, of which the Queen is patron, is well known, and the need for its existence is emphasised by the fact that, whereas in the year 1888–89 it dealt with only 737 cases, the number increased to 28,165 in 1898–99. Its operations are, of course, limited by the funds placed at its disposal, and though the income last year amounted to £51,300, a still larger sum is needed to meet all the claims which come before the society. In the organisation of yesterday's fête Lady Ancaster was assisted by the Ladies' Committee for London, of which the Hon. Mrs. Stephen Coleridge is hon. secretary. The list of stewards included Lady Blanche Conyngham, Lady Florence Bridgman, Lady Grizel Cochrane, Lady Victoria Grey, Lady Sybil Grey, Lady Agnes Noel, Lady Norah Noel, Lady Elizabeth Northcote, Lady Alice Willoughby, the Hon. Ethel Fraser, Miss Aermonda Burrell, Miss Nina Hill, Miss Ceciie Drummond, Miss Euphemia Drummond, and Miss Linda Oppenheim.&lt;/p&gt;

&lt;p&gt;The fête opened with a procession of children, a large number being in fancy costume, and many bearing wands and floral symbols. This was the prelude to the Floral Feast and many other events. The feast was arranged by Sybil Marchioness of Queensberry and Mrs. Wordsworth, and among the &quot;flowers&quot; who took part were Miss E. Grove (white lily), Misses Olline and Katherine Wyndham-Quin (tiger lily and bluebell), Misses Pamela, Sibyl, and Madeline Adeane (sweet pea, Canterbury bell, and daffodil), the Hon. May Charteris (rose), Miss Joyce Knatchbull-Hugessen (snowdrop), Miss Elsie Gorell Barnes (wild rose), Miss A. Smjth (daisy), Miss Currie (convolvulus), and Miss Clare Tennant (daisy). Master Terence Grove, the Hon. Ivor Charteris, Master Gorell Barnes, Master Desmond Smith, Master Edward Tennant, the Hon. Thomas Boscawen, Master Harold Farquhar, and Master Chanler also assisted.&lt;/p&gt;

&lt;p&gt;A gavotte arranged by Lady Helen Stewart was a very pretty feature, among those taking part being children of Lady Aline Beaumont, Lady Wenlock, Lady Doreen Long, Lady Meysey-Thompson, Lady Eden, Lady Gertrude Astley Corbett, and others.&lt;/p&gt;

&lt;p&gt;The Gainsborough quadrille, arranged by Lady Milner and Mrs. Wordsworth, was most charmingly executed by the Hon. M. and R. Thellusson, Miss Murray, Misses Beckett, the Hon. E. Gerard, Miss Stanley, Miss Muir Mackenzie, Miss Evelyn, Miss Padelford, Miss Hadow, Miss Grosvenor, the Hon. Marie Hay, and the Hon. Hilda Chichester.&lt;/p&gt;

&lt;p&gt;For the Highland dances the Countess of Ancaster and Mrs. Wordsworth were responsible, Miss Wickham, Miss Le Blanc, and the Masters Fairbairn doing full justice to the music of Pipe-Major Fraser, of the Scots Guards.&lt;/p&gt;

&lt;p&gt;A Pavane arranged by Lady Victoria Grey, an Irish jig by Mr. and Mrs. d'Egville, and pas seuls by Mrs. Walter Cave and Mrs. Gerald Maltby were most attractive. Of the pas seuls, the Spanish dance by Miss Hersey Maltby, and the gavotte by Miss Violet Asquith were greatly admired, and the same young ladies also performed a pas de deux.&lt;/p&gt;

&lt;p&gt;Perhaps the favourite events of the afternoon were the flower dance and the maypole dance, both being, as one might say, intermittent, recurring at intervals, for the young people, despite the heat, never seemed to tire. Lady Florence Astley was responsible for the flower dance, and the children who took part were the representatives of Lady Alwyne Compton, Lady de Trafford, Mrs. Stanley Wilson, the Countess of Yarborough, Lady Eden, Mrs. Hartmann, Lady Naylor-Leyland, Lady Barnard, the Hon. Mrs. Lambton, Lady Constance Combe, Lady Newton Butler, the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], the Hon. Mrs. Alwyne Greville, Lady Gertrude Astley Corbett, the Hon. Mrs. Pelham, Mrs. Walter Campbell, Lady Meysey-Thompson, the Duchess of Wellington, Lady Hastings, and Mrs. Parkinson Sharpe. This dance was given on a platform under the shade of the trees on the north-west side of the gardens, and was watched with much delight by the crowd of spectators seated around. The maypole, gaily adorned with the traditional ribbons, was erected on the opposite side of the grounds above the lake, and the dances were supervised by the Hon. Mrs. Cecil Bingham and Miss Miller. Most of the children were dressed in shades of pink or green.&lt;/p&gt;

&lt;p&gt;Near the maypole a flower market and a fruit market were disposed in a variety of tastefully-decorated stalls. Mrs. Charles Wilson arranged the flower market, and was assisted by Lady Mary Willoughby, Miss Gwladys Wilson, Lady Aldra Acheson, Lady Marjorie Carrington, the Countess of Chesterfield, Viscountess Castlereagh, Lady Alexandra Carrington, Lady Mary Acheson, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Mrs. Kenneth Wilson, the Hon. Alexandra Fellowes, Miss Madeline Stanley, Lady Florence Astley, and the [[Social Victorians/People/Bourke|Hon. Mrs. A. Bourke]]. Lady Faudel-Phillips conducted the fruit market, with the assistance of Mrs. Phillip Henriques, Miss Hope, Miss Cockerell, and the Misses Faudel-Phillips.&lt;/p&gt;

&lt;p&gt;In the course of the afternoon there was a juvenile cricket match between Lady Evelyn Ewart's eleven and an eleven from Mr. E. T. Bull's School, which resulted in a draw. The band of the Royal Artillery played a delightful selection of music, led by Cavalier Zavertal. The whole fête was most successful.&lt;/p&gt;

&lt;p&gt;The Princess of Wales, attended by Lady Suffield and Sir Dighton Probyn, visited the gardens shortly after four o'clock and remained until half-past five. Her Royal Highness, escorted by Lady Ancaster, witnessed the maypole and flower dances and other events of the fête, and on leaving expressed herself as having been greatly delighted with the juvenile revels.&lt;ref&gt;&quot;For the Protection of Children. A Charming Fête.&quot; ''Morning Post'' 18 July 1900, Wednesday: 5 [of 12], Col. 5a–b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19000718/033/0005. Same print title and p.&lt;/ref&gt;&lt;/p&gt;&lt;/blockquote&gt;

====27 July 1900, Friday====
The [[Social Victorians/People/Albert Edward, Prince of Wales|Prince of Wales]] had dinner at the Arthur Wilsons’:&lt;blockquote&gt;[[Social Victorians/People/Arthur Stanley Wilson|Mr and Mrs Arthur Wilson]] were honoured with the presence of the Prince of Wales at dinner on Friday night. Amongst the guests were the Portuguese Minister, Count Mensdorff, Duke of Roxburghe, Lady Georgina Curzon, Captain and Lady Sarah Wilson (arrived that morning from South Africa), Lord and Lady Tweedmouth, Lord Herbert Vane Tempest, Viscount Villiers, Lady Norreys, Lady Gerard, [[Social Victorians/People/Keppel|Hon Mrs Keppel]], Sir Edward and Lady Colebrook, Mr and Mrs Grenfell, Lady Lister Kaye, Mrs Arthur Paget, Mr and Mrs Arthur Sassoon, Hon. W. Erskine, Mr and Mrs J. Menzies, General Oliphant, Miss Jane Thornewell, Mrs Kenneth Wilson, and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]].&lt;ref&gt;&quot;Social Record.&quot; ''Hull Daily Mail'' 30 July 1900, Monday: 2 [of 6], Col. 5a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000324/19000730/007/0002 (accessed July 2019).&lt;/ref&gt;&lt;/blockquote&gt;

==== 30 July 1900, Monday ====

===== ''Barber of Seville'' at Covent Garden =====
&lt;blockquote&gt;In spite of the fast waning season there was a very considerable audience at Covent Garden to witness the performance of the &quot;Barber of Seville&quot; last Monday. The honours of the evening lay chiefly between Mine. Melba and Signor de Lucia, while M. Edouard de Reszké was a very humorous and entertaining ''Basilio''. Mme. Melba sang part of the mad scene (from &quot;Lucia di Lammermoor,&quot; in what is popularly known as the &quot;Music Lesson Scene&quot;; needless to say she was vociferously applauded, and for an encore she sang Tosti's &quot;Mattinata,&quot; accompanying herself very charmingly. Lady de Grey was in her box, and wore cream colour with a pink rose in her hair; Lady Charles Beresford was in Lily Duchess of Marlborough's box; and the Countess of Carnarvon wearing black, with touches of heliotrope and diamonds in her hair, was in Mr. Alfred Rothschild's box. Among others present were Lady Cynthia Graham, Lady Colebroke wearing pink, Lady Chelsea, and Mrs. Arthur Paget; Mrs. Higgins in white, Mrs. Hwfa Williams, and [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]]; Mrs. Murray Guthrie, Lord Westbury, and Captain Hedworth Lambton. The Princess of Wales, with the Duke of Sparta, was in the Royal box.&lt;ref&gt;&quot;'Barber of Seville' at Covent Garden.&quot; ''Gentlewoman'' 4 August 1900, Saturday: 20 [of 52], Col. 1c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19000804/104/0020. Same print title, p. 144.&lt;/ref&gt;&lt;/blockquote&gt;

===October 1900===
====31 October 1900, Wednesday====
Halloween.
===November 1900===
====5 November 1900, Monday====
Guy Fawkes Day
====9 November 1900, Friday====
A debutante dance for Miss Helyar:&lt;blockquote&gt;In honour of the coming of age of Miss Helyar, a small dance was given by Lady Savile, at Rufford Abbey, last night. The number of invitations was not so large as it would have been but for the war. The house party included Mrs. and Miss Cavendish Bentinck, Lady Juliet Lowther, Lady Evelyn Ward, Lady Mabel Crichton, Mrs Kenneth Wilson, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Sir Berkeley Sheffield, Miss Sheffield, Lord Hyde, Lord Herbert, the Hon. B. Ward, the Hon. E. FitzGerald, the Hon. W. Erskine, Mr. Laycock, Captain Brinton, the Hon. George Peel, Mr. Harris, Captain Tharp, Captain Heneage, and the Hon. G. Portman.&lt;ref&gt;&quot;Court and Personal.&quot; ''Yorkshire Post'' 10 November 1900, Saturday: 6 [of 14], Col. 4c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000687/19001110/099/0006 (accessed July 2019).&lt;/ref&gt;&lt;/blockquote&gt;

====27 November 1900, Tuesday====
Arthur Sullivan's funeral:&lt;blockquote&gt;At eleven o'clock on Tuesday, November 27th, the [366/367] funeral procession set forth from Victoria Street, Westminster, on its mournful way, first to the Chapel Royal, St. James's, where, by command of the Queen, part of the Burial Service was to take place, and thence to St. Paul's. Throughout the line of route flags drooped at half-mast, whilst beneath them people crowded in their thousands, bare-headed and in silence, waiting to pay their last tribute of respect and gratitude to the lamented master whose genius had done so much to brighten their lives for the past five-and-twenty years. [new paragraph] Into the Royal Chapel, where Arthur Sullivan had begun his career as a chorister, was borne the casket containing his remains. On either side stood men and women famous in society and the wider world of Art in all its branches. The Queen was represented by Sir Walter Parratt, Master of Music, who was the bearer of a wreath with the inscription: &quot;A mark of sincere admiration for his musical talents from Queen Victoria.&quot; Sir Hubert Parry represented the Prince of Wales; the German Emperor was represented by Prince Lynar, Attache of the German Embassy; Prince and Princess Christian by Colonel the Hon. Charles Eliot, and the Duke of Cambridge by General Bateson.

Among the congregation at the Chapel Royal were seen the United States Ambassador; the Earl and Countess of Strafford; Theresa, Countess of Shrewsbury; the Countess of Essex; Lord Glenesk; Lord Rowton; Lord Crofton; Lady Catherine Coke; the Dean of Westminster; Lady Bancroft; Lady [367/368] Barnby; Mr. Arthur Chappell; Mr. and Mrs. F. C. Burnand; Mr. Arthur W. Pinero; Mr. Haddon Chambers; Lieutenant Dan Godfrey; Signor Tosti; Mr. George Grossmith; Mr. Rutland Barrington; Miss Macintyre; Mrs. Ronalds; Canon Duckworth; Lady Lewis; Miss Ella Russell; Mr. Augustus Manns; Mr. Charles Wyndham; Captain Basil Hood; the Chairman and Secretary of Leeds Musical Festival; and Representatives of various British Musical Associations.

The Pall-bearers were Sir Squire Bancroft, Mr. Francois Cellier, Colonel A. Collins (one of the Royal Equerries), Sir Frederick Bridge, Sir George Lewis, Sir Alexander Mackenzie, Sir George Martin, and Sir John Stainer. [new paragraph] he chief mourners were Mr. Herbert Sullivan (nephew), Mr. John Sullivan (uncle), Mrs. Holmes, and Miss Jane Sullivan (nieces), Mr. Wilfred Bendall (Sullivan's secretary), Mr. B. W. Findon, Mr. Edward Dicey, Mr. C. W. Mathews, Mrs. D'Oyly Carte, Dr. Buxton Browne, Mr. Arthur Wagg, Mr. Fred Walker, Mr. Dreseden and Sir Arthur's servants. [new paragraph] Much to their regret, neither Mr. Gilbert nor Mr. Carte was able to attend the funeral. The first was on the Continent for the benefit of his health, the second was laid up by serious illness. The present writer also, having been absent from London at the time, has not the advantage of an eye-witness to give a graphic description of the funeral obsequies of his old friend; and so, rather than attempt to paint the picture from imagination, he gladly avails himself [368/369] again of the courtesy of his brother-author who is so generous as to lend the aid of his experience. [new paragraph] In these sympathetic words, Mr. Findon describes the scenes and incidents in which, as a chief mourner, he took part at the Chapel Royal and St. Paul's Cathedral: &lt;blockquote&gt;&quot;. . . As the casket was borne into the Chapel, it was impossible to avoid thinking of those days when Sullivan himself had worn the gold and scarlet coat of a Chapel Royal Chorister, and his sweet young voice had rung through the sacred edifice. Then the world and its honours lay before him, but we doubt if even in the most sanguine moments of impulsive boyhood he imagined the greatness that one day would be his, or that his bier would pass within those honoured walls amid the silent demonstration of a mourning people. The anthem, 'Yea, though I walk through the valley of the shadow of death,' from his oratorio 'The Light of the World,' was beautifully sung, and the pathos of the music bathed many a face in tears, and touched a tender spot in more than one loving heart. Another of the dead master's exquisite thoughts, ' Wreaths for our graves the Lord has given,' brought the Service at the Chapel Royal to an end, and the procession passed on its way to St. Paul's Cathedral, which was crowded with sympathetic spectators.

&quot;Clerical etiquette and cathedral dignity compelled the beginning of the Burial Service anew, and when the coffin had been lowered into the crypt there came the most poignant moment of the long ceremonial. [new paragraph] &quot;Close to the open vault sat the members of the Savoy Opera Company, including his life-long friend, Mr. Francois Cellier, who had been associated as chef d'orchestre with all his comic operas, and, after [369/370] the Benediction had been given, they sang in voices charged with emotion the touching chorus, 'Brother, thou art gone before us,' from ' The Martyr of Antioch.' The effect was quite remarkable, inasmuch as it was one of those incidents which come but rarely in a life-time.&quot;&lt;/blockquote&gt;It was not in London alone that people mourned for Arthur Sullivan on that November day. Throughout Great Britain and Ireland, on the Continent of Europe, in America and farther across the seas, thousands of fond and grateful hearts ached with grief at the thought that England's dear master of melody had passed away into the silent land. From high-born personages and from people of low estate came floral emblems, wreaths, crosses, and lyres innumerable. Conspicuous among them was a beautiful harp of purple blossoms with strings — one broken — of white violets. To this offering was attached a card bearing the inscription:&lt;blockquote&gt;In Memoriam

ARTHUR SEYMOUR SULLIVAN

Born 13 May, 1842. Died 22 Nov., 1900

FROM MR. D'OYLY CARTE'S &quot;ROSE OF PERSIA&quot; TOURING COMPANY IN TOKEN OF THEIR AFFECTIONATE REGARD
&lt;poem&gt;Dear Master, since thy magic harp is broken,
Where shall we find new melodies^ to sing?
The grief we feel may not in words be spoken;
Our voices with thy songs now heav'nward wing.
Whilst on thy tomb we lay this humble token
Of love which to thy memory shall cling.&lt;/poem&gt;
BELFAST,

24th November, 1900.&lt;/blockquote&gt; [370/371] These simple lines but half expressed the love and esteem in which Sir Arthur Sullivan was held by all whose privilege it was to have been associated with him, and to have served, however humbly, his proud and brilliant life-cause.&lt;ref&gt;Cellier, François, and Cunningham Bridgeman. ''Gilbert and Sullivan and their operas: with recollections and anecdotes of D''. Pp. 366-371. ''Google Books'': http://books.google.com/books?id=Au05AAAAIAAJ.&lt;/ref&gt;&lt;/blockquote&gt;

====30 November 1900, Friday====
The wedding between Lady Randolph Churchill and George Cornwallis West at St. Paul's, Knightsbridge, occurred about this time. [[Social Victorians/People/Muriel Wilson|Muriel Wilson]] attended, as did much of Society.&lt;ref&gt;&quot;Court Circular.&quot; ''Times'', 30 July 1900, p. 6. ''The Times Digital Archive'', http://tinyurl.galegroup.com/tinyurl/AHR8r5. Accessed 20 June 2019.&lt;/ref&gt;

===December 1900===
===25 December 1900, Tuesday===
Christmas Day
====26 December 1900, Wednesday====
Boxing Day
==1901==
===January===
&quot;There were no winter performances of opera at Covent Garden in those times: there was, in 1901, only a summer season&quot; (Baring-Gould II 704, n. 14, quoting Rolfe Boswell).
====1 January 1901, Tuesday, New Year's Day====
====16 January 1901, Wednesday====
Arnold Dolmetsch sent out notices that he was moving to 85 Charlotte Street, Fitzroy Square (Campbell 137-38).

====22 January 1901, Tuesday====
Queen Victoria died at Osborne House, on the Isle of Wight.

====23 January 1901, Wednesday====
Edward VII formally proclaimed “King of Great Britain and Ireland and Emperor of India, Defender of the Faith” &quot;at Temple Bar, on St. Paul's Cathedral steps and at the Royal Exchange.&quot; &quot;The Privy Council met in St. James' Palace at 2 o'clock in the afternoon for the purpose of signing the accession proclamation of Edward VII. The attendance at the meeting of the Council was more than 200.&quot; (Merrill, Arthur Lawrence, and Henry Davenport Northrop. Life and Times of Queen Victoria: Containing a Full Account of the Most Illustrious Reign of Any Soveriegn in the History of the World, Including the Early Life of Victoria; Her Accession to the Throne and Coronation; Marriage to Prince Albert; Great Events During Her Brilliant Reign; Personal Traits and Characteristics That Endeared Her to Her People; Graphic Descriptions of Her Charming Home Life; Noble Qualities as Wife and Mother; Royal Castles; Public Receptions; Wonderful Growth of the British Empire, Etc. To Which is Added the Life of King Edward VII., and Sketches of the Members of the Royal Family. Philadelphia, PA: World Bible House, 1901. Page 437. Google Books: http://books.google.com/books?id=Kx48AQAAIAAJ)

====26 January 1901, Saturday====
Arnold Dolmetsch gave a performance at his new domicile at 85 Charlotte Street, Fitzroy Square (Campbell 137-38).

===February 1901===
====2 February 1901, Saturday====
Queen Victoria’s funeral at St. George’s Chapel, Windsor Chapel. Consuelo (Vanderbilt), Duchess of Marlborough was there: &lt;blockquote&gt;The service itself was magnificent. The stalls of the Knights of the Garter were occupied by the German Emperor and a dazzling array of kings, queens, ambassadors extraordinary, Indian princes, Colonial dignitaries, generals, admirals and courtiers. Consuelo wore the prescribed deep black mourning and crepe veil, which rather suited her, and it had the effect of extracting what she describes as a 'rare compliment' from her husband who remarked: 'If I die, I see you will not remain a widow long' — a conceit which suggests that he was more of his father's son than he cared to acknowledge.

Consuelo later reflected that the funeral of Queen Victoria was a moment when it truly appeared that no other country in the world had an aristocrac so magnificent, nor a civil service so dedicated, which is precisely what was intended. The great doors were flung open as the royal cortege mounted the steps, a boom of distant guns and clanging swords the only sound other than the funeral march, until Margot Asquith broke the reverential silence with a quip. Consuelo thoroughly enjoyed herself at the reception in the Waterloo Chamber afterwards too. (Stuart, Amanda Mackenzie. Consuelo and Alva Vanderbilt: The Story of a Daughter and a Mother in the Gilded Age. New York and London: HarperCollins, 1005. Page 228. Google Books: http://books.google.com/books?id=44mhoIv12rEC)&lt;/blockquote&gt; Also Henry James saw the funeral procession.

====3 February 1901, Sunday====
1901 February 2–4?: Queen Victoria lay in state for 2 days between her funeral and her interment.

====4 February 1901, Monday====
Queen Victoria’s interment at Frogmore Mausoleum, Windsor Great Park.
====23 February 1901, Saturday====
The wedding of Hugh Richard Arthur, 2nd Duke of Westminster and Constance Edwina Cornwallis-West (1901-02-23 Cheshire Observer).

===March 1901===
Sometime in March 1901 Arthur Conan Doyle and Fletcher Robinson &quot;were on a golfing holiday at the Royal Links Hotel at Cromer in Norfolk,&quot; where Robinson told Doyle a Dartmoor legend of &quot;a spectral hound&quot; (Baring-Gould II 113).

Doyle's &quot;The Hound of the Baskervilles&quot; began publication in the ''Strand'' in January 1902.

===April 1901===
====18-20 April 1901, Thursday-Saturday====
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] and Mrs. Beerbohm Tree took part in 3 performances of &lt;quote&gt;Masks and Faces. The matinées have been organized by [[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]], of Tranby Croft, in aid of the local fund of the Soldiers’ and Sailors’ Families Association. It was originally intended that the matinées should have been given in January last, but, owing to the death of Queen Victoria, they were postponed until Thursday, Friday, and Saturday last week. Additional interest was centered in the event, owing to the cast including no less a name than that of Mrs. Beerbohm Tree, while the fact that Miss Muriel Wilson was to appear as Peg Woffington aroused expectation.&lt;/quote&gt; (1901-04-25 Stage)

===May 1901===

==== '''1901 May 30, Thursday''' ====
The London ''Daily Express'' reported on the opening of the Ladies' Dog Show:&lt;blockquote&gt;There was a very large attendance yesterday at the Botanic Gardens for the summer fête of the Ladies’ Kennel Association, which is under the patronage of the Queen, and the charming grounds had quite the aspect of a garden-party at tea-time, when the band played under the trees.

Among well-known exhibitors to be seen were Sir Claud and Lady Alexander, who was showing a number of cats, Lady Aberdeen, Lady Angela Foster, and the Princess de Moniglyon, who took a first prize. Neither Lady Decies nor Lady Maitland was exhibiting on this occasion. Others to be seen were Lady Algernon Gordon-Lennox in black and white, Mrs., Algernon Bourke all in mauve, the Duchess of Newcastle, Mrs. Baillie of Dochfour, and Mrs. Greville.

The Dogs’ Brigade Parade, which takes place to-day at 4.30, will be in aid of the Princess of Wales' Soldiers and Sailors' Widows and Orphans Fund.&lt;ref&gt;&quot;At the Botanic Gardens.&quot; ''Daily Express'' 31 May 1901, Friday: 4 [of 8], Col. 7a [of 7]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/BL/0004848/19010531/086/0004?browse=true https://www.britishnewspaperarchive.co.uk/viewer/BL/0004848/19010531/086/0004]. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;The ''Birmingham Daily Gazette'' has a different list of names:&lt;blockquote&gt;Yesterday the annual show of the Ladies' Kennel Association was held in the Royal Botanical Gardens, Regent's Park, and attracted a highly fashionable gathering. Among the ladies represented were Princess Victor Dhuleep Singh, Princess Sophie Dhuleep Singh, the Marchioness of Nottingham, the Duchess of Sutherland, the Countess of Aberdeen, Lady Evelyn Ewart, Lady Helen Forbes, the Hon. Mrs. Baillie, Lady Moor, the Hon. Mrs. Alwyne Greville, the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], Lady Alwyne Compton, Lady Chetwode, Lady Cathcart, Lady Angela Forbes, the Hon. Mrs. Fellowes, Lady Gooch, Princess de Montglyon, and Viscountess Southwell, Mrs. Samuelson, Miss Serena, Mrs. Bosanquet, Mrs. Williams, and Mrs. Ingle Bepler. Cats and poultry are also exhibited.&lt;ref&gt;&quot;Ladies' Dog Show.&quot; ''Birmingham Daily Gazette'' 31 May 1901, Friday: 6 [of 8], Col. 5b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000667/19010531/124/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1901===
Summer 1901: William B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).
====17 June 1901, Monday====
&lt;quote&gt;The &quot;Women Writers&quot; held their dinner at the Criterion on Monday, the 17th. Now Mr. Stephen Gwynn, in his paper entitled &quot;A Theory of Talk,&quot; roundly asserts that women are less amusing than men. He says that there is no reason in nature why they should be, but that their inferiority is obvious. He points out that &quot;thirty or forty men will meet at seven o'clock, dine together, and pass the evening very agreeably till midnight. Imagine thirty or forty women called upon to do the same; would they be able to amuse themselves?&quot; It seems almost a pity that the exclusiveness of the women writers would not allow Mr. Gwynn personally to observe whether they were amused or bored on Monday night. In number there were nearly two hundred, and there certainly did not appear to be any lack of enjoyment or of laughter, but then it is also a fundamental belief with men that women are early adepts at hiding their true feelings. / Lucas Malet occupied the chair, and her carefully prepared speech was read out by Miss Sydney Phelps. Standing at the base of the statue of one of the world's greatest authors, and that, we regret to say, not a woman but a &quot;mere man,&quot; Miss Phelps, speaking for Lucas Malet, said there was good cause for women to congratulate themselves that, whereas there had been Thackeray, Dickens, the brothers Kingsley, and Wilkie Collins among authors, authoresses could boast of George Eliot, Mrs. Gaskell, [33 Col B / 34 Col A] Miss Yonge, &amp;c, and she felt that in the future they might equal, she would not say rival, their &quot;brother man.&quot; At this courageous vaunt our glance involuntarily strayed to the statue, anticipating that it would be moved to at least a wink; but overwhelmed, perhaps, by the presence of so many &quot;sisterwomen,&quot; it gave no sign. The speech was long, lasting for over thirty minutes. It touched on the evils of lowering work to what might be a present commercial but fleeting value; it contained much that was excellent, and tendered some good sound advice; perhaps it dwelt a trifle too insistently upon the obvious, and it was serious even to solemnity. But then &quot;women are so serious.&quot; / Mme. Sarah Grand's reply was couched in far lighter vein. It slipped into the anecdotal, and was altogether more in the masculine line of after-dinner speaking. It offered no advice save on the advisability of laughter; it lingered for a moment on the sorrows of misinterpretation and misunderstanding, and included some amusing examples. Mme. Sarah Grand possesses a sympathetic voice, and is very pleasant to listen to. / It is characteristic of the gravity with which even in play hours women regard their &quot;work&quot; that the majority of guests preferred the more serious matter of Lucas Malet to the light personal note of Mme. Grand. The dinner itself was very good, and it was noticeable that whilst at the Authors' dinner on May 1 but few women availed themselves of the permission to smoke, at the women's function scarcely one was without a cigarette. Coffee was served at the table, and afterwards the company broke up into groups. / The committee numbered among its members Miss Beatrice Harraden, Mrs. Steel, Mrs. Craigie, Miss Christabel Coleridge, Miss Violet Hunt, and many other favourite writers. In the company present there were Dr. Jex-Blake, Mrs. Ady, Dr. Margaret Todd, Miss Adeline Sergeant, Mrs. Mona Caird, Mrs. Burnett-Smith, Mme. Albanesi, Miss Nora Maris, Miss Kenealy, and others; and the following presided at the tables : Lucas Malet, Mme. Sarah Grand, Mrs. de la Pasture, Miss Montresor, the Lady Mayoress, Mrs. L. T. Meade, Mrs. Alec Tweedie, Mrs. Walford, Mrs. B. M. Croker, Miss Violet Hunt, Miss Beatrice Harraden, Mrs. Belloc Lowndes, Miss Violet Brooke-Hunt, Miss Thorneycroft Fowler.&lt;/quote&gt; (&quot;The Women Writers' Dinner.&quot; The Author. Vol. XII, No. 2. 1 July 1901. Pp. 33–34.)

====26 June 1901, Wednesday====
There was apparently a regular celebration of Arthur Collins' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902.

====29 June 1901, Saturday====
&quot;To-day sees the public inauguration of the Horniman Musem at Forest Hill. This collection of marvels from many lands, gathered together by a member of the Horniman family, has been generously presented to the public and housed in a handsome new building — set in the midst of fifteen acres, which are now dedicated to use as a public park. The entrance to the museum will be free.&quot; (&quot;The Horniman Museum.&quot; Illustrated London News (London, England), Saturday, June 29, 1901; pg. 928; Issue 3245, Col. B)

===July 1901===

==== 1901 July 2, Tuesday ====
The Earl and Countess of Kilmorey hosted a children's party at the Botanic Gardens:&lt;blockquote&gt;The Earl of Kilmorey, K.P., and the Countess of Kilmorey gave a charming children's fête on Tuesday (2nd) at the Botanic Gardens. It began to rain just as the little people commenced to arrive, so the gardens were abandoned for the large pavilion, where a sumptuous birthday tea was provided in honour of little Lady Cynthia Needham's birthday, also a conjuror; and before leaving, they all danced or played games. The Countess of Yarborough was in a grey silk; Lady Naylor-Leyland, all in pale grey; Ellen Lady Inchiquin, with her little children, and pretty [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], in a mauve gown and and purple tulle toque. There were also present H.S.H. Prince Francis of Teck, Count Mensdorff; Mrs. Adair, smart in black and white; lady Hood , with the Ladies Conyngham; the Hon. Mr. George Keppel ' s pretty little girl; Lady Grey Egerton, in rose colour; Lady de Trafford's small schoolboys, Hon. &quot;Buddy&quot; Needham, and little Miss Knollys, who came with her mother, Lady Knollys.&lt;ref&gt;&quot;The Earl of Kilmorey, K.P.&quot; ''Gentlewoman'' 13 July 1901: Saturday, 50 [of 84], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010713/237/0050. Print: title the same, p. 60.&lt;/ref&gt;&lt;/blockquote&gt;

==== 1901 July 4, Thursday ====

===== The Countess of Yarborough's Children's Party =====
&lt;blockquote&gt;The Countess of Yarborough gave a charming children's party on Thursday (4th) afternoon at her beautiful house in Arlington Street. The spacious ballroom was quite filled with little guests and their mothers. Each little guest received a lovely present from their kind hostess. The Duchess of Beaufort, in grey, and with a large black picture hat, brought her two lovely baby girls, Lady Blanche and Lady Diana Somerset, both in filmy cream [Col. 2b–3a] lace frocks. Lady Gertrude Corbett came with her children, and Ellen Lady Inchiquin with hers. Lady Southampton, in black, with lovely gold embroideries on her bodice, brought her children, as also did Lady Heneage and Mr. and Lady Beatrice Kaye. Lady Blanche Conyngham, in écru lace, over silk, and small straw hat, was there; also Mrs. Smith Barry, in a lovely gown of black and white lace. The Countess of Kilmorey, in a smart grey and white muslin, brought little Lady Cynthia Needham, in white; Mrs. Arthur James, in black and white muslin; and the Countess of Powys, in mauve silk with much white lace; Lady Sassoon, in black and white foulard; Victoria Countess of Yarborough, came on from hearing Mdme. Réjane at Mrs. Wernher's party at Bath House; and there were also present Lord Henry Vane-Tempest, the Earl of Yarborough, Lady Naylor-Leyland's little boys; the pretty children of Lady Constance Combe, Lady Florence Astley and her children, and Lady Meysey Thompson (very smart in mauve and white muslin) with her children; also [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], in pale grey, with her pretty little girl.&lt;ref&gt;&quot;The Countess of Yarborough ....&quot; ''Gentlewoman'' 13 July 1901, Saturday: 76 [of 84], Col. 2b, 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010713/381/0076. Print p. xxxvi.&lt;/ref&gt;&lt;/blockquote&gt;

==== 1901 July 4–6, Thursday–Saturday ====

===== The Great County Sale =====
The Soldiers' and Sailors' Families Association held a benefit sale in the Imperial Gardens of the Earl's Court Exhibition. Alexandra's last act as Princess of Wales was to make an appeal for this organization.&lt;ref&gt;&quot;The Great County Sale.&quot; ''Gentlewoman'' 29 June 1901, Saturday: 42 [of 72], Col. 1a–3c [of 3] – 44, Col. 1a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0003340/19010629/222/0042. Same print title, pp. 678–680.&lt;/ref&gt; The coverage in the ''Gentlewoman'' was extensive in the 29 July issue, just before the event, as well as in issues after, in which the newspaper published portraits of some of the people who worked in the stalls.

====19 July 1901, Friday====
[[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]] hosted a concert at the Wilson house in Grosvenor-place in London:&lt;blockquote&gt;Mr. and Mrs. Arthur Wilson lent their house in Grosvenor-place on Friday afternoon for Miss Gwendoline Brogden’s concert. Miss Brogden, who is only eleven years old, is quite a prodigy. She sings quite exquisitely, and great many people, including Lady de Grey and Mrs. Arthur Wilson, are much interested in her future, which promises to be a very brilliant one. Lady Maud Warrender, Miss Rosamond Tufton, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Mr. Bernard Ralt, Signor Ancona, and Signor Tosti, all promised to assist at the concert, and the tickets were a guinea each.&lt;ref&gt;&quot;Stray Notes.&quot; ''Beverley Echo'' 24 July 1901, Wednesday: 2 [of 4], Col. 4b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001561/19010724/037/0002 (accessed July 2019).&lt;/ref&gt;&lt;/blockquote&gt;

==== 23 July 1901, Tuesday ====

===== Lord and Lady Algernon Gordon Lennox =====
&lt;blockquote&gt;Lord and Lady Algernon Gordon Lennox are entertaining at Broughton Castle, Banbury, Mr. and Mrs. Arthur Sassoon, Mr. Schomberg McDonnell, the Hon. Mrs. Bourke [possibly [[Social Victorians/People/Bourke|Gwendolen Bourke]]], Senator Walcot, Miss Naylor, and Mr. Moreton Frewen. Lady Algernon Gordon Lennox, the Duchess of Marlborough, Lady North, the Hon. Mrs. Albert Brassey, and Viscount Valentine will take part in opening a fete at Banbury next week for the National Schools.&lt;ref&gt;[&quot;Lord and Lady Algernon Gordon Lennox.&quot;] ''Leamington, Warwick, Kenilworth &amp; District Daily Circular'' 23 July 1901, Tuesday: 2 [of 4], Col. 5c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002102/19010723/028/0002. Print: ''Leamington Warwick &amp; District Daily Circular'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;

==== 25 July 1901, Thursday, 2:30 p.m. ====

The wedding of William Dixon Mann Thomson — Captain Mann Thomson in the Life Guards — and Violet Hemsley Duncan. Captain Mann Thomson's father had died in 1899. (Guests' names with their gifts set as an unordered list here, to save space; it was typeset as a long list of paragraphs in the newspaper story.)&lt;blockquote&gt;MARRIAGE OF CAPTAIN MANN THOMSON AND MISS DUNCAN.

The marriage of Captain Mann Thomson, Royal Horse Guards, and Miss Violet Duncan, eldest daughter of Mr. A. Lauderdale Duncan, Knossington Grange, Oakham, took place in St. Peter's Chnrch, Eaton-square, London, on Thursday, the inst., 2.30 p.m. The bride, who was given away her father, wore a dress of white satin, draped with white and old Brussels lace, wreath of orange blossoms, and tulle veil. Her ornaments were pearls. She was attended by seven bridesmaids, viz.: — Miss Adèle, Miss Marjory, and Miss Esmè Duncan, sisters; Miss Dorothy and Miss Sybil Thompson, cousins of the bride; Miss Villiers, cousin of the bridegroom; and Miss Joan Dawson. They wore dresses of the palest pink silk, covered with pink gauze, collars of white lace, and pale pink chiffon baby hats. The bride's train was carried by Miss Duncan, her youngest sister. The bridesmaids carried bouquets of pink carnations, and wore diamond brooches in the shape of a violet with sapphire centre, the gifts the bridegroom. A detachment of non-commissioned officers and men of the bridegroom's troop lined the aisle during the ceremony. The bridegroom was supported by the Earl Arran as best man. The officiating clergy were the Rev. Ravenscroft Stewart, Vicar of All Saints', Ennismore-gardens, the Rev. G. Tanner, Rector of St. Peter's, Knossington, Leicestershire, and the Rev. H. Trower. After the ceremony, a reception was held at 8, Rutland-gate, the residence of Mr. and Mrs. Lauderdale Duncan. Among those present were the Duke and Duchess of Westminster, Dowager Countess of Chesterfield, Sir William and Lady Houldsworth, the Hon. C. and Mrs. Stanhope, Miss Hay, Lord and Lady Eglinton, Lord and Lady Castlereagh, Lord Ernest St. Maur, Lord and Lady Pembroke, Mrs. Adair, Mrs. Mann Thomson, Miss Mann Thompson, Earl Arran, Lord Cecil Manners, Mrs. and Miss Wilton Phipps, and many others. Later, the bride and bridegroom left for Dover, ''en route'' for the Continent, where they will spend the honeymoon. The bride's travelling dress was of pale blue crepe-de-chine, and black hat. There were about five hundred gifts from relations and friends. The following is a list:—

* Bridegroom to Bride — Large diamond spray
* Mrs. Mann Thomson (mother of bridegroom) — Diamond ring, diamond and sapphire bangle, and cheque
* Mr. Lauderdale (father of bride) — Diamond and sapphire necklace
* Mrs. Duncan (mother of bride) — Silver-mounted travelling bag
* Dowager Lady Hay (bride's aunt) — Silver tea service
* Miss Mann Thomson (bridegroom's sister) — Brougham
* Mr. and Mrs. Butler Duncan (uncle and aunt) — Gold-mounted claret jug
* The Misses Jackson (bridegroom's aunts) — Silver plate
* Mr. H. Mann Thomson (brother) — Silver-mounted portmanteau
* Mr. Charles Hunt — Diamond and pearl brooch
* Miss Adele Duncan — Gold match-box
* The Earl Arran — Gold cigarette case
* Mr. and Mrs. Lucas — Bracelet
* Earl of Arran — Set of diamond and pearl studs
* Capt. and Lady Riddell — Bracelet
* Mrs. and Miss Wilton Phipps — Gold and ruby buckle
* Hon. H. Stanhope, R.N. — Brilliant buckle
* Mr. and Mrs. Pennington — Ruby necklace
* Mr. A. Butler Duncan — Necklace (old design)
* Mr. and Mrs. Gervase Beckett — Sleeve links
* Duke and Duchess of Westminster—Pair of silver candlesticks
* Duchess of Roxburgh—Dresden china coffee service
* The Countess of Shaftesbury — Walking-stick
* The Earl of Arran — Umbrella
* Lady Napier Magdala — Snuff-box
* Sir Richard Waldie Griffith — Fan
* Officers of the Royal Horse Guards — Massive silver vase
* Lady Houldsworth — Silver inkstand
* Viscount Ingestre — Silver waiter
* Miss Hay — Silver coffee pot
* Lady Hay — Silver tea caddy
* The Countess of Chesterfield — Silver and brilliant-mounted photo frame
* Lord Manners — Set four silver candlesticks
* Lord and Lady Eglinton — Silver cigarette box
* Earl and Countess of Ancaster — Pair of silver peppers
* Lady Augusta Noel — Book-slide
* Mr. and Mrs. Bradley-Martin — Old china coffee service in case
* Mr. and Lady Wilfred Renshaw — Leather-covered book, &quot;Where It?&quot;
* Mrs. Duncan — Silver-mounted stationery case and blotter
* Sir Arthur Fludyer — Hunting crop
* Lady Katherine Cole — Walking-stick
* Lord Hamilton — Oak card table
* Sir John Kelk — Writing case
* Capt. Hon. E. St. Aubyn — Set of silver spoons in case
* Capt. and Mrs. Burns-Hartopp — Set of silver asparagus tongs in case
* Capt. Trotter — Silver sealing-wax stand
* Capt. E. W. Clowes — Silver tobacco box
* Mr. and Mrs. Sands Clayton — Silver scent bottle
* Mr. and Mrs. John Hunt Clayton — Thermometer in silver-mounted case
* Mr. and Mrs. Evan Hanbury — Clock
* Major Atherley — Cigarette box
* Mr. and Mrs. Richard Tryon — Card case
* Mr. and Mrs. Hamilton Stubber — Table mirror in silver frame
* Mr. and Mrs. Gretton — Pair of silver candlesticks
* Miss Adele Duncan — Silver tea service
* Hon. G. Crichton — Silver-mounted paper-knife
* Mrs. Norman Lampson — Parasol
* Capt. Gregson — Photo, &quot;Guards at Pretoria&quot;
* Mr. Alfred Keyser — Leather bag
* Mr. and Mrs. Armytage — lvory paper knife
* Mrs. Boyce — Leather tray with two painted china plaques
* Mr. and Mrs. A. B. Norman — Silver-mounted paper knife
* The Master of Elibank — Pair of silver ash trays
* Mr. Adrian Rose — Pair of silver toast racks
* Mr. Archibald Smith — Hunting crop
* Major Bradford Atkinson — Walking-stick
* Mr. and Mrs. Stanhope — Painted china tea service
* Mr. G. A. Grant — Stationery case
* Mrs. Charles Inge — Copper and brass jardiniere
* Col. and Mrs. Makins — Hunting crop
* Mr. G. F. Trotter — Walking stick
* Mr. and Misses Cardwell — Fan
* Mrs. Dana — Thermometer
* Mrs. Nugent — Card case
* Mr. and Mrs. Ovey — Tortoiseshell box
* Mr. F. Peake — Writing table
* Capt. Boyce — Embroidered table cover
* Mrs. Duncan — Dressing bag case
* Mr. F. C. Fardell and Miss Gilbert Day — Brocaded satin cushion
* Mr. and Mrs. Niel Robson — Visiting book
* Mrs. R. B. Hay — Silver salts in case
* Mr. and Mrs. Harold Broadbent — Pair silver peppers in case
* —— Set silver knives in case
* Mr. and Mrs. Greville Clayton — Six silver vases in case
* Mr. and Mrs. Reginald H. Lewis — Pair silver peppers
* Lord Ernest St. Maur — Set four silver fruit spoons in case
* Rev. Geo. and Mrs. Tanner — Pair of silver salts
* Capt. Thomson's Valet and Groom — Pair of silver peppers
* Mr. Alick Duncan — Silver jug
* Mr. and Mrs. A. Brocklehurst — Silver timepiece in case
* Lieut.-Col. and Mrs. Blackburn — Silver fruit spoon
* Mr. and Lady Georgiana Mure — Silver-mounted ink [sic]
* Mrs. Gerald Fitzgerald — Silver-mounted inkstand
* Mrs. Ruthven — Set of silver knives in case
* Mrs. Blair — Umbrella
* Mrs. Willie Lawson — Hunting crop
* —— Three driving whips
* —— Tea tray
* Mr. and Mrs. Ramsay — Umbrella
* Mr. George Hunt — Silver flower bowl
* Mr. and Mrs. Reginald Cookson — Silver biscuit box
* Mr. Arthur and V. James — Silver two-handled cup and cover
* Mr. Robbio Stubber — Pair of silver scent bottles
* Mr. and Mrs. Geo. Baird — Silver bowl
* Mr. and Mrs. Harrison Broadley — Pair of silver flower vases
* Mrs. Grant—Silver flower-pot stand
* Mrs. Villiers — Silver corkscrew
* Capt. Spender Clay — Antique silver snuffbox
* Mr. and Mrs. Weir — Silver bacon dish
* Mr. Baird — Pair of silver candlesticks
* Mr. Athol Hay — Silver sugar bowl
* Capt. Ewing — Pair of silver fruit dishes
* Mr. and Mrs. C. J. Phillips — Pair of silver baskets
* Miss Esmé Duncan — Silver box
* Mr. and Mrs. Ronald Paton — lvory paper knife
* Dr. Freshfleld — Work case
* Mrs. Arkwright — Silver-mounted blotter
* Mr. and Mrs. Peake — Silver-mounted stationery case
* Miss Goddard — Book
* Mr. D. Baird — Silver inkstand
* J. G. and Jane B. Hay — lnkpot, with silver watch top
* Mr. and Mrs. Wadsworth Ritchie — Pair of silver dishes in case
* Mr. and Mrs. Guy Fenwick — Set of twelve silver knives in case
* Jane and Uncle Willie — Silver sugar basin in case
* Mr. and Miss Millington Knowles — Set of four silver dessert spoons in ease
* Herbert and Lady Beatrix Herbert — Silver flower dish
* Mr. and Mrs. J. B. Thorneycroft — Four silver candlesticks
* Mr. and Mrs. Russell? M [illegible, ink has spread] — Silver bowl [Col. 2c / Col. 3a]
* Mr., Mrs., and the Misses Wm. Cooper — Fan
* Miss Winearls — Silver-mounted scent bottle
* Sir Ernest Cassel — Diamond and enamel brooch
* Mr. John S. Cavendish — Gold pencil case
* —— Diamond and sapphire bracelet
* Miss Lottie Coats — Diamond and pearl brooch
* Hon. T. Robarts — Diamond brooch
* Mr. and Mrs. Chas. E. Hay — Enamel and pearl miniature holder
* Evelyn Ward — Cornomandel [sic] box
* Mr. and Mrs. Slade — China clock
* Lieut.-Col. Jervoise — Fan
* Mr. and Mrs. J. B. Fergusson—Set of four silver menu holders
* Mr. Guy R. F. Dawson — Silver card case
* Rev. E. V. and Mrs. Hodge — Silver dish
* Mr. C. S. and Mrs. Newton — Silver waiter
* Mrs. Metcalfe — Gold, turquoise, and ruby brooch
* Lord and Lady Erne — Set of three gilt decorated liqueur decanters
* Mr. and Mrs. Chas. Grant — Two silver-mounted spirit decanters
* Mr. and Mrs. George Baird — Set of three cut-glass decanters
* Mr. Peter Cookson—Pair of silver-mounted decanters
* Mrs. Featherstonehaugh — China ornament
* Aunt Mary — China coffee service in case
* Mr. H. S. Sykes — Silver-mounted telegram form case
* Capt. Meade — Pair of engraved claret jugs
* Lord and Lady Binning — Silver-mounted claret jug
* Mr. and Mrs. Baldock — Silver-mounted water jug, with inscription
* Mrs. and the Misses Chaplin — Pair of gilt decorated vases
* —— Silver-mounted claret jug
* Kittie, Margie, Hestie, Walter, Phillip, and Millicent Tanner — Pair of silver peppers case
* Mr. J. R. J. Logan — Silver-mounted claret jug
* Miss Ethel Baird — Painted china box
* Mrs. D. A. Neilson — Pair of female figures with Cupids
* M. M. Phillips — Painted china miniature box
* Lady Waldie Griffith — Stationery case
* —— Painted two-fold screen
* Miss Mabel Fitzgerald — Silver-mounted vase
* Major Bouverie — Silver-mounted match holder
* —— Enamelled inkstand and candlesticks to match
* Mrs. Duncan — Stationery case and blotter
* —— Silver-mounted stationery case
* —— Tortoiseshell and silver-mounted paper-knife
* Miss Mills — Dresden china vase, cover, and stand
* —— Six Vols. of Ruskin's &quot;Modern Painters&quot;
* Mrs. W. Baird — Leather bag
* Miss Langridge — Four silver spoons
* Miss Kirk and Miss Hemsley — Silver-mounted photo frame
* Miss Nessie Hemsley — Silver-mounted photo frame
* Captain and Mrs. St. Aubyn Loftus — Silver vase
* Decima Walker Leigh — Pair of silver-mounted menu stands
* Mrs. Charles Thomson — Mirror in silver frame
* Miss Reese — Silver crumb scoop
* —— Silver-mounted seal and case
* Mary Abercorn Alexander and Gladys Hamilton — Silver inkstand
* Mr. and Mrs. Cecil Chaplin — Silver pen, pencil, and knife in case
* Miss Gwendoline Brassey — Silver-mounted ice pail
* Mr. and Mrs. and Misses Clifford Chaplin — Pair of silver candlesticks
* Mr. and Mrs. Magee — lvory paper knife
* Misses Dorothy and Maude Pilcher — Scent bottle
* Miss Ashton — Silver-mounted clock
* Mrs. William Clarence and Miss Watson — Silver crumb scoop
* Major and Mrs. Ed. Baird — Egg-boiler on silver stand
* Mr. A. F. H. Fergusson — Pair of silver coffee pots
* —— Table mirror
* —— Pair of silver vases
* Mrs. R. B. Mnir — Silver fox ornament
* Mr. H. Brassey and Mr. H. R. Molynenx — Silver teapot
* —— Pair of silver sauce boats
* Mr. and Mrs. Heathcote — Silver cream jug
* Misses Thompson — Silver photo frame
* Mr. C. D. Rose — Pair of silver fruit dishes
* Mr. T. Archibald Hope — Silver toast-rack
* Mr. and Mrs. Robert Hunt — Pair of silver sauce boats
* Major and Mrs. Candy — Pair of silver fruit baskets
* Misses Trefusis — Silver-mounted owl mustard-pot
* Mrs. Frank Chaplin — Silver photo frame
* Major Vaughan Lee — Silver waiter
* Major Byng — Pair of silver menu stands
* Lady Wilton — Silver photo stand
* Geoffrey and Sibyll Palmer — Scent bottle
* Dr. Clement Godson — Silver salad cruet
* Mr. Mackenzie — Silver cigar case
* Mr. G. Colvin White — Set of four silver trays
* Mr. Edgar Brassey — Silver pipe lighter
* Miss Emily Dawson — Photo frame
* Mrs. Gerald FitzGerald — Silver match-box holder
* A. Barns — Silver waiter
* Miss Palmer — Letter-clip and dish
* Mr. and Mrs. Aubrey Coventry — Photo frame
* —— Silver bowl three feet
* Mr. and Mrs. Hornsby — Openwork silver basket
* —— Antique silver box
* Mr. and Mrs. H. R. Baird — Silver coffee-pot
* —— Pair of silver salts
* Mr. Hugh Wanemley — Silver-gilt match-box
* Captain Gordon Wilson — Silver snuff-box
* Mrs. Whitelaw — Silver mustard-pot
* Mrs. Palmer — Silver spoon
* Mr. Dudley Majoribanks — Silver bowl and cover
* Mr. Wilfred F. Ricardo — Pair silver candlesticks
* Indoor Servants at Knossington Grange and 8, Rutland Gate — Breakfast warmer and two silver entree dishes and covers
* Outdoor Servants at Knossington Grange — Silver stationery case
* Mr. Waterman (coachman) — Driving-whip
* Mr. Alexander (coachman) and Mrs. Alexander — lnk-stand
* Villagers of Knossington — Silver sugar bowl, sugar tongs, and cream ewer in case
* Silver vase, with inscription — &quot;Capt. Mann Thomson, Royal Horse Guards, from the Estate and Household at Dalkeith, on the occasion of his marriage, 25th July, 1901.&quot;
* Miss Baldock — Pair of scent bottles
* Captain Cook — Paper-knife
* Sir A. Baird — Pair of silver muffineers
* Rev. H. W. Trower — Pair of silver peppers
* Mr. T. Vandeleur — Silver cigarette box
* Lady Miller — Silver milk jug
* Mr. Hedworth Barclay — Silver muffineer
* Miss May A. Jackson — Photo frame
* Mr. Geoffrey Heneage — Silver ash tray
* Mr. and Mrs. R. B. Hay — Pair silver mustard-pots
* Mrs. George Charteris — Silver-mounted calendar
* Royal School of Art Needlework, Exhibition-road — Silvered copper heart-shaped box
* Mr. A. C. Newbigging — Silver fox ornament
* Mr. S. Schreiber — Silver match box
* Mr. and Mrs. J. H. J. Phillips — Silver muffineers
* Mr. and Mrs. Fyfe Jameson — Silver flask
* Mrs. Beaumont Lubbock — Silver bon-bon dish
* Lord Castlereagh — Salad bowl
* Captain Hambro — Silver card case
* Lord Longford — Silver bowl
* Captain —— Silver waiter
* Mrs. Forester — Silver frame
* Mrs. Martin — Tea cloth
* Mr. and Mrs. Cooper — Whip
* Earl Lonsdale — Silver tray
* Lady Augusta Fane — Red box
* Mr. Paul Phipps — Clippers
* Mr. E. Herlick — lnkstand&lt;ref&gt;&quot;Marriage of Captain Mann Thomson and Miss Duncan.&quot; ''Grantham Journal'' 27 July 1901 Saturday: 2 [of 8], Cols. 2a–3b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000400/19010727/003/0002.&lt;/ref&gt;
&lt;/blockquote&gt;

===August 1901===
====30 August 1901, Friday====
[[Social Victorians/People/Horos|The Horoses]] (troublesome members of the Golden Dawn) were thrown out of 99 Gower Street and moved to Gloucester Crescent (King 89 91).
===October 1901===

==== 26 October 1901, Friday ====

==== The Prince's Club Ice-skating Rink Opening ====
&lt;blockquote&gt;The season at the [[Social Victorians/London Clubs#Prince’s Skating Club|Prince’s Skating Club]] has opened up with better prospects of success than ever before. Friday, October 26th, was the night of the re-opening, and many of the best known women in London’s social world were present. There was a large attendance, including the following members of the strongest Committee the Club has ever known: The Duchess of Portland, Lady Carrington, Lady Granby, Lady Archibald Campbell (a very graceful skater), Lady Helen Vincent, Mrs. Harry Higgins and Mrs. Asquith. The Committee is headed by the Princess Louise. The men’s Committee includes Lord Edward Cecil, Sir William Hart Dyke, [[Social Victorians/People/Bourke|Mr. Algernon Bourke]], Sir E. Vincent, Mr. Evan Charteris and Viscount de Manneville. The skaters were perhaps not so numerous as on an ordinary occasion, but the crowd of guests was exceptionally large. Miss Marshall, who is perhaps one of the best skaters in the club, executed some daring and intricate figures with Mr. Clayton, of the Grenadier Guards, She looked very smart in a short black skirt with a white lace blouse. A hat of pale blue completed her costume. Another graceful and well-known skater is Miss Wood, who wore a black dress with black sequin blouse and white fox boa and blue hat. Among the spectators were Count de Vernon, Mrs. Forbes Robertson, Mrs. Nat Goodwin, Miss Cassel — a young American — and many others. The skating men included Lord Doneraile, Lord Archibald Campbell, and Mr. Algernon Grosvenor.&lt;ref&gt;Sportswoman, A. &quot;Roundabout Notes.&quot; ''Lady's Pictorial'' 2 November 1901, Saturday: 54 [of 84], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005980/19011102/146/0054. Same print title, p. 786.&lt;/ref&gt;&lt;/blockquote&gt;

====31 October 1901, Thursday====
Halloween.
===November 1901===
====5 November 1901, Tuesday====
Guy Fawkes Day
===December 1901===
====25 December 1901, Wednesday====
Christmas Day
====26 December 1901, Thursday====
Boxing Day
===Works Cited===
*[1901-02-23 Cheshire Observer] &quot;Duke of Westminster. Brilliant Function.&quot; Cheshire Observer 23 February 2901, Saturday: 6 [of 8], Col. 1a–6c [of 8]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000157/19010223/114/0006 (accessed July 2019).
*[1901-04-25 Stage] &quot;Provinces.&quot; &quot;Amateurs.&quot; The Stage 25 April 1901, Thursday: 11 [of 24], Col. 3c, 4b–c [of 5]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001179/19010425/028/0011 (accessed July 2019).

==1902==
Sometime in 1902, London publisher [[Social Victorians/People/Working in Publishing#George Newnes|George Newnes]] published an edition of [[Social Victorians/People/Arthur Conan Doyle|Arthur Conan Doyle]]'s first (1892) collection of Holmes stories.
===January 1902===

==== 1 January 1902, Wednesday, New Year's Day ====

==== 25 January 1902, Saturday ====
[[Social Victorians/Stewart-Stavordale Wedding 1902-01-25|Stewart-Stavordale Wedding]]

Lady Helen Vane-Tempest-Stewart, daughter of the Marquis and Marchioness of Londonderry and Giles Fox-Strangways, Lord Stavordale, son of the Earl and Countess of Ilchester

===February 1902===

==== 13 February 1902, Thursday ====

King Edward VII and Queen Alexandra were present with some of their friends at Niagara, which must have been an ice-skating rink. Mr. and [[Social Victorians/People/Churchill|Mrs. George West]] are Lady Randolph Churchill and George Cornwallis-West.&lt;blockquote&gt;SOCIAL &amp; PERSONAL

Royalty at Niagara.

Quite a record audience was present at Niagara yesterday, when the free skating and waltzing competitions were skated off to the sound of gay music in a brightly lighted, warm atmosphere.

The royal box made a goodly show with its trappings of Oriental hangings and decorations of palms.

The Royal Box.

The King and Queen were accompanied by Princess Victoria and Prince and Princess Charles of Denmark, the Prince and Princess of Wales having previously arrived. Their Majesties were conducted to the spacious box by Mr. Hayes Fisher.

All the royal ladies wore black, the Queen adding a bunch of yellow Lent lilies to her sombre attire. Her two daughters lightened their mourning with touches of white, and the Princess of Wales wore a bunch of violets in her toque, with a twist of white.

In the adjoining box, among members of the suite were the Countess of Gosford, Earl Howe, Mr. Sidney Greville, Mr. H. J. Stonor, Lieut.-Colonel Davidson, Lieut.-Colonel Legge, and Viscount Crichton.

In boxes on the other side of the royal box were Lady Alice Stanley, with the Ladies Acheson, the Countess of Derby, Countess De Grey and Lady Juliet Lowther, [Col. 3c/4b] Mr. and [[Social Victorians/People/Churchill|Mrs. George West]] [Lady Randolph Churchill and George Cornwallis-West], Sir Edgar and Lady Helen Vincent, the Duchess of Bedford and the Marquis of Tavistock, [[Social Victorians/People/de Soveral|M. de Soveral, the Portuguese Minister]], and Viscount and Viscountess Falmouth.

Others to be picked out in the crowd were Consuelo Duchess of Manchester, Viscountess Coke and Mrs. Ellis, Lady Archibald Campbell and her son, Mrs. Grenander, Lord and Lady Lilford, Mr. and Mrs. Edward Stonor, Mrs. [[Social Victorians/People/Bourke|Algernon Bourke]], Mr. Algernon Grosvenor, and Mr. and Mrs. Hwfa Williams.

The royal party took a great interest in the contests, and especially applauded the Swedish couple in their graceful evolutions. Their Majesties remained over an hour, the royal party taking their departure shortly after five.&lt;ref&gt;&quot;Social &amp; Personal.&quot; ''Daily Express'' 14 February 1902, Friday: 4 [of 8], Cols. 3c–4b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020214/088/0004. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

===March 1902===
The last time Bret Harte and Arthur Collins saw each other: &quot;They dined at the Royal Thames Yacht Club, and Collins found his 'poor old friend' 'saldly aged and broken, but genial and kind as ever.' They sat an hour at a music hall and Harte wrote afterwards to thank Collins for having 'forced him out.'&quot; (Nissen, Axel. Bret Harte: Prince and Pauper. Jackson, MS: U P of Mississippi, 2000: 262)
===April 1902===
====9 April 1902, Wednesday====
According to a letter to Lady Gregory, [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] dictated &quot;2000 words in an hour and a half&quot; &quot;to a typewriter; he was working on his novel (Wade 370). At this point, a typewriter was a person who used the machine called typewriter to type.
====10 April 1902, Thursday====
[[Social Victorians/People/William Butler Yeats|W. B. Yeats]] wrote to Lady Gregory from 18 Woburn Buildings about working on his novel &quot;-- dictating to a typewriter&quot; (Wade 370).

===May 1902===
====5 May 1902, Monday====
Bret Harte died. Arthur Collins does not seem to have been there at his death; “his dear friend Madame Van de Velde and her attendants” were, though (Pemberton, T. Edgar. The Life of Bret Harte. Dodd, Meade, 1903. http://books.google.com/books?id=eZMOAAAAMAAJ). Not sure when the funeral occurred, but he is buried “in quiet Frimly churchyard,” (341) and &lt;quote&gt;In accordance with his well-known views on such subjects the funeral was a very simple one. Among the few who followed him to his ivy-lined grave were Mrs. Bret Harte, his son and daughter-in-law, Mr. and Mrs. Francis King Harte, his daughter, Miss Ethel Harte, Madame Van de Velde, Colonel Collins, Mr. A.S. Boyd, and a small cluster of grief-stricken friends.&lt;/quote&gt; (Pemberton, T. Edgar. The Life of Bret Harte. Dodd, Meade, 1903. http://books.google.com/books?id=eZMOAAAAMAAJ (accessed November 2014).

====8 May 1902, Thursday====
Bret Harte's funeral:&lt;blockquote&gt;On Thursday, May 8, 1902, in the squat, mid-Victorian church of St. Peter's in the Surrey village of Frimley, a group of about twenty people had come to show their final respects to Francis Bret Harte. Outside it was raining steadily . In the subdued light from the stained-glass windows, one cold discern a small group at the front of the church consisting of Anna Harte, her son Frank, her daughter-in-law Aline, and her daughter Ethel. Another small group was formed around Madame Van de Velde, including one of her unmarried daughters, Miss Norris (the sister of her son-in-law Richard Norris), and Mrs. Clavering Lyne. Of Harte's closest friend, only Arthur Collins and Alexander Stuart Boyd were present. Pemberton had written to Frank the day before that he wished to attend the funeral but that in his &quot;deplorable state of health&quot; it was impossible for him to travel. Beside the small group of family and old friends, the rest of the people who heard the service conducted by the rector of Frimley, Reverend W. Basset, were recent acquaintances from among the local gentry. As one newspaper noted: &quot;The funeral was of the simplest possible character and the phrase 'this our brother' had a peculiar poignancy, for, though a group of villagers stood in the rain under the trees as the hearse arrived, there were few in the church, who had not the right to call Mr. Bret Harte friend.&quot; The simplicity of the service was in keeping with Bret Harte's wishes.&lt;ref&gt;{{Cite book|title=Bret Harte: Prince and Pauper|last=Nissen|first=Axel|publisher=University Press of Mississippi|year=2000}}&lt;/ref&gt;{{rp|263}}&lt;/blockquote&gt;

==== End of May 1902 ====
The Duke and Duchess of Marlborough hosted a party at Blenheim Palace:&lt;blockquote&gt;The Duke and Duchess of Marlborough entertained a party at Blenheim Palace last week. Their guests included the Duke of Roxburghe, Lord and Lady Churchill, Sir George and Lady Maud Warrender, Lady Juliet Lowther, Mr. Cecil and Lady Lilian Grenfell, [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], Lady Norah Spencer-Churchill, Lady Lurgan, Mr. lan Malcolm, Mr. Frank Mildmay, and Mr. Beaumont.&lt;ref&gt;&quot;The World of Fashion.&quot; ''Clifton Society'' 05 June 1902, Thursday: 6 [of 16], Col. 2a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002164/19020605/018/0006. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1902===
Summer 1902: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until Yeats bought the Tower at Ballylee. (I got this from Wade?)
====3 June 1902, Tuesday====
[[Social Victorians/People/William Butler Yeats|W. B. Yeats]] wrote Arnold Dolmetsch, asking him to &quot;chair ... a lecture he [was] soon to give&quot;: &quot;You are the only one, I suppose, in the world now, who knows anything about the old music that was half speech, and I need hardly say that neither [[Social Victorians/People/Florence Farr|Miss Farr]] nor myself, could have done anything in this matter of speaking to notes without your help&quot; (Campbell 142).
====7-9 June 1902, Saturday-Monday====
The [[Social Victorians/People/Warwick|Earl and Countess of Warwick]] hosted a house party:&lt;blockquote&gt;The Earl and Countess of Warwick entertained a distinguished house party from Saturday to yesterday, including the Grand Duke Michael of Russia and the Countess of Torby, the Earl and Countess of Craven, the Earl and Countess of Kilmorey, Earl Cairns, Lord and Lady Savile, Lord Chesham, Sir Frederick and Lady Milner, Colonel and Lady Gwendoline Colvin. Lady Margaret Orr-Ewing, Lady Eva Dugdale. Mrs. Kenneth Wilson, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Right Hon. H. Chaplin, M.P., Hon. H. Stonor, Mr. J. Pease, M.P., Captain Brinton, and Captain J. Forbes.&lt;ref&gt;&quot;Court and Personal.&quot; ''Manchester Courier and Lancashire General Advertiser'' 10 June 1902, Tuesday: 5 [of 10], Col. 3c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000206/19020610/033/0006 (accessed July 2019).&lt;/ref&gt; (1902-06-10 Manchester Courier and Lancashire General Advertiser)&lt;/blockquote&gt;

====10 June 1902, Tuesday====
[[Social Victorians/People/Florence Farr|Florence Farr]]'s first public performance in which she &quot;recit[ed] to her own accompaniment on the psaltery was at the Hall of Clifford's Inn, Fleet Street, on 10 June 1902 (Campbell 144, n. 18).

==== 11 June 1902, Monday ====

===== Ladies' Kennel Association Show =====
The newspaper report was on 11 June, the show likely before that.&lt;blockquote&gt;A Maharajah's Trophy.

It will be recollected that the Ladies’ Kennel Association possesses the most valuable challenge cup offered at any dog show. This is the trophy given by the late Maharajah of Dholpore, and won the first year by the Queen with her borzoi Alix. It is to be competed for by black pugs this time, and every champion in existence (except the judge's own) will stand in the ring amongst the 42 competitors for judgment this afternoon.

The Countess of Lonsdale won three first prizes and one second prize with her beagles, and amongst other society ladies who sent their pets to the show-pens were Princess Alexis Dolgorouki, Princess Victor Duleep Singh, Princess Sophie Duleep Singh, Lady Alexandra Darby, Lady Hope, Lady Algernon Lennox, the Duchess of Sutherland, the Hon. Mrs. Alwynne Greville, [[Social Victorians/People/Bourke|the Hon. Mrs. Algernon Bourke]], Lady Cathcart, Lady Evelyn Ewart, Lady Decies, the Hon. Sybil Edwardes, Lady Good, the Hon. Mrs. McLaren Morrison, Lady Harris, Lady Sybil Tollemache, Lady Edith Villiers, and the Marchioness of Waterford. 

For Cats and Pouitry.

There are also sections in the show for cats and poultry. The exhibitors of cats include the Princess Victoria of Schleswig-Holstein, the Countess of Aberdeen, and Lady Decies, while in the poultry section can be seen twelve pens of bantams sent by the Queen from Sandringham, and exhibits from the Countess of Aylesford, the Countess of Craven, the Hon. Helena Coventry, Lady Alington, the Hon. Florence Amherst, and the Hon. Mrs. Anson.

Amongst the attractions of the show today will be the parade of champions on the lawn and the presentation of the Queen's Cup prizes. To-morrow two attractive competitions are announced, one for dogs belonging to actresses, the other for children's pets.

Given fine weather the Coronation Show should be one of the events of the season. There is military music, and even the crisp weather did not prevent a host of society people from visiting the Botanic Gardens yesterday afternoon.&lt;ref&gt;&quot;A Maharajah's Trophy.&quot; ''Morning Leader'' 11 June 1902, Wednesday: 3 [of 8], Col. 2a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/19020611/037/0003. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

==== 12 June 1902, Thursday====
12 June 1902:&lt;blockquote&gt;Thursday, the 12th inst., being the grand day of Trinity term at Gray's-inn, the Treasurer (Mr. Herbert Reed, K.C.) and the Masters of the Bench entertained at dinner the following guests: The Right Hon. Lord Strathoona and Mount Royal, the Right Hon. Lord Avebury, the Right Hon. H. H. Asquith, K.C, M.P., the Right Hon. Sir Frank Lascelles, G.C.B. (British Minister at Berlin), General Sir Edward Brabant, K.C.B., the Right Hon. Sir Edward Carson (Solicitor-General), Sir Squire Bancroft, Colonel Alfred Egerton, C.B. (Equerry to H.R.H. the Duke of Connaught), Mr. Austen Chamberlain,M.P., Colonel Royds, M.P., and Mr. Frank Dicksee, R.A. The Benchers present in addition to the Treasurer were H.R H. the Duke of Connaught, Lord Ashbourne, Lord Shand, Mr. Henry Griffith, Sir Arthur Collins, K.C, Mr. Hugh Shield, K.C, His Honour Judge Bowen Rowlands, K.C, Mr. James Sheil, Mr. Arthur Beetham, Mr. John Rose, Mr. Paterson, Mr. Mulligan, K.C, Mr. Mattinson, K.C, Mr. Macaskie, K.C., Mr. C. A. Russell, K.C., Mr. Montague Lush, K.C., Mr. Dicey, C B., Mr. Barnard, Mr. H. C. Richards, K.C., M.P., Mr. Duke, K.C., M.P., Sir Julian Salomons, K.C., with the Preacher (the Rev. Canon C. J. Thompson, D.D.).&lt;ref&gt;''The Solicitor's Journal and Reporter''. June 21, 1902. Volume XLVI. 1901-1902 [November 2, 1901, to October 25, 1902]: 588. Google Books: http://books.google.com/books?id=9T84AQAAIAAJ&amp;pg=PA588&lt;/ref&gt;&lt;/blockquote&gt;

====26 June 1902, Thursday====
Edward VII crowned King of England. 26 June 1902.

There was apparently a regular celebration of Arthur Collins' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare.&lt;ref&gt;Nissen, Axel. Brent Harte: Prince and Pauper. 2002. Google Books http://books.google.com/books?id=WEDewmUnapcC.&lt;/ref&gt; (239) Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in May 1902, so the celebration with Harte present did not take place this year. Did it take place at all?

===July 1902===
====3 July 1902, Thursday====
[[Social Victorians/People/Mathers|MacGregor and Moina Mathers]] were living at 28 Rue Saint Vincent, Buttes Montmartre, Paris (Howe 244).

===September 1902===
''Tristan and Isolde'' at the Covent Garden.

==== 22 September 1902, Monday ====

===== Earl and Countess of Mar and Kellie's House Party =====
&lt;blockquote&gt;The Earl and Countess of Mar and Kellie have a large houseparty at Allca [?] House, Clackmannanshire. Their guests include Lord Charles Montagu, Viscount Chelsea, the Hon. Alexander M'Donnell, the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], and Sir George and Lady Maud Warrender.&lt;ref&gt;&quot;Rank and Fashion.&quot; ''St James's Gazette'' 22 September 1902, Monday: 17 [of 20], Col. 1b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/19020922/105/0017. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

====25 September 1902, Thursday====
&quot;There were no winter performances of opera at Covent Garden in those times .... In 1902 an autumnal series was added, and there were several Wagner nights, the last of which was on Thursday, 25 September, when Philip Brozel and Blanch Marchesi were starred in ''Tristan and Isolda'' with Marie Alexander as Brangane&quot; (Baring-Gould II 704, n. 14, quoting Rolfe Boswell).

===October 1902===

==== Annual Opening of the Prince's Ice-skating Rink ====
The newspapers reported on 2 Fridays in 1902, October 24th and 31st, on the opening of the [[Social Victorians/London Clubs#Prince's Skating Club|Prince's Club]] Ice-skating Rink.

===== 24 October 1902, Friday =====

The ''Daily Express'' reported on the annual opening of the Prince's ice-skating rink, revealing who had an interest in skating:&lt;blockquote&gt;The first ice of the season was skated upon yesterday. It was the carefully-prepared ice which Mr. H. W. Page and Mr. Nightingale offer to the members of Prince’s Skating Club, in Knightsbridge, and was in grand condition.

The [[Social Victorians/People/Bourke|Hon. Algernon Bourke]] opened the rink for the seventh season, and in the afternoon and evening the West End patronized the popular club to skate or to lounge to the pleasant strains of the Viennese band.

[[Social Victorians/People/Princess Louise|Princess Louise]] is again at the head of the ladies’ committee, with the [[Social Victorians/People/Portland|Duchess of Portland]] and [[Social Victorians/People/Londonderry|Marchioness of Londonderry]] as co-members, and Lord Edward Cecil and many other well-known skaters are identified with the committee work.

The skating hours are from 9.30 to 1 and 3 to 7, and on Sundays 3 to 7 only.&lt;ref&gt;&quot;Prince's Rink Opens.&quot; ''Daily Express'' 25 October 1902, Saturday: 5 [of 8], Col. 6c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19021025/132/0005.&lt;/ref&gt;&lt;/blockquote&gt;

===== 31 October 1902, Friday =====

==== Halloween. ====
The 7th seasonal opening of the [[Social Victorians/London Clubs#Prince's Skating Club|Prince's Skating Club]] and its committees:&lt;blockquote&gt;Until some genius, at present undiscovered, can cheapen the process of the manufacture of “real ice” we are not likely to become a nation of figure skaters, but where there are opportunities for practising the fascinating art of edges and turns development has proved to be rapid. This was noticeable on Friday at the opening of the seventh season of Prince’s Skating Club, a large number of really good skaters being present, who all found the fine hard surface to their Iiking, and there was a capital display of ice waltzing, the true poetry of motion, to the music of the Blue Viennese Band. Mr. [[Social Victorians/People/Grosvenor|Algernon Grosvenor]], an enthusiastic member of the committee, who presided at the little ceremony preceding the opening to members, referred to the prospects of continued success for the present season, which lasts until April next, and said that improvement might be expected, as the end of the war had brought many competent skaters home. A well-deserved tribute was paid to the work of Mr. H. W. Page, the secretary, on behalf of the club, which includes on its ladies' committee [[Social Victorians/People/Princess Louise|Princess Louise]] (Duchess of Argyll), the [[Social Victorians/People/Portland|Duchess of Portland]], [[Social Victorians/People/Londonderry|Lady Londonderry]], [[Social Victorians/People/Campbell|Lady Archibald Campbell]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], and [[Social Victorians/People/Asquith|Mrs. Asquith]]; and on the men's committee, Lord Edward Cecil, Lord Redesdale, Mr. [[Social Victorians/People/Bourke|Algernon Bourke]], Mr. [[Social Victorians/People/Lyttelton|Alfred Lyttelton]], Sir Edgar Vincent, Sir William Hart Dyke, and Mr. [[Social Victorians/People/Grenfell|W. H. Grenfell]].&lt;ref&gt;&quot;What the 'World' Says.&quot; ''Northwich Guardian'' 01 November 1902, Saturday: 6 [of 8], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001975/19021101/134/0006. Print title: The ''Guardian'', p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

===November 1902===
====5 November 1902, Wednesday====
Guy Fawkes Day.

==== 8 November 1902, Saturday ====
The Earl and Countess of Warwick hosted a shooting party at Easton Lodge:&lt;blockquote&gt;The [[Social Victorians/People/Warwick|Earl and Countess of Warwick]] are entertaining a large party at Easton Lodge this week-end for [?] shooting, and among their guests are the Grand Duke Michael of Russia and Countess Torby, the Duc d'Alba, the Duke of Sutherland, Earl Howe, Earl Cairns, Lord Dalmeny, Lord Herbert Vane-Tempest, the Hon. John and Lady [Choely?] Scott-Montagu, the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], the Right Hon. Henry Chaplin, M.P., General and Mrs. Arthur Paget, and Miss Leila Paget, Miss Naylor, Miss Deacon, and Mr W. M. Low.&lt;ref&gt;&quot;Guests at Easton Lodge.&quot; ''Birmingham Mail'' 08 November 1902, Saturday: 2 [of 6], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000644/19021108/091/0002. Print title: ''Birmingham Daily Mail''; p. 2.&lt;/ref&gt;&lt;/blockquote&gt;The Friday 14 November 1902 ''Melton Mowbray Times'' reported a slightly different list of people present:&lt;blockquote&gt;Lord and Lady Warwick's party for shooting at Easton Lodge, Dunmow, last week included the Grand Duke Michael and Countess Torby, the Duke of Sutherland, the Duc d’Albe, M. de Soveral, Lord Howe, Lord Cairns, Lord Herbert Vane-Tempest, Lord Dalmeny, Mr John and Lady Cecil Scots-Montagu, Mr Henry Chaplin, [[Social Victorians/People/Bourke|Mrs Algernon Bourke]], and General and Mrs Arthur Paget and Miss Leila Paget. — ''The World''.&lt;ref&gt;&quot;Local News.&quot; ''Melton Mowbray Times and Vale of Belvoir Gazette'' 14 November 1902, Friday: 8 [of 8], Col. 1c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001806/19021114/144/0008. Print title ''Melton Mowbray Times'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;

====29 November 1902, Saturday====
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]]’s cousin, Lady Hartopp, was involved in a divorce case:
&lt;blockquote&gt;Society Women in a Law Court Case.

Mr. Justice Barnes’s Court is now crowded by society people. What is the strange fascination which brings elegantly dressed ladies, accustomed to luxurious surroundings and all the external refinements of life, to sit for hours in stuffy court, where the accommodation is all the plainest, and the surroundings are none too attractive. It would need some assurance to invite a Belgravian Countess, or the wife of Mayfair Millionaire to spend the morning under such conditions unless there were the attraction of a very strong piece of scandal. One could not presume to suggest she should attend Missionary meeting, or social reform movement, under any such conditions. At least I must confess that I never heard of one being packed with a West End crowd as the Court just now. Of course it cannot be mere idle curiosity. Our higher education for girls must have cured Mother Eve’s failing long ago. Cynics suggest that it is the survival in our highly-civilised modern conditions of that instinct of the wild creature which incites attack on the wounded or injured fellow. Wild birds will sometimes peck injured bird to death. Are these fair and soft-voiced ladies animated by the same spirit when they throng witness the ordeal through which a woman of their own class is passing?

The Latest Divorce Case.

Lady Hartopp, the heroine of the story which has been occupying the tongues and thoughts of the upper ten thousand for the last 48 hours, is a member of a well-known and wealthy family, and is herself remarkable for her beauty. Her two sisters are as famous for their charms as herself, and society has given them many flattering titles. The daughters of Mr. C. H. Wilson, the great shipowner, whose sails are on every sea, are as favoured by Fortune as Venus. Miss Muriel Wilson, the society beauty, is a cousin of Lady Hartopp, and Lady Chesterfield is her sister. It was at Tranby Croft, near Hull, the residence of Mr. and Mrs. Arthur Wilson, that the famous baccarat case occurred some years ago. Lady Hartopp is the niece of Mr. Arthur Wilson, and no doubt recollects that incident, and all the consequent stir. It attracted all the more notice at the time, because the then Prince of Wales had taken part in the game; but the Prince, who had nothing to be ashamed of, with characteristic straightforwardness, asked to go into the box and state all he knew. (1902-11-29 Norwich Mercury)&lt;/blockquote&gt;

===December 1902===

==== 9 December 1902, Tuesday ====
&quot;Severe weather&quot; did not prevent Lady Eva Wyndham's &quot;at home&quot; from being a success:&lt;blockquote&gt;Lady Wyndham-Quin's &quot;At Home.&quot;

The severe weather proved to be no detriment to the many visitors who had accepted Lady Eva Wyndham-Quin's invitation to an &quot;at home&quot; at the Welch Industrial depot on Tuesday afternoon, and the admirers and purchasers of the fascinating Christmas gifts were numerous. Lady Eva received her quests wearing a coat of Persian paw and a white feather toque, whilst her two tittle daughters the Misses Olein and Kethlean Wyndham-Quin wore pelisses and hats of pale blue Welsh frieze, trimmed with grebe. Amongst those present were Lady George Hamilton, all in black; Lady Brassey, wearing a lovely sable cape; the [[Social Victorians/People/Bourke|Hon. Mrs Algernon Bourke]], in a fur coat and a black picture hat; and the Hon. Mrs Herbert, of Llanever; Mrs Brynmor Jones was fall of her coming visit to Paris to see her young daughter, and Mrs Richard Helme came with her son, Mr Ernest Helme. Mrs Brenton and her sister, Mrs Ashurst Morris, were also present, as were Lady Eafield, the Dowager Lady Hylton, Lady Dennison Pender [Ponder?], and Lady Blanche Conyngham. Mrs Grinnell Milne brought Miss Murray end Mrs Shelley Bontens, and Mrs James Head came in for a few minutes. Everybody bought largely and the Welsh Christmas cards were an attractive feature, as were some artistic muff chains. Another specimen of Welsh lace sent by Miss Jenkins, of Denbighshire, was much admired and resembles Irish lace both in style and design.&lt;ref&gt;&quot;A Lady Correspondent.&quot; &quot;Society in London.&quot; ''South Wales Daily News'' 11 December 1902, Thursday: 4 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000919/19021211/082/0004. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

====16 December 1902, Tuesday====
A poem satirizing Florence Farr and Arnold Dolmetsch was published in ''Punch''.
====25 December 1902, Thursday====
Christmas Day
====26 December 1902, Friday====
Boxing Day
===Works Cited===
*[1902-11-29 Norwich Mercury] &quot;Society Women in a Law Court Case.&quot; And &quot;The Latest Divorce Case.&quot; Norwich Mercury 29 November 1902, Saturday: 5 [of 12], Col. 1b [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001669/19021129/072/0005 (accessed July 2019).

==1903==
From sometime in 1891 to sometime in 1903 Eduoard de Reszke was &quot;a leading bass&quot; at the New York Metropolitan Opera (Baring-Gould II 112, n. 114).

&quot;[I]n England in 1903, gramophone distinctly meant the Berliner-Gramophon &amp; Typewriter disc machine, while cyclinder machines were known as phonographs or graphophones &quot; (Baring-Gould II 745, n. 15).

Gerald Balfour was &quot;largely responsible for getting the important Land Acts of 1903 under way&quot; (O'Connor 163).
===January 1903===
====1 January 1903, Thursday, New Year's Day====
====3 January 1903, Saturday====
Madame Troncey was doing a portrait of [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] (Wade 392).

=== February 1903 ===

==== 6 February 1903, Friday ====

===== Dinner Party Hosted by Lord Lieutenant of Ireland and the Countess of Dudley =====
&lt;blockquote&gt;Their Excellencies the Lord Lieutenant and Countess of Dudley gave a dinner party last night at the Castle. Prince Francis of Teck was present, and the following had the honour of receiving invitations: — The Duke and Duchess of Abercorn and Lady Alexandra Hamilton, Catherine Duchess of Westminster and Lady Mary Grosvenor, the Earl and Countess of Essex, the Countess of Fingall, the Earl and Countess of Drogheda, the Earl and Countess Annesley, the Earl of Enniskillen, the Viscountess Castlerosse, Viscount Crichton, Viscount Braskley [?], Lady Mabel Crichton, Lady Evelyn Ward, Lady Plunket, Lady Lurgan, Lord Vivian, Lord and Lady Fermoy, the Hon. Sybil Roche, Lady Barrymore and Miss Post, the Hon. Gerald Ward, Colonel the Hon. Charles Crichton, the [[Social Victorians/People/Bourke|Hon. Mrs. A. Bourke]], Hon. Hugh Fraser, the Hon. H. and Mrs. Bourke, the Right Hon. the Attorney-General, M.P., and Mrs. Atkinson; the Hon. Kathleen Plunket, Hon. Arthur Crichton, the Hon. Clare U’Brien, Sir Algernon and Lady Coots, Lady Milbanke, Sir John and Lady Colomb, Sir John and Lady Colthurst, Sir Arthur Vicars, Sir James and Lady Henderson, Admiral Singleton, C.B., and Mrs. Singleton; President of the Queen's College, Belfast, and Mrs. Hamilton; the President of the Queen's College, Galway; Colonel and Mrs. Vandeleur, Major and Mrs. Pakenham, Mr. and Mrs. H. White and Miss White, Miss Madeline Bourke, Colonel Sitwell, Captain and Mrs. Greer, Mrs. and Miss Hastings, Captain Fetherstonehaugh, Mr. H. R. Reade, D.L.; Mr. Dunbar Buller, Mr. A. More [?] O'Ferrall, D.L.; Captain Hall, Lord Plunket, Private Secretary; Lord Lurgan, State Steward; Major Lambart, Comptroller; Sir Gerald Dease, Chamberlain; the Viscount Castlerosse, Master of the Horse; Mr. Lionel Earle, Additional Private Secretary; Mr. H. Fetherstonhaugh, Gentleman-in-Waiting; Captain the Hon. Gerald Cadogan, A.D.C.; Lord Cole, A.D.C.; Hon. Cyril Ward, R.N., A.D.C.; Major the Hon. M. O'Brien, and Major C. Heseltine, Aides-de-Camp in-Waiting.&lt;ref&gt;&quot;Viceregal Court.&quot; ''Irish Times'' 7 February 1903, Saturday: 7 [of 12], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001683/19030207/177/0007. Same print title and p.&lt;/ref&gt; &lt;/blockquote&gt;

==== 9 February 1903, Monday ====
The beginning of the Viceregal season in Dublin with a house party at Dublin Castle hosted by the Lord Lieutenant and Countess of Dudley:&lt;blockquote&gt;Monday last week the Viceregal season commenced, and the following guests arrived at Dublin Castle, where the Lord Lieutenant and Countess of Dudley have been in residence since the preceding Friday: H. H. Prince Francis ot Teck, Catherine Duchess of Westminster and Lady Mary Grosvenor, the Duke and Duchess of Abercorn and Lady Phyllis Hamilton, the Earl and Countess of Annesley, Earl and Countess of Essex, Countess of Fingall, Viscount Brackley, Lord Vivian, Lady Barrymore and Miss Post, Hon. H. Fraser, [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]] and Miss Madelaine Bourke, Mr. and Miss White.&lt;ref&gt;&quot;The Irish Gentlewoman. The Dublin Season Commences.&quot; ''Gentlewoman'' 14 February 1903, Saturday: 42 [of 60], Col 2a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19030214/194/0042. Same print title, p. 222.&lt;/ref&gt;&lt;/blockquote&gt;

=== March 1903 ===

==== 1903 March 17, Tuesday ====
Aristocratic women supporting Irish-made laces, needlework, and clothing:&lt;blockquote&gt;It was unfortunate weather for the St. Patrick’s Day sale of the Irish Industries Association, yesterday afternoon; but, in spite of this disadvantage, the rooms were crowded, and orders wore being given and taken on all sides. [[Social Victorians/People/Londonderry|Lady Londonderry]] was, as usual, presiding over the laces of the London depôt, though she often left her stall to her assistants and went about receiving her friends. The lace shown on her stall was beautiful. The needlepoint, Limerick, and Carrickmacross flounces, collars, and coatees finding many buyers during the afternoon. The Dowager Lady Downshire presided over the Association’s stall of embroideries, and Lady Gage arrived betimes to arrange them, wearing a dress of black lace over white, trimmed with appliques, also in black and white. Lady Aberdeen, as usual indefatigable, was at the Association’s stall of knitting, carving, and baskets. And Mrs. Marjoribanks was with her, showing in her own white dress how well Irish tweeds can look when made up. Lady Marjorie Gordon was also helping her mother. As for the 21 stalls representing the various cottage industries, these were once again covered with the beautiful work the Irish peasants, or (as in the case of the Gentlewomen’s Guild Handicrafts, the Ulster Ladies’ Work depôt, and the Irish School of Art Needlework) with work done by Irish ladies. The art needlework done by the Irish School needs little recommendation, it known so well for its excellence. And there were beautiful things on its stall this year, including many portières and some very finely-worked pictures. The stall was in charge of [[Social Victorians/People/Mayo|Lady Mayo]], [[Social Victorians/People/Dudley|Georgina Lady Dudley]], [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], and [[Social Victorians/People/Beresford|Miss Beresford]]. [[Social Victorians/People/Lucan|Lady Lucan]], being always on the watch for extending the sale of the tweeds woven by the Castlebar Homespun Industry, this year shows some of a rather heavy description, made for motor coats, and one of these was on show yesterday afternoon. A pretty coat it looked, too, being carried out in cream cloth, with strapped back, and narrow collar of black velvet. Toys and furniture came from the Cushenhall and the Killarney Industries respectively, and were by no means the least patronised yesterday afternoon, whilst there was steady sale of little bunches of shamrock, which came from poor Ulster lady, who grows and gathers the plant for such occasions as these. The sale is continued to-day from 12 until 6.&lt;ref&gt;&quot;A Sale of National Work.&quot; ''Daily News'' (London) 18 March 1903, Wednesday: 12 [of 12], Col. 5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/19030318/236/0012. Print p. 12.&lt;/ref&gt;&lt;/blockquote&gt;In a display of &quot;too little, too late,&quot; on March 18, the day after St. Patrick's Day, the ''Daily Mail'' talks about events in London and Dublin in honor of St. Patrick's Day:&lt;blockquote&gt;&lt;p&gt;The bells of St. George’s Chapel, Windsor Castle, were rung yesterday morning in honour of Ireland’s patron Saint. Sprays of shamrock were worn as “button-holes” by some of the residents in Windsor, Eton, and the surrounding districts.&lt;/p&gt;

&lt;p&gt;For the first time on record, St. Patrick’s Day was observed as a general holiday in Dublin. A large crowd witnessed the ceremony of the trooping of the colour by the 4th Battalion Royal Warwickshire Regiment, in Upper Yard, Dublin Castle. The Lord Lieutenant, on horseback, attended by his staff, was present.&lt;ref&gt;&quot;A Sale of National Work.&quot; ''Daily News'' (London) 18 March 1903, Wednesday: 12 [of 12], Col. 5c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/19030318/236/0012. Print p. 12.&lt;/ref&gt;&lt;/p&gt;&lt;/blockquote&gt;

===June 1903===
Summer 1903: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

==== 19 June 1903, Friday ====

===== Grand Ball in the Waterloo Chamber at Windsor Castle =====
King Edward and Queen Alexandra hosted a grand ball at Windsor Castle as &quot;a wind-up to the Ascot festivities.&quot;&lt;ref&gt;&quot;The Court at Windsor. Grand Ball in the Waterloo Chamber. Eight Hundred Guests.&quot; ''London Daily Chronicle'' 20 June 1903, Saturday: 4 [of 10], Cols. 6b–7c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0005049/19030620/053/0004. Print title: ''The Daily Chronicle'', p. 4.&lt;/ref&gt;

==== 1903 June 23, Tuesday ====

A children's party at Buckingham Palace:&lt;blockquote&gt;(From the Court Circular.)

Their Majesties gave a children’s party in the garden of the Palace this afternoon in honour of the ninth birthday his Highness Prince Edward of Wales, at which their Royal Highnesses the Prince and Princess of Wales with their children, Princess Louise, Duchess of Fife, and the Duke of Fife, with their children, the Princess Victoria and their Serene Highnesses the Duke and Duchess of Teck, with their children, were present.

The following, with their children, some of whom were unable to obey their Majesties' command, had the honour of receiving invitations: The Duke and Duchess of Beaufort, the Duke and Duchess of Buccleuch and Lady Constance Scott, the Duke and Duchess of Leeds, the Duke and Duchess of Marlborough, the Duke and Duchess of Portland, the Duke and Duchess of Sutherland, Catherine, Duchess of Westminster, the Marquis and Marchioness of Granby, the Marquis and Marchioness of Hamilton, the Countess of Airlie, the Earl and Countess of Albemarle, the Countess of Antrim, the Earl and Countess Carrington, the Earl and Countess of Dalkeith, the Earl and Countess of Denbigh and Desmond, the Earl and Countess of Essex, the Earl and Countess of Mar and Kellie, the Earl and Countess of Normanton, the Earl and Countess of Pembroke and Montgomery, the Earl and Countess of Selborne, the Earl and Countess of Stradbroke, the Countess de Mauny-Talvande, Viscount and Viscountess Chelsea, Viscount and Viscountess Castlereagh, Viscount and Viscountess Churchill, Viscount and Viscountess Coke, Viscount and Viscountess Cranborne, Viscount and Viscountess Falmouth, Lord and Lady Balfour of Burleigh, Lord and Lady De Ramsey, Lady Farquhar, Lady Cynthia Graham, Lord and Lady Hastings, Lord and Lady Hillingdon, Lord and Lady Knollys, Lord and Lady Lurgan, Lord and Lady St. Oswald, Lord and Lady Settringto, Lord and Lady Alice Stanley, Lord and Lady Suffield, Lord and Lady Wolverton, Mr and the Hon. Mrs. Gervase Beckett. Hon. [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], Mr. and the Hon. Mrs. Lionel Cust, Hon. Mrs. Geoffrey Glyn, Lientenant-Colonel Hon. Charles and Mrs. Harbord, Hon. Charles and Mrs. Hardinge, Hon. Sydney and Lady Mary Holland, Hon. Derek and Mrs. Keppel, Hon. George and Mrs. Keppel, Hon. Frederick and Mrs. Lambton, Hon. Lancelot and Mrs. Lowther, Sir Richard and Hon. Lady Musgrave, Hon H. and Lady Feodorowna Sturt, Hon. Dorothy Violet and Hon. Alexandra Vivian, Mr and Lady Aline Beaumont, Mr. and Lady Katherine Brand, Mr. and Lady Violet Brassey, Mr. and Lady Moyra Cavendish, Mr. and Lady Evelyn Cavendish, Sir E. and Lady Colebroke, Captain and Lady Jane Combe, Sir H. and Lady de Trafford, Mr. and Lady Eva Dugdale, Sir E. and Lady Edmonstone, Major-General Sir R. and Lady Beatrice Pole-Carew, Sir G. and Lady Maud Warrender, Mr. and Mrs. Rupert Beckett, Revd. Canon and Mrs. Dalton, Mr. and Mrs. Farquharson of Invercauld, Mr. and Mrs. W. Grenfell, Mr. and Mrs. A. Hay-Drummond, Mr. and Mrs. W. James, Mr. and Mrs. Blundell Leigh, Mr. and Mrs. Sartoris.&lt;ref&gt;&quot;Prince Eddie's Birthday.&quot; ''Daily News'' (London) 24 June 1903, Wednesday: 7 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/19030624/197/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

=== July 1903 ===

==== Party Hosted by the Duke and Duchess of Marlborough ====
1903 July 10, Friday, or so, the ''World'' reported (reprinted by the ''Melton Mowbray Times'') on a party hosted by the Duchess of Marlborough:&lt;blockquote&gt;The Duke and Duchess of Marlborough's week-end party consisted of the Duchess of Sutherland, Lord Rosebery, Lady Lansdowne, Lord and Lady Tweedmouth, the Russian Ambassador, Lady Huntingdon, Count Albert Mensdorff, Lord Percy, Sir lan and Lady Hamilton, Mr. and Mrs. Charles Hardinge, [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], Mr. and Mrs. George Cornwallis-West, Colonel W. Lambton, Mr. and Mrs. Maguire, Miss Deacon, and Captain Brinton. — ''The World''&lt;ref&gt;&quot;Local News.&quot; ''Melton Mowbray Times and Vale of Belvoir Gazette'' 17 July 1903, Friday: 8 [of 8], Col. 2b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001806/19030717/166/0008. Print title: ''Melton Mowbray Times'', n.p.&lt;/ref&gt;&lt;/blockquote&gt;

=== August–September 1903 ===

==== 20 and 25 August and 3 September 1903 ====
The 1903 America's Cup yacht race in New York Harbor with Nathaniel Herreshoff's ''Reliance'' for the US and Sir Thomas Lipton's ''Shamrock III'' for the UK,&lt;ref&gt;{{Cite journal|date=2022-09-11|title=1903 America's Cup|url=https://en.wikipedia.org/w/index.php?title=1903_America%27s_Cup&amp;oldid=1109663279|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/1903_America%27s_Cup.&lt;/ref&gt; the 12th challenge for the cup and &quot;the most expensive Cup challenge in history.&quot;&lt;ref name=&quot;:0&quot;&gt;{{Cite web|url=https://www.americascup.com/history/26_LIPTONS-THIRD-CHALLENGE|title=LIPTON’S THIRD CHALLENGE|last=Cup|first=America's|website=37th America's Cup|language=en|access-date=2024-07-02}} https://www.americascup.com/history/26_LIPTONS-THIRD-CHALLENGE.&lt;/ref&gt; The first race was run on 20 August 1903, the 2nd on 25 August and the 3rd on 3 September.&lt;ref name=&quot;:0&quot; /&gt; Because the ''Reliance'' won the first 3 races, the best 3-out-of-5 race ended after the 3rd one.

===October 1903===
Sometime in October 1903, [[Social Victorians/People/Arthur Conan Doyle|Arthur Conan Doyle]]'s &quot;The Adventure of the Empty House,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 331).
====31 October 1903, Saturday====
Halloween.
===November 1903===
Sometime in November 1903 Arthur Conan Doyle's &quot;The Adventure of the Norwood Builder,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 415).
====5 November 1903, Thursday====
Guy Fawkes Day
===December 1903===
Sometime in December 1903 Arthur Conan Doyle's &quot;The Adventure of the Dancing Men,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 529).
====16 December 1903, Wednesday====
&quot;On 16 December, Punch satirised an activity in which Dolmetsch was concerned. [[Social Victorians/People/Florence Farr|Florence Farr]] was acting as secretary for a newly-formed fellowship known as 'The Dancers', a body whose aim was to 'fight the high and powerful devil, solemnity'. In a poem entitled L'Allegro up to date, the final stanza is devoted to Dolmetsch:
&lt;poem&gt;:The old forgotten dancing-lore,
:The steps we cannot understand,
:DOLMETSCH agrees to take in hand,
:These on the well-trod stage anon,
:When next our learned sock is on,
:We’ll show, while ARNOLD, Fancy’s child,
:Tootles his native wood-wind wild.&lt;/poem&gt;
This verse is curiously prophetic for Dolmetsch had not yet introduced the recorder into his concerts, although he occasionally included a flute. Dolmetsch did know something of the steps of the old dances but it was his wife who later researched the subject most thoroughly and wrote two books on the subject.&quot; (Campbell 151–52)

===25 December 1903, Friday===
Christmas Day
====26 December 1903, Saturday====
Boxing Day
===Works Cited===
*Baring-Gould.
*Campbell.

==1904==
===January 1904===
Sometime in January 1904 [[Social Victorians/People/Arthur Conan Doyle|Arthur Conan Doyle]]'s &quot;The Adventure of the Solitary Cyclist,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 399).
===March 1904===
Sometime in March 1904 Arthur Conan Doyle's &quot;The Adventure of Black Peter,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 384).

===April 1904===
Sometime in April 1904, Arthur Conan Doyle's &quot;The Adventure of Charles Augustus Milverton,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 558, n. 1, and 559).

===May 1904===

==== 17 May 1904, Tuesday ====

===== Countess Cadogan's Great Bazaar =====
The ''London Daily Chronicle'' reported about this event but does not name the date. Also, this report mentions outbreaks of measles and chicken pox among children.&lt;blockquote&gt;Sir Philip Burne-Jones has offered to arrange the tableaux vivants that are to take place at the Albert Hall on the opening day of Countess Cadogan’s great bazaar. One of the tableaux will represent &quot;Mary, Mary, quite contrary, how does your garden grow?” and a very pretty little girl has been selected as the central figure. A pleasing feature will be the grouping of children dressed as flowers to represent the garden. Many well-known people in London have been asked to allow their children to take part, but as there is at the present time a good deal of sickness about, such as measles and chicken-pox, a considerable number have had to decline. The following ladies, however, have consented to let their children appear: — The Marchioness of Granby, the Countess of Huntingdon, the Countess Bathurst, the Countess of Mar and Kellie, Lady St. Oswald, Lady Dickson-Poynder, Lady Griffin, the wife of Sir Lepel Griffin, the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], Mrs. Drake, and Mrs. Calverley.&lt;ref&gt;&quot;Society and Personal.&quot; ''London Daily Chronicle'' 17 May 1904, Tuesday: 4 [of 10], Col. 4a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/19040517/073/0004. Print title: ''The Daily Chronicle'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1904===
Sometime in June 1904 Arthur Conan Doyle's &quot;The Adventure of the Three Students,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 370).

Summer 1904: [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

===July 1904===
Sometime in July 1904, Arthur Conan Doyle's &quot;The Adventure of the Golden Pince-Nez,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 351).
===August 1904===
Sometime in August 1904, Arthur Conan Doyle's &quot;The Adventure of the Missing Three-Quarter,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 476).

===September 1904===
Sometime in September 1904, Arthur Conan Doyle's &quot;The Adventure of the Abbey Grange,&quot; illustrated by Sidney Paget, was published in the ''Strand'' (Baring-Gould II 491).

==1905==
===April 1905===
====3 April 1905, Monday====
[[Social Victorians/People/William Butler Yeats|W. B. Yeats]] wrote to Lady Gregory from Dublin, saying he had &quot;dictated a rough draft of a new Grania second act to Moore's typewriter&quot; (Wade 368).

==== 1905 April 26, Wednesday ====

===== New Forest United Hunt Ball =====
&lt;blockquote&gt;The annual New Forest United Hunt ball was held at the New Forest Hall, Lyndhurst, on Wednesday night, and it was a very brilliant and highly successful and enjoyable gathering, other hunts being represented, besides those of the New Forest. The decorations were, as usual, entrusted to Mr. W. Gerrard, the proprietor of the hall, who carried it out in a most artistic manner. The ball-room presented a very grand appearance with the green and white muslin curtains draped at the windows, and the panels on the walls, while the ceiling beams were also festooned in green and white. The room was exceedingly well lighted, and plants and flowers for the front of the orchestra were lent by Mr. R. G. Hargreaves, J.P., of Cuffnells Park, and those for the windows and other parts by Mr. H. F. Compton, J.P., of Manor House, Minstead. The floor was in splendid order for dancing, and the company were quite delighted with it. The supper room was adorned with red and white, the retiring rooms with pink and white; the cool retreats from the ballroom were lit with fairy lamps, and the tea-room was adorned in white and gold. The stewards were the Hon. Gerald Lascelles and Mr. E. L. Wingrove (hon. sec. of the New Forest Hunt Ciub), and Mrs. Lascelles and Mrs. Compton took a leading part in carrying out the arrangements, which left nothing to be desired to secure the comfort and enjoyment of the guests, who commenced to arrive about ten o'clock, soon after which dancing began to the strains of Leader’s Radelki Band, from London, conducted by Norman Denarius. The programme was as follows:—

Valse — Wein, Weib und Gesang . . . . . . . . . Strauss&lt;br&gt;
Valse — Tout Passe . . . . . . . . . Berger&lt;br&gt;
Valse—Veronique . . . . . . . . . Messager&lt;br&gt;
Two Step — Mosquito Parade . . . . . . . . . Bendix&lt;br&gt;
Valse — L’Amour et a la vie Vienne . . . . . . . . . Kornzak&lt;br&gt;
Lancers — The Orchid . . . . . . . . . Caryll&lt;br&gt;
Valse — Choristers . . . . . . . . . Phelps&lt;br&gt;
Valse — Luna . . . . . . . . . Lincke&lt;br&gt;
Valse — Les Amourettes . . . . . . . . . Dubois&lt;br&gt;
Polka — Whitling Rufus . . . . . . . . . Mills&lt;br&gt;
Valse — Amoureuse . . . . . . . . . Berger&lt;br&gt;
Lancers — Veronique . . . . . . . . . Messager&lt;br&gt;
Valse — Midsummer . . . . . . . . . Marigold&lt;br&gt;
Valse — Gold and Silver . . . . . . . . . Lehar&lt;br&gt;
Valse — Casino Tanze . . . . . . . . . Gung'l&lt;br&gt;
Two Step — Hiawatha . . . . . . . . . Moret&lt;br&gt;
Valse — Bleue . . . . . . . . . Marcis&lt;br&gt;
Valse — Caressante . . . . . . . . . Lambert&lt;br&gt;
Lancers — Earl and the Girl . . . . . . . . . Caryll&lt;br&gt;
Valse — Blue Danube . . . . . . . . . Strauss&lt;br&gt;
Valse — Eton Boating Song . . . . . . . . . Kapa [?]&lt;br&gt;
Galop — John Peel . . . . . . . . . Hunt&lt;br&gt;

In addition to this there were a couple of valses extra, at the conclusion of the programme, and it was not until four o’clock on Thursday morning that the playing of the National Anthem announced the conclusion of the ball, which will be long remembered by those who participated in it for the great amount of enjoyment it afforded, and the admirable manner in which it was carried out, thanks to the indefatigable exertions of the stewards. All the guests expressed their extreme pleasure and satistaction with it, and it was unanimously voted as one of the most delightful reunions of the kind ever held in connection with the hunts. The refreshment department was again entrusted to Mr. G. Etheridge, of Southampton, who gave the utmost satisfaction, his catering being deservedly praised. The menu is appended:—

Soups.&lt;br&gt;
Clear Turtle. Consomme. Printeniere.&lt;br&gt;
Lamb Cutlets and Peas.&lt;br&gt;
Cold.&lt;br&gt;
Quenelles of Chicken en Aspec.&lt;br&gt;
Salmon Plain. Salmon Mayonnaise.&lt;br&gt;
Roast Turkeys.&lt;br&gt;
Boned Turkey and Cailles Farcie.&lt;br&gt;
Roast Chicken.&lt;br&gt;
Braized Ox Tongues. York Hams.&lt;br&gt;
Raised Pies.&lt;br&gt;
Pressed Spiced Beef. Galantine of Chicken.&lt;br&gt;
Galantine of Veal.&lt;br&gt;
Patties — Assorted. Lobsters Plain.&lt;br&gt;
Lobster Salad. Plain Salads.&lt;br&gt;
Foi Gras en Aspec.&lt;br&gt;
Plovers Eggs.&lt;br&gt;
Sweets.&lt;br&gt;
Maraschino Jellies. Pine Apple Jellies.&lt;br&gt;
Noyeau, Vanilla, and Strawberry Creams.&lt;br&gt;
Meringnes [sic]. Triffles. Fancy Pastry.&lt;br&gt;
Maids of Honour.&lt;br&gt;
Buffet.&lt;br&gt;
Tea. Coffee. Home Made Lemonade.&lt;br&gt;
Claret Cup. Hock Cup.&lt;br&gt;
Sandwiches — Assorted.&lt;br&gt;
Cakes (Fancies), etc. Ices.&lt;br&gt;
Strawberry and Vanilla Creams. Lemon Water.&lt;br&gt;

The number present was 205, some fifty more than last year, and among them — and many gentlemen were in scarlet coats — were Lord Leconfield, M.F.M., Lord Wodehouse, Hon. E. Perrlepont [Perriepont?], Hon. John Scott-Montagu, M.P., and Lady Cecil Scott-Montagu, Sir Charles and Lady Darling, Miss Darling, Hon. Dudley Carleton, Hon. Gerald and Mrs. Lascelles, Miss Lascelles, Captain R. C. H. Sloane Stanley and Olivia Countess Cairns, [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]], Sir George Meyrick, Lady Meyrick, Miss Meyrick, Miss Phipps, the Count de Miremont, Hon. Mrs. Alwyn Greville, Captain G. D. Jeffreys (Grenadier Guards) and the Viscountess Cantelupe, Mr. G. and Lady Augusta Fane, Mr. B. Howard, Miss Clara Howard, Mr. F. M. Sibbald Scott (3rd Battalion Royal Scots), Mr. Camellan (Hampshire Regiment), Miss M. Bowden Smith, Miss Cumberbatch, Miss Sibbald Scott, Mr. and Miss Pitcher, Captain and Mrs. Maitland, Miss Maitland, Mr. Vachell, Mr. Noel Baxendale, Mrs. Heathcote, Miss Heathcote, Miss M. Heathcote, Miss Bainbridge, Mr. Woodyatt, Mr. Noel, Miss Laura Jones, Major Dalrymple, Mrs. Dalrymple, Miss Dalrymple, Miss Anderson, Mr. H. R. Dalrymple, Mr. Gordon, Mr. Nevile Henderson, Mr. C. L. Hargreaves, Mr. R. Gand, Mrs. Hargreaves, Mr. John Jeffreys, Mrs. Jeffreys, Miss Gwendolin Jeffreys, Miss Mildred Jeffreys, Mr. Cosmo Douglas, R.N., Lieutenant R. D. Ward, R.N., Mr. J. L. Forbes, R.A., Mr. E. Scott Mackirdy, Mr. Robert Pearce and Mrs. Pearce, Miss E. Ward, Major H. L. Powell, Mrs. Powell, Mr. Salt, R.H.A., Mr. Balston, R.H.A., Miss Inagh Frewen, Mr. W. S. D. Craven, Mr. Gerald Duplessis, Miss Duplessis, Captain and Mrs. Standish, Miss Beatrice Pulteney, Mrs. Pigott, Captain Granville, Mrs. Granville, Mr. and Mrs. Henry Martin Powell, Colonel Fowle, Captain Halaban, Captain Bathurst, Mr. Gillson, Lieutenant Eric Fullerton, R.N., Mr. C. Herbert, Colonel Barklie McCalmont, C.B., Mrs. McCalmont, Miss McCalmont, Miss M. Phelps, Captain A. C. Herbert, Captain and Mrs. Burns Hartopp, Miss Bodkin, Mr. Edward Hawkins, Mrs. Hawkins, Miss Abercromby, Mr. A. Bazley-Worthington, Mr. Meyrick, Mr. Nugent, Miss Morant, Captain H. T. Timson, Mrs. Timson, Mr. G. Eyre Matcham, Mrs. Matcham, Miss Jeffreys, Mr. Ralph Macan, Captain W. A. Grant and Mrs. Grant, Mr. and Mrs. A. G. Glasgow, Miss Alyn Mazall, Dr. Hastings Stewart, Mr. Fitzgerald, Mr. Butler, Miss Arnold, Mrs. Robinson, Captain Synars, Mr. N. Learmonth, Captain Warren Peacocke, Mrs. Peacocke, Mr. John Peacocke, Miss Wade, Miss Frewen, Miss Pryor, Miss Bodkin, Mr. Marriott, Mr. and Mrs. Dixon, Mr. H. Fane, Mr. Robinson, Mr. and Mrs. Rayleigh Phillpotts, Miss Lyon, Mrs. Butler, Mr. and Mrs. Morgan, Mr. Arthur L. Watson, Mr. C. H. Wilmer, Miss M. Farquharson, Mr. Merric Bovill, Mr. Skeene, Miss Chandos Pole, Colonel and Mrs. Spurgin, Captain Johnston Browne, Mr. J. Darling, Mr. Hugh Neville, Miss G. Milne, Mr. E. Martin, Miss Gossip, Mr. J. Blake, Mr. R. E. S. Pearce, Rev. C. Maturin, Major Wyndham Pain, Mrs. Wyndham Pain, Mr. A. C. Crossley, Captain Innes, Mr. L. R. Hargreaves, Miss Bryan, Mr. A. K. Hargreaves, Miss Skene, Miss Merehouse, Mr. Thornhill, Mr. and Mrs. Price, Mr. Freeland, Mr. E. Meade-Waldo, Mrs. Meade-Waldo, Mr. W. I. Whitaker, the Hon. Mrs. Whitaker, Miss Blythe, Mr. and Mrs. Walter Douglas Scott, Major R. E. Bolton (Scots Guards), Mr. E. Harington, Miss Meade-Waldo, Miss Dorothy Meade-Waldo, Mr. Ernest L. Wingrove, Mr. H. F. and Mrs. Compton, Miss Jeffray, Mr. Farquharson, Captain Godfrey Heseltine, Mr. D. Grimmell-Milne, Mrs. Godfrey Baring, Mr. T. C. Musgrave, Mr. H. W. Eaden, Mrs. Eaden, and party, Captain Granville, Mr. A. L. Duncan, Miss Arkwright, Mrs. Crofton, Captain Ellis.&lt;ref&gt;&quot;New Forest United Hunt Ball. A Brilliant Gathering at Lyndhurst.&quot; ''Hampshire Advertiser'' 29 April 1905, Saturday: 6 [of 12], Col. 2a–b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/19050429/163/0006. Print title ''Hampshire Advertiser County Newspaper'', p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1905===
Summer 1905: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).
===July 1905===
====10 July 1905, Monday====
1905 July 10, the Austro-Hungarian Ambassador hosted a dinner party:&lt;blockquote&gt;The Austro-Hungarian Ambassador entertained the Duke and Duchess of Connaught and Princess Patricia of Connaught at dinner at the Embassy in Belgrave-square on Monday evening. There were also present the Spanish Ambassador and Mme. Bernabé, the United States Ambassador and Mrs. and Miss Whitelaw Reid, Princess Hohenlohe, Prince Francis of Teck, Princess Teano, the Earl of Essex, the Earl and Countess of Crewe, Viscount Villiers, Viscount Errington, Viscount Newry, Mrs. J. Leslie, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Mr. R. Graham, Mrs. Astor, Lady Maud Warrender, Prince Furstenburg, Count Szenchenyi, Captain A. Meade, and Miss Pelly and Colonel Murray in attendance on the Duke and Duchess.&lt;ref&gt;&quot;Court Circular.&quot; ''Times'', 12 July 1905, p. 7. ''The Times Digital Archive'', http://tinyurl.galegroup.com/tinyurl/AHRNq6. Accessed 20 June 2019.&lt;/ref&gt;&lt;/blockquote&gt;

==== Last week of July, 1905 ====
Lady Cadogan hosted a children's party at Chelsea House:&lt;blockquote&gt;Lady Cadogan’s children’s party last week at Chelsea House was one of the prettiest sights imaginable. Her grandchildren, the little Chelseas, came to help entertain the guests, and nearly all the smart women in London brought their small folk. One of loveliest little girls present was Daphne Bourke, Mrs. [[Social Victorians/People/Bourke|Algernon Bourke]]’s only child; and Lady De Trafford’s young daughter Violet was much admired, and Lady Maud Ramsden’s little people were among daintiest of the small children.&lt;ref&gt;&quot;Court and Social News.&quot; ''Belfast News-Letter'' 01 August 1905, Tuesday: 7 [of 10], Col. 6b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/19050801/157/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

===September 1905===

==== 1 September 1905, Friday ====

===== Society Sportswomen =====
The ''Willesden Chronicle'' published a piece on sportswomen, as did the ''Kilburn Times Hampstead and North-Western Press''.&lt;ref&gt;&quot;Society Sportswomen.&quot; ''Kilburn Times Hampstead and North-Western Press'' 1 September 1905, Friday: 7 [of 8], Col. 5c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001813/19050901/191/0007.&lt;/ref&gt; The article does not list Lady Violet Greville, who did deer-stalking in Scotland, but perhaps she wasn't as good as these women or she was not socially important the way many of these women were; she was certainly not in the social networks that included some of them.&lt;blockquote&gt;Each season sees new recruits in the ranks of Society sportswomen. Princess Charles of Denmark is a skilled shot, and as a child was taught to shoot at a target. Princess Victoria Melita of Saxe-Coburg, formerly Grand Duchess of Hesse, and niece to King Edward, is another famous markswoman.

The Duchess of Bedford is a splendid shot, and so is the Duchess of Newcastle, who killed many head of big game in the Rocky Mountains. The Marchioness of Breadalbane is a first-rate rife shot and deer-stalker. Lady Loch shoots well, and many fine stags have fallen to her rifle. Lady Sandhurst and the [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]] must also be included among noted deerstalkers. Lady Hindlip is another big game shot, and brought down and brought home a giraffe from her recent travels in East Africa. Lady Delamere has also secured some notable trophies from the African jungle.

Lady Wolverton, Lady Helen Stavordale, Lady Vivian, and Lady Juliet Duff are all good markswomen, and Lady Constance Stewart- Richardson is, of course, second to none as a noted sportswoman. She has shot stags in Scotland, big game in the jungles of Ceylon, and wild hogs on the plains of South-West Texas. Lady Beatrice Pole-Carew is another splendid shot, and the list also includes Lady Wickham, sister to the Marquis of Huntly, Lady Constance Scott, daughter of the Duke and Duchess of Buccleuch, Mrs. Asquith, and Miss Muriel Wilson.

Mrs. Alan Gardner, daughter Sir James Blyth, has killed big game in the four quarters of the globe; and Mrs. George Cornwallis West shoots as well she writes or plays on the piano. The Hon. Mrs. Lancelot Lowther is a good rabbit shot, and Violet Lady Beaumont and the Countess of Warwick are deadly with partridges and pheasants.&lt;ref&gt;&quot;Society Sportswomen.&quot; ''Willesden Chronicle'' 1 September 1905, Friday: 7 [of 8], Col. 5c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001721/19050901/127/0007. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

===October 1905===

==== 1905 October 14, Saturday ====
A &quot;send-off dinner&quot; for Jerome K. Jerome before his trip to the U.S. occurred at the Garrick Club &quot;the other evening&quot; before October 14:&lt;blockquote&gt;Jerome K. Jerome has undertaken a six months lecturing tour in the United States. I believe that this tour will be a great success, particularly when the Americans come to realise that Mr. Jerome is not only a humorous writer but a brilliant, serious writer with very genuine pathos. His appeal on this side has not, perhaps, gone home to the English people as much as it should, but the quick-witted Americans will not be slow to recognise his talents of both kinds, nor will they fail to appreciate the significance of the fact that the other evening a send-off dinner was given to Mr. Jerome at the Garrick Club. The hosts of the evening were Mr. Pett Ridge and Mr. W. W. Jacobs, which shows that there is no such thing as literary jealousy among our best humorists.

The presence of quite a galaxy of novelists to the dinner to Mr. Jerome, including Mr. Barrie, Sir Arthur Conan Doyle, Mr. Max Pemberton, Mr. H. G. Wells, Mr. G. B. Burgin, Mr. Arthur Morrison, and Mr. Israel Zangwill, serve to indicate the existence of a pleasant brotherhood among the writers of fiction. The readers of ''Three Men in a Boat'' may be interested to know that there were also present Mr. Jerome's companions in that famous journey — Mr. Carl Hentschel and Mr. C. Wingrove.

When I have named further the presence of three artists in Mr. A. S. Boyd, Mr. John Hassall, and Mr. Will Owen, and two journalists in Dr. Robertson Nicoll and [[Social Victorians/People/Rook|Mr. Clarence Rook]], I have given some record of an exceedingly pleasant dinner party. The essential point, however, of this enumeration of names is that many of them are among the most highly honoured of Englishmen in the United States, and that thus Mr. Jerome cannot fail to reap additional benefit from this dinner so thoughtfully given in his honour by Mr. Jacobs and Mr. Pett Ridge.&lt;ref&gt;S., C. K. &quot;A Literary Letter.&quot; ''The Sphere'' 14 October 1905, Saturday: 16 [of 20], Col. 2a–c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001861/19051014/022/0016. Print p. 56.&lt;/ref&gt;&lt;/blockquote&gt;

===November 1905===
Sometime in November 1905, &quot;Arnold Dolmetsch was again asked to provide music for a Been Greet season in New York — an engagement that brought about his first meeting with two young actors on their first American tour, Sybil Thorndike, and her brother, Russell&quot; (Campbell 169). Dolmetsch's return to the US; was [[Social Victorians/People/Horniman|Annie Horniman]] still with the Thorndikes?

==1906==
===March 1906===
====5 March 1906====
&quot;Mr. Frederick John Horniman, who died on March 5, in his seventy-first year, was the son of that well-known Quaker and tea-merchant, John Horniman, who made a magnificent fortune by retailing tea in air-tight packets, and, like his father, devoted both time and wealth to charitable objects. A great traveller, both for business and pleasure, Mr. Horniman gathered togther an admirable collection of curios, and this is housed at Forest Hill in the museum that bears his name. His private benefactions were also large. Mr. Horniman, who was a Liberal, sat in two Parliaments, representing Penrhyn and Falmouth Boroughs in one. He did not seek re-election in January last.&quot; (&quot;The World's News.&quot; Illustrated London News (London, England), Saturday, March 10, 1906; pg. 338; Issue 3490, Col. C)
===June 1906===
Summer 1906: [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

=== December 1906 ===

==== 1906 December 10, Monday ====
Lady Dudley's sale of Irish needlework:&lt;blockquote&gt;Quite a large number of Americans attended Lady Dudley's sale of beautiful Irish needlework at 7, Carlton-gardens on Monday. The Duchess of Roxburghe, in mouse-coloured velvets and sable, was one of the earliest buyers. Mrs. Astor was another American who bought extensively, and the Duchess of Marlborough, who visited the sale on Sunday, secured a couple of charming water-colours, &quot;Dusk in Glasnevin &quot;and &quot;The Circus Clown,&quot; while Lady Essex bought the six-guinea cushion cover made at [[Social Victorians/People/William Butler Yeats|Miss Yeats]]'s school at Dundrum.

[[Social Victorians/People/Mayo|Lady Mayo]], who came over from Ireland especially to help, had a table heaped with embroidery, and Adeline Duchess of Bedford presided over the raffles, and disposed of guinea chances for an exquisite panel enamelled on silver.

Lady Mar and Kellie remained until her sister, Lady Maud Warrender, had sung her last song, and Lady Dickson-Poynder came with her pretty little daughter and Mrs. Asquith. Lady Kenmare and her daughter were selling from a central table, and the Duchess of Rutland, in deep black, Mrs. Harry Lindsay, [[Social Victorians/People/Bourke|Mrs. Algernon Bourke]], and Lady Grosvenor were among those to be seen in the tea-room downstairs.&lt;ref&gt;&quot;London Gossip.&quot; ''American Register'' 15 December 1906, Saturday: 4 [of 8], Col. 5c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003338/19061215/035/0004. Print title and p. the same.&lt;/ref&gt; &lt;/blockquote&gt;

==1907==
===April 1907===
April 1907, [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] went to Italy with Lady Gregory (Harper 80 28).
===June 1907===
Summer 1907: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

'''1907 June 22, Saturday'''
The annual dinner of the Correctors of the Press was held at De Keyser's Royal Hotel:&lt;blockquote&gt;The London Association of Correctors of the Press held their annual dinner at De Keyser’s Royal Hotel on Saturday. The Chairman was the Lord Mayor, and among his supporters were Sir John Cockburn, Colonel David Bruce, Colonel Earl Church, Lieutenant-Colonel Alsager Pollock, Sheriff Dunn, Mr. J. W. Cleland, M.P., Mr. R. Donald, Mr. T. Seccombe, Mr. Francis H. Skrine, Major H. F. Trippel, Mr. Walter Haddon, Mr. W. Pett Ridge, Mr. W. H. Helm, Mr. R. Warwick Bond, Mr. F. W. Rudler, Major Vane Stow, [[Social Victorians/People/Rook|Mr. Clarence Rook]], Mr. J. Randall (Chairman of the Association), Mr. Foxen, and Mr. Feldwick. Proposing the toast of &quot;Literature,” Mr. W. H. Helm speculated as to what would follow the banning of &quot;Mary Barton&quot; by the Education Committee of the London County Council. In his opinion &quot;The Swiss Family Robinson&quot; was a more immoral book, because beyond any other work it had fostered the Micawber view of life. (Laughter.) The LORD MAYOR [init caps large, rest sm, throughout], submitting the toast of &quot;The Readers' Pension Fund,” apologised for appearing in morning dress. The reason was that he had been to the King’s Garden Party at Windsor, and whlle he was returning to London by motor something burst. (Laughter.) Only that morning he had arrived from Berlin, where he learned some lessons useful to people who give dinners. When the Oberburgomeister of Berlin proposed the health of, say, the Lord Mayor of London, there was an end of the business. He did not push forward the Houses of Parliament, the Navy and Army, or even Literature. (Laughter.) Being a practical people the Germans when they met for a particular purpose applied themselves to no other, and the English would well to copy them. (Hear, hear.) Mr. J. RANDALL said that last year the Association helped five readers and one reader’s widow to pensions, and this year it had done the same for two readers and two widows. One of the men assisted last March had taught himself Greek, Arabic, and Sanscrit, and in leisure moments amused himself by making object glasses for microscopes and telescopes. At this very gathering there was a printer’s reader who was Hebrew scholar. (Hear, hear.) With regard to finance Mr. Randall was happy to say that this dinner would enable the Association to establish a fourth pension. (Cheers.) The Lord Mayor, [[Social Victorians/People/Borthwick|Lord Glenesk]] (President of the Readers' Pensions Committee), the Clothworkers’ Company, and the Cutlers’ Company had contributed ten guineas each, and the total addition to the fund resulting from the dinner was £l90. During the evening excellent entertainment was provided by Miss Helena Foxen, Miss Kathleen Dwyer, Mr. T. C. Bell, Mr. P. E. Syrett, Mr. Prank Rhodes, and Mr. E. Croft-Williams, the last-named being the hon. musical director.&lt;ref&gt;&quot;Correctors of the Press.&quot; ''Morning Post'' 24 June 1907, Monday: 4 [of 14], Col. 3c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19070624/074/0004. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

===August 1907===

==== Polo Week at Eaton Hall, Duke and Duchess of Westminster ====
On 24 August, the Queen reported about the week at Eaton Hall:&lt;blockquote&gt;My Cheshire friends have written me a most interesting account of the polo week at Eaton Hall, where the Duke and Duchess of Westminster have been entertaining a large party, including the Duke's sister, Lady Beauchamp; his cousin, Mrs Ivor Guest, and her husband; Lady Constance Stewart-Richardson, Lord Cholmondeley and his lovely daughter, Lady Lettice Cholmondeley; and Miss Millicent Grosvenor, whose engagement to Mr Wallis, of the Scots Guards, was announced at the end of the season. Others of the party at Eaton were Lord and Lady Arthur Grosvenor (of caravan fame), Mr and Mrs Frank Bellville (who had been entertaining at Papillon Hall the week before for the Rugby polo tournaments), Mr G. and Mr C. Miller and their wives, Lord Shrewsbury, Lord Wodehouse, Lord Ingestre, Mr Osmond Hastings, Capt. de Crespigny, [[Social Victorians/People/Bourke|Mr Algernon Bourke]], and several others. At Saighton Grange Lady Grosvenor's guests included Lady Marjorie and Lady Violet Manners, Lady Mildred Follet and her husband, Lord Hugh Cecil and Mr Banbury, as well as Lady Grosvenor's handsome young son, Mr Percy Wyndham; and these were all day at Eaton taking part in the polo or looking on. Capt. Miller, who helps the Duke to organise the tournament, brought with him his pack of beagles from Rugby, and when not following these in the early morning the indefatigable guests were cubhunting at dawn. This in addition to the polo matches every afternoon held on the Duke' s private ground — one of the best in England — in the beautiful park. Eight teams competed, and the play was most exciting, especially in the final on Friday, contested by the two teams that had hitherto won all the ties. These were Hotspurs — Mr Banbury, Capt. de Crespigny, Mr Nickalls, and Capt. Campbell — and Eaton Hall — Mr Percy Wyndham (the Duke's half brother), Major Hobson. Mr J. A. Miller, and the Duke of Westminster. The Hotspurs won a most thrilling game by five goals to four.

The Duchess had engaged Gottlieb's delightful band for the week, and in the evening she often sang to the accompaniment of some of its members, which delighted her guests, for her voice is quite beautiful. On Thursday the party was joined by Lord and Lady Mary Crichton and Lord and Lady Hugh Grosvenor; Lady Grosvenor brought over her guests from Saighton, and there was a small dance in the evening. The day before, it being too wet to play polo, a cinematograph show was got up for everyone's amusement in the ballroom. On Saturday the party scattered, and the Duke and Duchess went north to Lochmore, and are due in Ireland later on for the horse show week. Princess Henry of Pless, the Duchess of Westminster's only sister, has been thrown into mourning by the death of her father-in-law, the Duke of Pless, to whose title and vast possessions her husband now succeeds.&lt;ref&gt;Mouche. &quot;My Social Diary.&quot; ''The Queen'' 24 August 1907, Saturday: 18 [of 68], Col. 2c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19070824/115/0018. Same print title, p. 348.&lt;/ref&gt;&lt;/blockquote&gt;

===November 1907===
====10 November 1907====
&lt;quote&gt;On 10 November, Dolmetsch, 'awfully tired and disquieted with overwork', writes to Horne, 'longing for Florence'.

7, Bayley Street&lt;br /&gt;W.C.&lt;br /&gt;My concert went very well last night. Melodie quite distinguished herself, and a sister of [[Social Victorians/People/George Bernard Shaw|Bernard Shaw]] Lucy Carr Shaw sang delightfully. …&lt;br /&gt;But Symmons [sic] … did not go before 1 o'cl. and yet, by the first post this morning, I got a charming poem on Rameau. … He must have spent all night on it.&lt;/quote&gt; (Campbell 120)

==1908==
In 1908 Sidney Paget died in 1908 in some &quot;untimely&quot; fashion (Baring-Gould II 239).

=== April 1908 ===

==== 1908 April 9, Thursday ====
The Provisional Committee for the Shakespeare Memorial demonstration at the Lyceum Theatre met at the Hôtel Métropole:&lt;blockquote&gt;SHAKESPEARE MEMORIAL.

A meeting of the Provisional Committee for the forthcoming Shakespeare Memorial demonstration at the Lyceum Theatre was held yesterday at the Hôtel Métropole. Mr. T. P. O’Connor, M.P., presided, and there were present : The Earl of Lytton, Mr. Percy Alden, M.P., Mr. Henry Ainley, Mr. Percy Ames, Mr. Robert Barr, Mr. Arthur à Beckett, Mr. Austin Brereton, Mr. Acton Bond (General Director of the British Empire Shakespeare Society), Mr. Dion Boucicault, Mrs. Bateman-Crowe, Professor Boss, Mr. Norreys Connell, Mr. W. M. Crook, Mr. John Cutler, K.C., Mr. J. Comyns Carr, Mr. Ernest Carpenter, the Rev. P. H. Ditchfleld, Mr. Robert Donald, Mr. A. C. Forster Boulton, M.P., Mr. and Mrs. Laurence Gomme, Mr. A. A. Gardiner, Mr. C. T. Hunt (hon. secretary London Shakespeare League), Mr. Laurence Housman, Mr. J. A. Hobson. Mr. Ford Madox Hueffer, Mr. Selwyn Image, Mr. Henry Arthur Jones, Mr. Jerome K. Jerome, Mr. Frederick Kerr, Miss Gertrude Kingston, Professor Knight, Mr. Matheson Lang, the Hon. Mrs. Alfred Lyttelton, Miss Lillah McCarthy, Mr. Justin Huntly McCarthy, Colonel Henry Mapleson, Dr. Gilbert Murray, Mr. T. Fairman Ordish, Mr. A. W. Pinero, Mr. Ernest Rhys, [[Social Victorians/People/Rook|Mr. Clarence Rook]], the Rev. J. Cartmel Robinson, Mr. George Radford, M.P., Mr. Clement Shorter, Mr. Otto Salimann (hon. secretary of the Elizabethan Society), [[Social Victorians/People/George Bernard Shaw|Mr. Bernard Shaw]], Mr. H. W. Smith, Mr. Herbert Trench, [[Social Victorians/People/Todhunter|Dr. Todhunter]], and Mr. James Welch. It was agreed that the Lyceum demonstration should take place in May, and a resolution should be moved in favour of the establishment of a National Theatre as a memorial to Shakespeare.&lt;ref&gt;&quot;Shakespearea Memorial.&quot; ''Morning Post'' 10 April 1908, Friday: 7 [of 12], Col. 3c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19080410/126/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1908===
Summer 1908: [[Social Victorians/People/William Butler Yeats|W. B. Yeats]] summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

==== 1908 June 21, Sunday ====
Very large demonstration for women's suffrage in Hyde Park coming from &quot;seven points in London.&quot;&lt;blockquote&gt;WOMAN'S VOTE.
SUFFRAGISTS' GREAT MARCH TO HYDE PARK TODAY.

WHITE DEMONSTRATION.

AMUSING ADDRESS TO M.P.'s. FROM RIVER LAUNCH.

From seven points in London to-day seven big prossesions will march to Park, and there jointly demand the Parliamentary franchise for women.

The whole town will be alive with demonstrating suffragists. The streets will resound with the cry of &quot;Votes for Women.&quot; In Hyde Park eighty speakers will voice the demand from twenty platforms.

London has been divided into districts for the purposes of the mighty demonstration, and each of theee has an assembling place, from which the processions will move off to Hyde Park, as given in the following official list: —

A. — Euston-road. — Form up at 12 o'clock, east of Euston Station. Start at 1 p.m. March via Euston-road, Portland-place, Upper Regent-street, Oxford-street, to the Marble Arch.

B. — Trafalgar-square. — Form up 12.30. Start 1.30. March via Pall Mall, Regent-street, Piccadilly, Berkeley-street, and Mount-street to the Grosvenor Gate.

C. — Victoria Embankment. [sic] Form up 12.30. Start from Westminster Bridge 1.30. March via Victorla-street, Grosvenor-place, to Hyde Park Corner.

D. — Chelsea Embankment. — Form up 12.30. Start 1.30. March via Oakley-street, King's-road, Sloane-square, Sloane-street to Albert Gate.

E. — Kensington High-street. — Form up 1 o'clock. Start 1.30. March via Kensington into the Alexandra Gate of the Park.

F. — Paddington Station. — Form up 1 p.m. Start 2 p.m. March via Victoria Gate into Hyde Park.

G. — Marylebone-road. — Form up 12.30. Start 1.30. March via Seymour-place, Seymour-street, and Into the Park close to the Marble Arch.

The demonstrators will come from all parts of the country, some seventy special trains being run from the big towns in the provinces. These will be met at the London stations by white-garbed &quot;Captains&quot; and &quot;Stewards,&quot; and their occupants marshalled in proper divisions.

Literature and the drama will be represented in several of the processions. Mr. and Mrs. Bernard Shaw will join in Trafalgar-square, and so will Mr. Pett Ridge. Starting from Euston-road will be a coach carrying Mrs. Parkhurst, Miss Beatrice Harraden, Mrs. Mona Caird, and Miss Elizabeth Robins.

Mrs. Israel Zangwill will chaperon a party on a coach from the Thames Embankment, which will include Professor and Mrs. Ayrton, Madame Sarah Grand, Miss Lillah McCarthy (Mrs. Granville Barker), Miss Marian McCarthy, Mr. Lucien Wolf, Professor Perry, F.R.S. (scientist), Mrs. H. G. Wells, Mrs. Alice Meynell, and Suffragist leaders from Sweden, Finland, and Norway. In Finland women not only have the vote, but they sit in Parliament. Madame Stromberg, from that country, is now in London attending the Horse Show at Olympia, and will be present at to-day's demonstration. Mr. H. Nevinson and Mr. H. N. Brailsford will walk in the Embankment procession.

On the Kensington four-in-hand coach will be:— [[Social Victorians/People/Rook|Mrs. Clarence Rook]], Mrs. Jopling Rowe, Mlle. Stavance (Norwegian editor and authoress), Mrs. French Sheldon, F.R.G.S., and Miss Christine Silver. 

...

In addition to seven four-horse coaches — one for each procession — there will be more than sixty brakes, filled with country suffragists, and elaborately decorated. [Story continues.]&lt;ref&gt;&quot;Women's Vote. Suffragists' Great March to Hyde Park To-day. White Demonstration. Amusing Address to M.P.'s from River Launch.&quot; ''Lloyd's Weekly Newspaper'' 21 June 1908, Sunday: 1 [of 28], Col. 1a–c [of 5], 2, Col. 5. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003216/19080621/002/0001. Print p. 1.&lt;/ref&gt;&lt;/blockquote&gt;

===Works Cited===
*Baring-Gould

=== July 1908 ===

==== 30 July 1908, Thursday ====

===== Glorious Goodwood. Cup Day and Dresses. =====
&lt;blockquote&gt;Cup day at Goodwood, says the “Daily Telegraph,” is always looked upon as the occasion for a display of beautiful toilettes, and Thursday was no exception to the rule: in fact, the scene reminded one more of Ascot on a miniature scale. Some very beautiful Directoire gowns were to be seen, and in all materials. There was the ever-delightful satin charmeuse, silk voile, ninon, embroidered muslin, chiffon, and hand-painted muslins in endless variety. Shantung, too, played its part, and so did broderie Anglaise, and other cool and diaphanous materials. One could not help noticing the important part that embroidery plays in modern toilettes. Some of it is very elaborate, the most fashionable being worked in floss silks, while old Oriental patterns have been copied with considerable success. Persian, Indian, and Algerian motifs were to be seen on many wearers. Marquisette is an admirable material to embroider on, and here again floss silk was used in profusion. The embroidered linens seem to grow more elaborate every year. In many cases beautiful incrustations were used half way up the skirt, and many little coats were almost covered with these elaborate designs. Gold, silver, and platinum have also played a great part in the decoration of toilettes this year, and these tinsels, when skilfully blended with colours, have proved extremely beautiful.

The great heat last week made the fashionable long satin cloaks of various colours quite unnecessary, and in their place were seen sleeveless coats of silk muslin or short jackets of Irish lace. One lady was noted wearing a little hanging cape of cyclamen-coloured satin over a white dress, and the touch of colour was very becoming. Large hats have again been to the fore, and those trimmed with aigrettes of various colours have been very plentiful, but not to the extent one saw at Ascot. A tendency to introduce antumn flowers has been distinctly noted, and more than one smart hat has been decorated, with cornflowers and poppies. The blossoms of iris, fuschia, wistaria [sic], and roses have been the ideal floral decoration, and, here again, gold, silver, and platinum tissue have played a great part. One or two mole-coloured hats, trimmed with plantinum tissue, were very becoming. The reign of the natural ostrich feather, too, continues, and wings on a very large scale have also been seen. Quills of parti-colours found many wearers, and shaded feathers, going from very dark to light tones, have been greatly in evidence. The Elizabethan ruffle, which at the beginning of the season promised to be so fashionable, has almost disappeared, and in its place were to be seen short ruffles of tulle finished off with rosettes and ends of coloured satin. Another fashionable item at Goodwood was the wearing of coloured shoes and stockings to match the gowns, the more popular being those made of suede, and one lady was wearing a gown of grey silk muslin, with grey silk stockings to match, and shoes of grey suede, with paste buckles. Much jewellery has been seen, nearly every woman having a pearl necklace, and the vogue of the emerald must certainly be noted. The Queen set the example by wearing a long emerald pendant, from which fell a cabochon ruby. Jewelled hat pins, too, have played their part, and jewelled butterflies have been very fashionable to fasten veils.

The King and Queen, with Princess Victoria and the Duke of Richmond, arrived about a quarter past one. Some very lovely toilettes were to be noted in the Royal party. The Queen chose a delicate toilette of lavender grey, with a cross-over bodice, and a small grey toque trimmed with ostrich feathers. Princess Victoria wore a delicate shade of blue, with a hat trimmed with black and white feathers and pink roses. The Countess of Mar and Kellie appeared to great advantage in white crepe de chine and a large floral-trimmed hat. The Countess of Ilchester's gown of small black and white checked muslin was relieved by a mauve waistbelt and a large shady bat, trimmed with mauve irises. Lady Helen Gordon Lennox was in white, striped with mauve, the revers of the bodice being of pale mauve satin, and ber hat was trimmed with roses. Lady Anne Lambton wore white, with a hat of dull purple flowers and leaves relieved by pink roses here and there. Lady Muriel Beckwith was in blue, and the Hon. Mrs. George Keppel wore white crepe de chine, with many upstanding feathers in her hat. The Marchioness of Salisbury chose a very light gown, with a purple hat, trimmed with a purplish-blue feather, the brim of the hat being lined with rose colour. Lady Cooper was another of the many ladies present to appear in white embroidered muslin, and her hat was trimmed with many flowers. Lady Bernard Gordon-Lennox wore painted crepe, and a flower-trimmed hat. Miss Ivy Gordon-Lennox was in girlish white, the Hon. Charlotte Knollys wore a toilette of mauve and pink and white, Lady Sassoon in black and white striped silk muslin. Viscountess Crichton was wearing embroidered muslin: Lady Juliet Duff wore a mauve neck ruff, and a pale coloured hat with a dress of white lace and muslin. The King wore a lilac tie and a pink flower, with a blue frock coat and grey trousers and a tall grey hat.

Quite a bevy of beautifully-dressed women were to be seen sitting in the shade of the telegraph pavilion, which is situated in between the club enclosure and the paddock. Here were noted the Countess of Lonsdale, in dahlia-coloured crepe and satin, and Lady de Trafford, who chose a very successful gown of black and white striped muslin, the effect being almost grey, and with this she wore a beautiful hat of pure moonlight blue, which suited her to perfection. Lady Noreen Bass, in rose-red silk gauze, had a large white hat, with upstanding ospreys, and by her side sat Lady Rowena Paterson, in white, with a hat trimmed with lilac and roses. The [[Social Victorians/People/Bourke|Hon. Mrs. Algernon Bourke]] chose a beautiful shade of salmon-pink [Col. 1c–2a] voile, and her hat had flowers of the same colour. By her side might have been seen the Hon. Mrs. Lancelot Lowther, in pervenche-coloured silk voile, striped with bands of satin of the same shade. Mrs. Farquharson, of Invercauld, looked charming in white, with a mauve waistband and parasol, and mauve and pink flowers in her hat. The Hon. Mrs. Rochfort Maguire chose white crepe de chine, slightly trimmed with gold embroidery; and yet another to be seen here was Mrs. William James, who was in ivory crepe de chine, with touches of gold embroidery on the bodice. The Hon. Mrs. William Lawson was in mauve and white striped gauze, and Mrs. Arthur James wore rose pink voile.

The scene in the paddock was as interesting as ever. Here were noted Earl and Countess Fitzwilliam, who motored to the races from Portsmouth Harbour, where they entertained a party of friends on the “Kathleen.” Her ladyship's gown was most original. It was of orchid mauve silk gauze, with a short over-skirt of golden gauze, a mauve hat slightly touched with gold, and her cream sunshade was veiled in gold gauze. The Countess of March, in unrelieved black, was accompanied by her three children, Lady Amy and Lady Doris Gordon-Lennox, and little Lord Settrington. Her sister-in-law, Lady Evelyn Cotterell, in a large black and white checked gown, accompanied her also. Lady Teynham's white embroidered muslin, with a short cloak of rose pink satin, was greatly admired, and so was the black satin charmeuse toilette, with gold embroideries, on a blue ground, worn by Mrs. Turner. The Countess of Sefton wore a simple little frock of silver grey silk ninon, and a low-crowned hat trimmed with lace, and the Hon. Mrs. Cyril Ward looked very pretty in white linen, with a large straw hat trimmed with blue ribbons and pink roses.

The large general attendance included: the Marquis of Cholmondeley, the Earl of Sefton, the Earl of Essex, Lord Albert Osborne, Lady Clifford of Chudleigh, General Sir Albert Williams, Colonel Sir Augustus FitzGeorge, Lord Wolverton, Viscount Valletort, Major Eustace Loder, Colonel Holford, Colonel Sir Arthur Davidson, the Countess of Aylesford, Lady Theo. Acheson, the Hon. Cyril Ward, the Hon. Sidney Greville, Mr. Blundell Leigh, Mr. Montagu Elliott, Sir Hill Child, Lord Algernon Gordon Lennox, and Miss Ivy Gordon-Lennox, Lord and Lady Gifford, Viscount Royston, Captain and Mrs. Bingham Turner, the Countess of Verulam, and Lady Vera Grimston, Lord Somers, Major Trotter, and very many others.

Among the local gentry were to be seen: Mrs. John Orr-Ewing with the Misses Orr-Ewing (both in white), Lady Gifford in grey satin with hat to match, Mrs. Agar in grey, Mrs. W. Dundas in black, and Mrs. Hankey, Miss Leslie, charmingly gowned in yellow, Mrs. Lacaita (of whose party was Lady Isobel Browne), Miss Gladys Grace, Mrs. Bradey Frith, Mrs. and the Misses Lees (the former wearing a charming cream dress and mauve hat), Major and Mrs. Layton, Capt. and Mrs. Bellamy, Capt. and Mrs. Griffin, Miss Buchanan, Mrs. and Miss Wood, Mr. and Mrs. P. de Bathe, Lady Dorothy Mercer Henderson in white stripped [sic] ninon and a large black picture hat, Miss Millicent James in pale blue with a black hat, and Miss Drexel.&lt;ref&gt;&quot;Glorious Goodwood. Cup Day and Dresses.&quot; ''Chichester Observer'' 5 August 1908, Wednesday: 6 [of 8], Col. 1a–2b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001917/19080805/074/0006. Print title ''Chichester Observer and West Sussex Recorder'', p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

==1909==
===January 1909===
====1 January 1909====
Rev. [[Social Victorians/People/Ayton|W. A. Ayton]] died (Howe 85 10-11).

==== 20 April 1909, Tuesday ====
The wedding of [[Social Victorians/People/Bourke|Lady Rosemary Cairns]] and Wyndham Portal in St. Margaret's, Westminster.&lt;blockquote&gt;The marriage of Mr. Wyndham Portal and Lady Rosemary Cairns takes place on the 20th at St. Margaret's, Westminster. The bride will be given away by her stepfather, Mr. [[Social Victorians/People/Bourke|Roger Sloane Stanley]]. She will wear a gown of white meteor satin, embroidered with crystals and silver. The train will be of silver tissue, also embroidered with crystals.
The bridesmaids are Miss Sherborne (a cousin of the bride), Miss Glynn, Miss Comb, Miss Alex [comics panel on &quot;Clothes to Wear During the Holidays&quot;] Bertie (a daughter of Lord and Lady Norreys), Miss Taylor, and Miss Larnach. These young ladies will wear gowns of pale primrose and silver, with black hats trimmed with pale yellow feathers.

There are also five small bridesmaids, these being the bride's two baby sisters, Miss Lavender Sloane Stanley and Miss Diana Sloane Stanley, Lady Ursula Cairns, Miss Timson, and Miss Fetherstonhaugh. The bridegroom's nephew, Master Henry Monck, will act as train-bearer. Lord Gifford (eldest son of Lord Tweeddale, and a brother-officer in the 1st Life Guards) will act as best man. After the ceremony, which will be performed by the Bishop of Peterborough, Olivia Lady Cairns, mother of the bride, will hold a reception at 78, Harley-street.&lt;ref&gt;&quot;This Morning's Gossip.&quot; ''Daily Mirror'' 10 April 1909, Saturday: 7 [of 16], Col. 2a, 2c [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000560/19090410/067/0007. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

===June 1909===
Summer 1909: W. B. Yeats summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).

=== September 1909 ===

==== Visitors in Venice from the U.K. ====
&lt;blockquote&gt;Venice has become a great rendezvous of cosmopolitan society in the early autumn, and the Piazza San Marco and the Grand Canal have been full of animation all this month.

The Duke of Marlborough, Louise Duchess of Devonshire, with her daughter, the Countess of Gosford, the [[Social Victorians/People/Bourke|Hon. Algernon Bourke]], Lady Lilian Wemyss, the Hon. Mrs. Page-Roberts, Mr. Gordon-Lennox, Mr. and Mrs. Guy Paget, Lady Hadfield, who motored from Lucerne, Sir Benjamin Whitney, has been at Aix-les-Bains, Sir Charles and Lady Swinfen Eady, General de Horsey, and Mr. Claud Phillips have been among the many English visitors.

Lady Helen Vincent has been entertaining at Palazzo Giustiniani. Lady Layard has returned to Casa Capella. Prince Frederick Charles pf Hohenlöhe is at his residence on the Grand Canal. Princess Edmond de Polignac is residing at her palace. Mr. and Mrs. Hummphrey Johnston are back at Santa Maria dell'Arto. Mrs. and Miss Gebhardt and Countess A. Morosini have return3ed once more.&lt;ref&gt;&quot;Venice.&quot; ''Daily Express'' 29 September 1909, Wednesday: 4 [of 8], Col. 8c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19090929/052/0004. Same print title and p.&lt;/ref&gt;&lt;/blockquote&gt;

== Bibliography ==
#&quot;Calendar for the Year 1900.&quot; Jumk.de Webprojects. https://kalender-365.de/public-holidays.php?yy=1900. Accessed November 2023.
#Howe

== Footnotes ==
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--&gt;[[File:Squid Game resources QR Code.svg|alt=QR code that includes a shortened URL to the resource page|thumb|QR code to save or share this page]]

=='''''Squid Game'''''&lt;ref name=&quot;:0&quot;&gt;{{Cite journal|date=2022-02-13|title=Squid Game|url=https://en.wikipedia.org/w/index.php?title=Squid_Game&amp;oldid=1071609561|journal=Wikipedia|language=en}}&lt;/ref&gt;--Mental Health Resources for Triggering Topics==
[[File:Cosplay of Squid Game Guards at Sutera Cosplay Fest 2021.jpg|thumb|left|220x220px|alt=Image depicts a cosplay of one of the guards from Squid Game from the Sutera Cosplay Fest in 2021.|Cosplay of Squid Game Guards at Sutera Cosplay Fest 2021.]]
[[File:Squid Game dalgona cookies.jpg|alt=Image depicts a recreation of &quot;dalgona cookies&quot;, or honeycomb candy-like treats, depicted in Episode 3 of Squid Game in the ppopgi game.|thumb|Recreation of &quot;Dalgona Cookies&quot; depicted in Squid Game]]
[[wikipedia:Squid_Game|Squid Game]] (Hangul: 오징어 게임, Romanization: Ojing-eo Geim) is a South Korean television drama created by [[wikipedia:Hwang_Dong-hyuk|Hwang Dong-hyuk]] for Netflix. Named after a common but often violent South Korean children’s game, Squid Game portrays 456 contestants, all of varying backgrounds but all facing deep financial turmoil, desperately trying to win the significant sum of cash held in a tank above the room in which they sleep&lt;ref name=&quot;:0&quot; /&gt;. Early on, however, the contestants realize they have become involved not in a simple game, but rather in a battle for survival.

Quickly ascending to international fame, the show is popular for its high-stakes, action-packed plot, emotionally compelling moments, and complicated characters. However, the violence displayed and heavy topics covered are likely to leave many viewers rattled, and may even recall to mind personal traumas and negative emotions for some. Many potentially triggering topics, including but not limited to suicide, terminal illness, and physical violence, are portrayed in the drama. Unfortunately, the show does not follow up on the troubling topics shown with education regarding resources or support opportunities.

Passionate about promoting better, more accessible mental health support, our team, a subgroup of the group [https://www.hgaps.org/ Helping Give Away Psychological Science (HGAPS)] {{Dotorg}}, has worked to compile applicable resources to address the various triggering topics incorporated throughout the show. If you have viewed Squid Game or plan to view it in the future and feel affected by the themes included in the drama, please feel free to seek support and resources through the links compiled below.


== '''Season 1''' ==

&lt;strong&gt;Each episode block contains a list of a number of triggering topics displayed in the show. Please note that there may be many triggering topics that were not included on this page. Some themes recur throughout the series, and may therefore be listed in more than one episode. In such cases, the repeat-occurrences of a theme will not have content in the corresponding box, but instead the triggering topic itself will be linked so that you will be redirect to the information corresponding to the first instance.&lt;/strong&gt;

''[[w:Squid Game#Episodes|Here's a link to]] a synopsis of the episodes (major spoilers!).''

==== About the resources: ====
We prefer sites that are not trying to sell a good or service, and that do not have other conflicts of interest. We have added tags so that you can see what type of resource it is without clicking on it. 
{| class=&quot;wikitable&quot;
!Icon
!Description
|-
|{{Dotgov}}
|[[w:.gov|.gov]] links go to pages hosted by government agencies.
|-
|{{Dotorg}}
|[[w:.org|.org]] links to pages that are usually nonprofit organizations. 
|-
|{{Dotnet}}
|[[w:.net|.net]] links to pages that use the .net Internet domain. These originally were mostly technology companies, but now this is a widely used alternative to .com for commercial companies. 
|-
|{{Dotwiki}}
|links to [[w:Wikipedia|Wikipedia]] or [[Wikiversity:Introduction|Wikiversity]] articles.
|-
|{{Dotcom}}
|[[w:.com|.com]] links to pages built by groups with a commercial interest. Some of these are altruistic and well done. We had psychologists review these to see if the material seemed accurate, helpful, and balanced. 
|-
|}
 
{|style=&quot;margin: 0 auto;&quot;
|-
| [[File:Squid Game logo (Korean).png|thumb|right|500px|alt=This is the Korean logo for the popular show Squid Game.|Korean logo for [https://en.wikipedia.org/wiki/Squid%20Game Squid Game].]]
| [[File:Squid Game logo.png|thumb|left|680px|alt=This is the English logo for the popular show Squid Game.|English logo for [https://en.wikipedia.org/wiki/Squid%20Game Squid Game].]]
|}

----

The resources are organized two different ways. Use whichever is more convenient. One is a sortable table, listing more than 30 different topics, and showing which themes occur in each episode. The link goes to the episode section containing helpful resources. It may take some scrolling -- some episodes packed in more than ten different major themes!  You can sort the table by each column, simply by clicking the triangles in the column name. The table may be the easiest way to see the range of topics shown in the series, as well as exploring resources.

The second format has an episode-by-episode structure. If people want to unpack all the themes covered in one installment, they are grouped together here. 

==Table of psychological topics==

{| class=&quot;wikitable sortable mw-collapsible&quot; 
|+ Topic Breakdown Per Episode
|-
!Theme
!Topic
!Ep 1
!Ep 2
!Ep 3
!Ep 4
!Ep 5
!Ep 6
!Ep 7
!Ep 8
!Ep 9
|- style=&quot;text-align: center;&quot;
|Trauma
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Trauma]]
|[[File:Porsa-logo.png|20x20px|link=HGAPS|HGAPS]]
|
|[[File:Porsa-logo.png|20x20px]]
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Gambling Problems]]
|[[File:Porsa-logo.png|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Joblessness/Employment Difficulties]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Financial Trouble]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Physical 
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Physical Violence]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Illness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Terminal Illness]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Physical (or family)
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Domestic Abuse]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Physical
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Physical Abuse]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Witnessing
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Gun Violence]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Witnessing
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Mass Casualty/Trauma]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Financial Distress]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Illness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Chronic Illness]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Living Uninsured]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Medical Expenses]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Housing Instability]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Foster Care/Orphanage]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Separation from Family]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Mental Health
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Suicide]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Divorce/Custody Issues]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Food Insecurity]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Organ Trafficking]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Witnessing 
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Mass Violence]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Illness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Memory Impairment/Illness]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Discrimination]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Relational Abuse]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Illness/Injury
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Workplace Injury]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Mental Health
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 5 &quot;A Fair World&quot;|Post Traumatic Stress Disorder (PTSD)]]
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 5 &quot;A Fair World&quot;|Strike]]
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Sexual Violence
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 5 &quot;A Fair World&quot;|Rape]]
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Illness/Injury
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 5 &quot;A Fair World&quot;|Incontinence]]
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 6 &quot;Gganbu&quot;|Acculturation Problems]]
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|- style=&quot;text-align: center;&quot;
|Witnessing
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 6 &quot;Gganbu&quot;|Witnessing a Crime]]
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|- style=&quot;text-align: center;&quot;
|Mental Health
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 7 &quot;VIPS&quot;|Anxiety/Fear]]
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|- style=&quot;text-align: center;&quot;
|Sexual Violence
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 7 &quot;VIPS&quot;|Sexual Harassment/Assault]]
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|- style=&quot;text-align: center;&quot;
|Sexual Violence
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 7 &quot;VIPS&quot;|Workplace Sexual Harassment/Assault]]
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Loss of a Friend]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Resources for Children]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Resources for Adults]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Resources for Widows/Widowers]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Mental Health
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Depression]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Homelessness/Destitution]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Illness/Injury
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 8 &quot;Front Man&quot;|Terminal Injury]]
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 8 &quot;Front Man&quot;|Being hunted down]]
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|- style=&quot;text-align: center;&quot;
|Illness/Injury
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 8 &quot;Front Man&quot;|Significant injury]]
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|- style=&quot;text-align: center;&quot;
|Witnessing
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 8 &quot;Front Man&quot;|Murder (stabbing]]'')''
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| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 8 &quot;Front Man&quot;|Shooting]]
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===Episode 1 &quot;Red Light, Green Light&quot;===
{| class=&quot;wikitable sortable mw-collapsible&quot;
&lt;!-- starting to add section names so that we can retrieve content from specific topics without repetition --&gt;

|-
!Episode 1:
!&quot;Red Light, Green Light&quot; (''Mugunghwa Kkoch-i Pideon Nal'' 무궁화 꽃이 피던 날)&lt;ref name=&quot;:0&quot; /&gt;
&lt;section begin=Job_Employment /&gt;
|-
|Joblessness/Employment Difficulties
|[https://www.usa.gov/unemployment '''USA Gov Unemployment Help'''] {{Dotgov}}

* USAGov provides resources for those who face employment difficulties to reach out and apply for unemployment benefits, worker’s compensation, and welfare for families. This website on their page compiles a list of helpful links and webpages depending on the individual’s needs and what situation they may be facing.

[https://www.careeronestop.org/LocalHelp/UnemploymentBenefits/Find-Unemployment-Benefits.aspx '''Career OneStop - Unemployment Benefits'''] {{Dotorg}}

* Sponsored by the U.S. Department of Labor, CareerOneStop is a website dedicated to compiling resources for careers, education, and professional development. This specific page on their website allows users to find unemployment resources based on what state they live in.
[https://www.helpguide.org/articles/stress/job-loss-and-unemployment-stress.htm '''Dealing with Job Loss and Unemployment Stress''']{{Dotorg}}

* This article from HelpGuide provides resources and practical, psychologically-backed tips for coping with the stress of unemployment and job loss.

&lt;section end=Job_Employment /&gt;
&lt;section begin=Financial_Trouble /&gt;
|-
|Financial Trouble
|[https://www.mentalhealth.org.uk/explore-mental-health/a-z-topics/debt-and-mental-health '''Information on Debt and Mental Health'''] {{Dotorg}}

* This article from the UK Mental Health Foundation outlines how debt and financial difficulty can have an impact on people psychologically, and how mental health difficulties contribute to financial problems. It also provides information on how to get help for these issues.
[https://consumer.ftc.gov/articles/how-get-out-debt '''How To Get Out of Debt'''] {{Dotgov}}

* Tip sheet from the Federal Trade Commission about getting out of debt 

[https://www.benefits.gov/categories/Financial%20Assistance '''US Government Financial Assistance Database'''] {{Dotgov}}

* The link provided leads to a database which those who are undergoing financial hardship of many different forms can put in specific search criteria to find assistance specific to the state they live in as well as what they need financial assistance for (Loan Repayment, Tax Assistance, Living Assistance, Insurance, etc.)
&lt;section end=Financial_Trouble /&gt;
&lt;section begin=Gambling_Problems /&gt;
|-
|Gambling Problems 
|'''National Problem Gambling Helpline Network (1-800-522-4700)'''
[[wikipedia:Problem_gambling#Signs_and_symptoms|'''Symptoms of problematic gambling''']] {{Dotwiki}}

'''[https://www.helpguide.org/articles/addictions/gambling-addiction-and-problem-gambling.htm Gambling Problem]''' {{Dotorg}}

* This article provides details on the signs and symptoms of gambling disorder, and it offers self-help tips and treatments.

[[wikipedia:Problem gambling#Treatment|'''Treatment options''']] {{Dotwiki}}

* This page provides a list of treatment options to help with gambling problems.

[https://recovery.org/support-groups/gamblers-anonymous/ '''Gamblers Anonymous'''] {{Dotorg}}

* Gamblers Anonymous is a 12-step recovery program for people with gambling addiction.
&lt;section end=Gambling_Problems /&gt;
&lt;section begin=Physical_Violence /&gt;
|-
|Physical Violence 
|&lt;u&gt;Note&lt;/u&gt;: Physical Violence is an act that can ultimately affect anyone of any race, gender, sexual orientation, religion. Squid Game episode one sets the precedent for a multitude of physically violent acts that will continue to take place throughout the series. 


[https://victimsofcrime.org/ '''National Center for Victims of Crimes'''] {{Dotorg}}
* '''Phone''': 1-202-467-8700
* The National Center for Victims of Crime is a 35 year old nonprofit organization with a plan tailored to fit the needs of those who experience any type of physical violence and also for the families of those victims. 

[http://www.nationalcenterdvtraumamh.org/ '''National Center on Domestic Violence, Trauma &amp; Mental Health'''] {{Dotorg}}

* '''Phone''': 1-312-726-7020, ext. 2011
* The National Center on Domestic Violence, Trauma &amp; Mental Health provides training, support, and consultation to mental health professionals and policymakers in addition to resource education for the general population. 

[https://www.med.unc.edu/beacon/get-help/child-abuse-resources/ '''UNC Hospital's Beacon Program'''] {{Dotedu}}

* UNC Hospital’s Beacon Program lists many resources on their website to aid those affected by all types of abuse. The link attached proivdes specific resources for those affected by child abuse. The Beacon Program provides comprehensive, coordinated care to the UNC System’s patients, families, and employees experiencing a variety of interpersonal abuse.
&lt;section end=Physical_Violence /&gt;
&lt;section begin=Terminal_Illness /&gt;
|-
|Terminal Illness
|'''[[wikipedia:Terminal_illness|Cancer Care]]''' {{Dotwiki}}
* Cancer Care provides resources and expectations for advanced cancer patients, setting expectations, giving advice, and suggesting ways to spend valuable time.

[https://www.cancerresearchuk.org/about-cancer/coping/dying-with-cancer/after-someone-dies/coping-with-grief '''Coping with Grief''']  {{Dotorg}}
* This article, by Cancer Research UK, is directed to someone who has lost a loved one and overviews the stages of grief, different types of grief, and coping skills. Containing many facts and helpful statistics, this article gives insight to all sides of the situation, setting expectations for the future.


[https://www.verywellhealth.com/coping-with-anticipatory-grief-2248856 '''Coping with anticipatory grief'''] {{Dotcom}}
* This website, aimed toward someone who has lost a loved one, focuses on the distinction between anticipatory grief (before someone dies) versus conventional grief (afterwards), utilizing many of the same coping strategies in a more tailored way.
&lt;section end=Terminal_Illness /&gt;
&lt;section begin=Domestic_Abuse /&gt;
|-
|Domestic Abuse
|'''911 Emergency Call'''
* If you are facing an emergent situation regarding domestic abuse, please call 911; it's one of the fastest ways to get help in an emergency situation.

'''National Domestic Violence Hotline: Call 800-799-7233 or Text &quot;START&quot; to 88788'''

* If you need immediate help and/or want to enquire specific information about domestic abuse, you can Call 800-799-7233 or Text &quot;START&quot; to 88788. There are professionals on domestic abuse to give you immediate help.

'''[https://www.americanbar.org/content/dam/aba/administrative/domestic_violence1/Resources/charts/6%2019%202013%20LGBT%20CPO%20statutory%20chart_FINAL.pdf Domestic Violence Civil Protection Orders (Document)]''' {{Dotorg}}

* This chart, provided by Commission on Domestic and Sexual Violence, entails state-by-state information about definition of domestic violence as well as legal rights for domestic violence victims.

[[wikipedia:Domestic_violence#Forms|'''Forms of Domestic Violence''']] {{Dotwiki}}
*This is a wiki page explaining different forms of domestic violence.
&lt;section end=Domestic_Abuse /&gt;
&lt;section begin=Physical_Abuse /&gt;
|-
|Physical Abuse
|'''Call 911'''[https://www.healthyplace.com/abuse/adult-physical-abuse/physically-abused-where-to-get-help-for-physical-abuse '''Where to Get Help for Physical Abuse'''] {{Dotcom}}
* This website lists immediate and additional helping resources for physical abuse victims. There are also resources for teenagers and underrepresented groups.
&lt;section end=Physical_Abuse /&gt;
&lt;section begin=Gun_Violence /&gt;
|-
|Gun Violence
|&lt;u&gt;Note&lt;/u&gt;: Gun violence can be emotionally taxing to not just those directly affected by loss, but by even community members and those from afar. Squid Game has a multitude of depictions of gun violence throughout the show, starting from episode 1.
'''Call [[wikipedia:The_Center_to_Prevent_Youth_Violence#Speak_Up|1-866-SPEAK-UP]]''' {{Dotwiki}} to report threats of violence


[[SCCAP/Resources for Dealing with a School Shooting|'''SCCAP/Resources for Dealing with a School Shooting''']] {{Dotwiki}}

* A Wikiversity page on resources to deal with school shooting.


[https://everytownsupportfund.org/everytown-survivor-network/resources-for-victims-and-survivors-of-gun-violence/finding-help/ '''Everytown Support Fund'''] {{Dotorg}}
* The Everytown Support Fund offers basic resources and information on their website to help victims and survivors of gun violence. Please note that the resources listed are not comprehensive and there may be other resources available to you in your community.
&lt;section end=Gun_Violence /&gt;
&lt;section begin=Mass_Casualty /&gt;
|-
|Mass Casualty/Trauma
|[https://www.ptsd.va.gov/understand/types/resources_disaster_violence.asp '''National Center for PTSD''']  {{Dotgov}}
* This resource specifically provides aids for veterans dealing with PTSD, but also provides great resources for all individuals who face PTSD. This page specifically provides resources on what to expect when faced with mass violence and a virtual PTSD coach.

'''Veterans Crisis Line: Call 1-800-273-8255'''

* Press 1 (available 24/7)
* Chat live
* Text 838255


'''Call 911''' if it is urgent - check '''[https://www.veteranscrisisline.net/signs-of-crisis/ Signs of Crisis]''' {{Dotnet}}


[https://en.m.wikipedia.org/wiki/Mass-casualty_incident '''What is a Mass Casualty Incident?'''] {{Dotwiki}}

* A wiki page one the definition of mass casualty incident and helping resources.
&lt;section end=Mass_Casualty /&gt;
&lt;section begin=Trauma /&gt;
|-
|Trauma
|[[Helping Give Away Psychological Science/Coping with traumatic event|'''Helping Give Away Psychological Science/Coping with traumatic event''']] {{Dotwiki}}


[[Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit2020|'''Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit 2020''']] {{Dotwiki}}

[https://www.aaets.org/trauma-information/helpful-information-during-and-after-a-traumatic-event '''Helpful Information During and After a Traumatic Event'''] {{Dotorg}}
* The American Academy of Experts in Traumatic Stress (AAETS) is made up of a committee of professionals who are dedicated to informing the public and providing resources about how to cope with trauma. In collaboration with the National Center for Crisis Management, this page provides detailed information on what to do during and after a traumatic event, including healthy ways to cope with traumatic stress.

[https://www.nctsn.org/ '''National Child Traumatic Stress Network'''] {{Dotorg}}
* The website gathers cumulative information about child trauma (definition, signs, risk factors etc.). It is updated to the latest events, including documents ‘Talking to Children About War’.
&lt;section end=Trauma /&gt;
|}

----

===Episode 2 &quot;Hell&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!'''Episode 2:'''
!&quot;Hell&quot; (''Ji-ok'' 지옥)&lt;ref name=&quot;:0&quot; /&gt;
|-
|Financial Distress
|&lt;u&gt;Note&lt;/u&gt;: Financial Distress is a dilemma that both companies and individuals might confront. It is the core cause of ‘Squid Game’ and one of the motives that drive participants to perform violence, return the game, and struggle to win.


[https://aamft.org/Consumer_Updates/Financial_Distress.aspx '''The American Association for Marriage and Family Therapy (AAMFT)'''] {{Dotorg}}
* For families, couples encountering mental health issues, joblessness, and parenting problems resulting from financial stress.
* 1. Helps with job seeking, financial management, and mental health issues. 2. Useful LINKS attached at the bottom of the page.
* Financial distress severely influences family life, probably causing depression, alcohol/drug use, panic, etc. The website specifically helps families recognize distress and seek financial help.

[https://financiallit.org/resources/downloadable-forms-and-worksheets/' '''Downloadable Financial Forms and Worksheets'''] {{Dotorg}}

* For you to manage incomes and expenditures.
* Worksheets that help to manage budgets, measure debts, and set financial goals.
* Under ‘Other resources’, there are a bunch of useful docs and website addresses that help to make life more affordable.

'''[https://www.mymoney.gov/ Financial Management Resources]''' {{Dotgov}}

* For anyone who needs financial managing resources.
* Click ‘LIFE EVENTS’ to find appropriate resources targeting specific issues. Click ‘TOOLS’ to access multiple calculators, budgeting worksheets, and checklists.
* Mymoney is a US government website consisting of cumulative finance-related resources that provide various aids to all groups of all ages.

'''[https://studentaid.gov/h/apply-for-aid/fafsa Apply for Student Financial Aid (FAFSA)]''' {{Dotgov}}

* This website provides comprehensive resources about finding financial aid for students.

'''[https://www.usa.gov/unemployment Unemployment Help]''' {{Dotgov}}

* '''Unemployment Help page under the USA government website, where we can find links to health coverage, compensation, temporal assistance, etc.'''

|-
|Chronic Illness
|'''[https://www.cdc.gov/chronic-disease/?CDC_AAref_Val=https://www.cdc.gov/chronicdisease/resources/infographic/chronic-diseases.htm Chronic Diseases in America]''' {{Dotgov}}
* The CDC’s guide to prevention and resources for chronic illness. Includes statistics, study interventions, and funding guides.


[https://www.ncoa.org/article/evidence-based-chronic-disease-self-management-education-programs '''Chronic Disease Self-Management Programs'''] {{Dotorg}}

* This website includes programs that help with managing chronic illness, as well as facts on chronic diseases and recommendations for self-management.
|-
|Living Uninsured
|'''[https://www.healthcare.gov/screener/ See if You Are Eligible for Health Coverage]''' {{Dotgov}}
* HealthCare.Gov provides information on types of federal and state health insurance programs and helps a person see which program would work best for them. Also provides access to local resources so the person can seek assistance closer to them.
* Call 1-800-318-2596 (for questions on healthcare)


[https://www.ruralhealthinfo.org/topics/rural-health-clinics#overview '''Rural Health Clinic Program'''] {{Dotorg}}

* This program is designed to increase healthcare access to those living in rural communities, and it covers treatment from doctors and nurses. 


[https://nhchc.org/directory/ '''National Health Care for the Homeless Council'''] {{Dotorg}}

* This is a great resource that could help homeless or displaced individuals get health care coverage as it connects them to local services and helps provide them with potential coverage options.


[https://khealth.com/urgent-care/ '''Cash pay out and out of pocket options'''] {{Dotcom}}

* For those who necessarily do not have the means to pay for health insurance, this resource can help people get the healthcare that they need without having to pay the extra costs that come with not having insurance. K health is essentially virtual urgent care, where you use an app that connects with a healthcare provider without the additional cost. 


[https://www.medicare.gov/basics/get-started-with-medicare '''Medicare'''] {{Dotgov}}
* Medicare is a federally sanctioned health insurance program that offers coverage for prescription medication, hospital visits, doctor’s visits, etc. It is for people who are 65 years or older and for those who are younger than 65 who have health conditions or disabilities. 


[https://www.kff.org/uninsured/issue-brief/key-facts-about-the-uninsured-population/ '''Facts about the Uninsured Population'''] {{Dotorg}}

* This website provides information on the uninsured population living in the US to educate more people on the implications of living uninsured.


[https://en.m.wikipedia.org/wiki/Health_insurance_coverage_in_the_United_States '''Health Insurance Coverage in the United States'''] {{Dotwiki}}

* A wiki page on health insurance coverage in the U.S.
|-
|Medical Expenses
|[https://www.ssa.gov/benefits/medicare/prescriptionhelp.html '''Extra Help with Medicare Prescription Drug Plan Costs'''] {{Dotgov}}
* &quot;MeMedicare beneficiaries can qualify for Extra Help paying for their monthly premiums, annual deductibles, and co-payments related to Medicare prescription drug coverage.
* We estimate the Extra Help is worth about $5,100 per year. To qualify for Extra Help, you must be receiving Medicare and have limited resources and income.”
* Apply online, over the phone: 1-800-772-1213, request a paper application, or apply at your local Social Security Office.


'''[https://www.healthwellfoundation.org/ Health Well Foundation]''' {{Dotorg}}
* Health Well is an organization that provides financial assistance by assisting with copays, premiums, deductibles and out-of-pocket expenses when health insurance is not enough.


[https://www.panfoundation.org/ '''Patient Access Network Foundation'''] {{Dotorg}}
* PAN Foundation helps underinsured individuals with diseases with out-of-pocket costs, allowing them to get the medications and treatments they need and advocating for improved access and affordability.


'''[https://nafcclinics.org/ National Association of Free and Charitable Clinics]''' {{Dotorg}}

* The National Association of Free &amp; Charitable Clinics (NAFCC) focuses on connecting economically disadvantaged individuals to free and charitable clinics. NAFCC has a goal in mind of making healthcare more accessible to individuals based on location.


'''[https://www.cancercare.org/copayfoundation CancerCare Co-Payment Assistance Program]''' {{Dotorg}}

* This program helps people with cancer overcome financial stress and treatment barriers by assisting them with co-payments for treatments.


[https://en.m.wikipedia.org/wiki/Medical_debt '''Medical Debt'''] {{Dotwiki}}

* A wiki page on medical debt.
|-
|Housing Instability 
|'''[https://www.coabode.org/ Home Sharing Program for Single Mothers]''' {{Dotorg}}
* This is a homes sharing program designed to help single mothers connect and find a home to share together. This decreases the chance of housing instability and helps support single mothers in raising their children.


[https://www.rd.usda.gov/about-rd/agencies/rural-housing-service '''Rural Housing Services'''] {{Dotgov}}
* This resource offers housing assistance to those in rural communities. They also help improve housing and essential community facilities through the offering of loans and grants. 


'''[https://www.habitat.org/housing-help/apply Habitat for Humanity]''' {{Dotorg}}

* This is a program where people with housing instability can apply to live in a home of another homeowner’s construction. For example a person will buy a home or construct a home for another person to live in. This is called sweat equity.


[https://www.hud.gov/program_offices/public_indian_housing/pha/contacts '''Public Housing Agency Plan'''] {{Dotgov}}
* This provides information on housing instability along with a place where someone can apply for housing assistance. This resource specifically allows people to apply for an emergency housing voucher.


[https://www.consumerfinance.gov/coronavirus/mortgage-and-housing-assistance/renter-protections/find-help-with-rent-and-utilities/ '''Consumer Financial Protection Bureau'''] {{Dotgov}}
* This website allows people to find rental assistance in their area to help with housing costs.
|-
|Foster Care/Orphanage
|'''Foster Parent Advice Line: +1 800-829-3777'''
* Call the hotline to get advice with issues such as navigating the foster care system, probate court and legal guardianship, understanding child development.


'''[https://kidsmatterinc.org/for-youth/how-to-help-a-younger-sibling/ How to Help a Younger Sibling in Foster Care]''' {{Dotorg}}

* This website provides information about requirements, guidelines and assistance hotline for older siblings/relatives who wish to foster or adopt younger siblings or relatives.


[https://nfpaonline.org/ '''National Foster Parent Association'''] {{Dotorg}}

* This program provides foster families with opportunities for advocacy, networking, and education. Resources include adoption information, foster parents training and education, etc.


'''[https://www.familylawselfhelpcenter.org/self-help/custody-paternity-child-support Family Law Self-Help Center]''' {{Dotorg}}
* This is a self-help center for foster parents to access common Q&amp;A about legal issues regarding custody and child support.


[https://en.m.wikipedia.org/wiki/Foster_care_in_the_United_States '''Foster care in the US'''] {{Dotwiki}}

* A wiki page on foster care system in the U.S.

|-
|Separation from Family
|'''[https://www.therecoveryvillage.com/mental-health/self-harm/how-to-help-a-friend-with-separation-anxiety/ How to Help a Friend with Separation Anxiety]''' {{Dotcom}}
* Call: 877-782-7659
* The Recovery Village is a website focused on providing resources for a wide variety of mental health concerns, including separation anxiety. This particular article on their website lists ways to help a friend who is facing separation anxiety as well as methods to cope with it.


'''[https://raisingchildren.net.au/for-professionals/mental-health-resources/parent-mental-health-and-wellbeing/separation-and-divorce Support During Separation &amp; Divorce] 🇦🇺''' {{Dotnet}}

* This site provides support for parents after a separation or divorce, including how to help children in various age groups facing the same conflicts. This resource provides support for single parents, children living in two separate homes, teenagers, and conflict management between parents.

|-
|Suicide
|'''[https://988lifeline.org/ National Suicide Prevention Lifeline]: Call 1-800-273-8255''' {{Dotorg}}
* This is a national network of local crisis centers that provides 24/7 and free online support.


'''[https://www.crisistextline.org/ Crisis Textline]''' {{Dotorg}}
* Text HOME to 741741
* Connects people who need online counseling with a crisis counselor.


'''[https://988lifeline.org/ 988 Suicide &amp; Crisis Lifeline] {{Dotorg}}'''

* National network of local crisis centers in the US that provide free and confidential support to people in suicidal crisis or emotional distress at any time.


'''Wikipeadia pages on suicide help resources:'''

[[wikipedia:Suicide#Risk_factors|'''Risk Factors of Suicide''']] {{Dotwiki}}

[[wikipedia:Suicide#Prevention|'''Suicide Prevention''']] {{Dotwiki}}

[[wikipedia:Suicide_prevention#Interventions|'''Suicide Interventions''']] {{Dotwiki}}

[[wikipedia:Suicide_prevention#Risk_assessment|'''Suicide Risk Assessment''']] {{Dotwiki}}

[[wikipedia:Suicide_prevention#Support_organizations|'''Support Organizations''']] {{Dotwiki}}
|-
|Divorce/Custody Issues
|[https://www.divorcecare.org/healing '''Divorce Care'''] {{Dotorg}}
* This is an organization that offers divorce recovery and support services that help people heal from the pain of divorce.


[https://www.helpguide.org/articles/parenting-family/children-and-divorce.htm '''Children in Divorce'''] {{Dotorg}}
* This website provides tips to communicate with kids about divorce and ways to work with experts to help kids cope with parents’ divorce.


[https://www.womansdivorce.com/state-divorce-resources.html '''State Divorce Resource Directory'''] {{Dotcom}}
* Click the link to the directory that provides access to state-specific divorce laws and guidelines, along with divorce lawyers in the surrounding area.


[[wikipedia:Child_custody#Physical_custody|'''Forms of Domestic Violence''']] {{Dotwiki}}


[https://simple.wikipedia.org/wiki/Children%27s_rights '''Children's Rights'''] {{Dotwiki}}


[[wikipedia:Alimony#By_country|'''Alimony in Different Countries''']] {{Dotwiki}}
|}

----

=== Episode 3 &quot;The Man with the Umbrella&quot; ===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
&lt;!-- starting to add section names so that we can retrieve content from specific topics without repetition --&gt;

|-
!Episode 3:
!&quot;The Man with the Umbrella&quot; (Usan-eul Sseun Namja 우산을 쓴 남자)&lt;ref name=&quot;:0&quot; /&gt;
&lt;section begin=Physical_Violence /&gt;
|-
|Physical Violence 
|&lt;u&gt;Note&lt;/u&gt;: Physical Violence is an act that can ultimately affect anyone of any race, gender, sexual orientation, religion. Squid Game episode one sets the precedent for a multitude of physically violent acts that will continue to take place throughout the series. 


&lt;section end=Physical_Violence /&gt;
&lt;section begin=Gun_Violence /&gt;
|-
|Gun Violence
|&lt;u&gt;Note&lt;/u&gt;: Gun violence can be emotionally taxing to not just those directly affected by loss, but by even community members and those from afar. Squid Game has a multitude of depictions of gun violence throughout the show, starting from episode 1.
'''Call [[wikipedia:The_Center_to_Prevent_Youth_Violence#Speak_Up|1-866-SPEAK-UP]]''' {{Dotwiki}} to report threats of violence


[[SCCAP/Resources for Dealing with a School Shooting|'''SCCAP/Resources for Dealing with a School Shooting''']] {{Dotwiki}}

* A Wikiversity page on resources to deal with school shooting.


[https://everytownsupportfund.org/everytown-survivor-network/resources-for-victims-and-survivors-of-gun-violence/finding-help/ '''Everytown Support Fund'''] {{Dotorg}}
* The Everytown Support Fund offers basic resources and information on their website to help victims and survivors of gun violence. Please note that the resources listed are not comprehensive and there may be other resources available to you in your community.
&lt;section end=Gun_Violence /&gt;
&lt;section begin=Trauma /&gt;
|-
|Trauma
|[[Helping Give Away Psychological Science/Coping with traumatic event|'''Helping Give Away Psychological Science/Coping with traumatic event''']] {{Dotwiki}}


[[Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit2020|'''Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit 2020''']] {{Dotwiki}}


[https://www.aaets.org/trauma-information/helpful-information-during-and-after-a-traumatic-event '''Helpful Information During and After a Traumatic Event'''] {{Dotorg}}
* The American Academy of Experts in Traumatic Stress (AAETS) is made up of a committee of professionals who are dedicated to informing the public and providing resources about how to cope with trauma. In collaboration with the National Center for Crisis Management, this page provides detailed information on what to do during and after a traumatic event, including healthy ways to cope with traumatic stress.


[https://www.nctsn.org/ '''National Child Traumatic Stress Network'''] {{Dotorg}}
* The website gathers cumulative information about child trauma (definition, signs, risk factors etc.). It is updated to the latest events, including documents ‘Talking to Children About War’.
&lt;section end=Trauma /&gt;
|}

----

===Episode 4 &quot;Stick to the Team&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!Episode 4:
!&quot;Stick to the Team&quot; (''Jjollyeodo Pyeonmeokgi''쫄려도 편먹기)&lt;ref name=&quot;:0&quot; /&gt;
|-
|Food Insecurity
|[[wikipedia:Food_security|'''Food security''']] {{Dotwiki}}
* Wiki page for food security definition.


[https://www.fns.usda.gov/contacts/contact-map?f%5B0%5D=program%3A27 '''Food Distribution Programs Map (click on state for more programs)'''] {{Dotgov}}

* Provide a list of programs on food and nutrition services by state.


[https://www.fns.usda.gov/snap/supplemental-nutrition-assistance-program '''Supplemental Nutrition Assistance Program (SNAP)'''] {{Dotgov}}

* SNAP provides nutrition benefits to add to the food budget of families in need so they can buy healthy food and move towards being self-sufficient.


[https://www.fns.usda.gov/wic '''Special Supplemental Nutrition Program for Women, Infants, and Children (WIC)'''] {{Dotgov}}

* “The Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) provides federal grants to states for supplemental foods, health care referrals, and nutrition education for low-income pregnant, breastfeeding, and non-breastfeeding postpartum women, and to infants and children up to age 5 who are found to be at nutritional risk.”


[https://www.fns.usda.gov/sfmnp/senior-farmers-market-nutrition-program '''Senior Farmers' Market Nutrition Program'''] {{Dotgov}}

* This program provides low-income seniors with access to locally grown fruits, vegetables, honey and herbs. 


'''[https://uwcf.org/8-ways-to-help-people-who-are-food-insecure/ 8 Ways to Help People Who are Food Insecure] {{Dotorg}}'''

* United Way of Central Florida's tips for mutual aid and helping people who are food insecure.

|-
|Organ Trafficking
|[https://humantraffickinghotline.org/resources '''National Human Trafficking Hotline'''] {{Dotorg}}
* Instant Help Number: 1-800-373-7888 or Text: 233733
* An organization for those who have been a survivor of human trafficking to seek out support or a way to alert authorities of a potential trafficking situation. 
* It is also a useful source if you want to learn more about the signs of trafficking and the story of the victims.  


[https://en.m.wikipedia.org/wiki/United_Nations_Voluntary_Trust_Fund_for_Victims_of_Trafficking_in_Persons '''Trust Fund for Victims of Trafficking in Persons'''] {{Dotwiki}}

* Background on organ trafficking in the global context. Links to United Nations Trust Fund webpage provides the latest news on organ trafficking and fundraising events. 


[https://en.m.wikipedia.org/wiki/United_Nations_Voluntary_Trust_Fund_for_Victims_of_Trafficking_in_Persons '''United Nations Voluntary'''] {{Dotwiki}}
|-
|Mass Violence
|[https://www.ptsd.va.gov/professional/treat/type/violence_trauma_effects.asp '''The Impact of Disaster and Mass Violence Events on Mental Health'''] {{Dotgov}}
* This article from the US Department of Veterans Affairs details information about survivors’ reactions to disasters and mass violence events, and it distinguishes the pathology of PTSD (post-traumatic stress disorder) from an expected reaction to such traumas.


[https://www.samhsa.gov/find-help/disaster-distress-helpline/disaster-types/incidents-mass-violence '''Incidents of mass violence'''] {{Dotgov}}

* This article from the Substance Abuse and Mental Health Services Administration describes common reactions to incidents of mass violence and how to get help for those experiencing distress due to these events.

|-
|Memory Impairment/Illness
|[https://www.healthline.com/health/memory-loss '''Heathline article on memory loss'''] {{Dotcom}}
* Learn about causes and coping skills of memory loss.


[https://alzheimersprevention.org/alzheimers-info/memory-quiz/ '''The Alzheimer’s Research and Prevention Foundation Memory Quiz'''] {{Dotorg}}
* Visit this website for a quiz to quickly assess the degree of memory loss (*should not be considered diagnostic).


[https://www.alz.org/ '''The Alzheimer Association'''] {{Dotorg}}
* Visit this website or call 1-800-272-3900 if you need dementia services and support groups for memory loss due to Alzheimer disease.
|-
|Discrimination
|[[wikipedia:Caste_discrimination_in_the_United_States|'''Caste discrimination in the United States''']] {{Dotwiki}}

* Overview of caste discrimination and social hirearchy in the US.
[https://en.m.wikipedia.org/wiki/Economic_discrimination '''Economic Discrimination'''] {{Dotwiki}}


[https://www.eeoc.gov/laws/guidance/facts-about-racecolor-discrimination '''Workplace Racial/Color Discrimination'''] {{Dotgov}} (U.S. Equal Employment Opportunity Commission)

* In-depth facts about race/color discrimination in the workforce, gives informations about Title VII of the Civil Rights Act of 1964 (Act which protects people from being discriminated because of gender, religion, sexuality, race, or color of their skin) and includes examples of how Title VII can protect people from being discriminated in workplace settings.

'''[https://www.dol.gov/general/migrantworker/rights Migrant Worker Rights and Combating Migrant Worker Discrimination] {{Dotgov}}'''

* Resources from the U.S. Department of Labor describing the rights afforded to migrant workers. 


'''[https://myusf.usfca.edu/caps/self-help-resources/discrimination USF Discrimination and Racism Resources]{{Dotedu}}'''

* List of resources compiled by the University of San Francisco. 

|-
|Relational Abuse
|'''National Dating Abuse Helpline''': 1-866-331-9474

* If you need immediate help and/or want to enquire specific information about relational abuse, you can call this hotline. There are professionals on relational abuse to help you immediately.


'''[https://kidshealth.org/en/teens/abuse.html Abusive Relationships (TeensHealth)]''' {{Dotorg}}

* This provides information on definitions/signs of abusive relationships,  tips for getting out of an abusive relationship, and how to deal with the mental and emotional struggles. 
|-
|Workplace Injury
|[https://www.wilg.org/ '''Workers’ Injury Law &amp; Advocacy Group (WILG)'''] {{Dotorg}}
* A national non-profit membership organization dedicated to help workers and their families who suffer the consequences of work-related injuries or occupational illnesses and who need expert legal assistance to obtain medical care and other relief under workers’ compensation programs.


[https://www.osha.gov/workers '''OSHA Worker Rights and Protections'''] {{Dotgov}}

* Visit website or call 1-800-321-6742 about health and safety issues at work. The website provides good information on worker’s rights such as how to file a claim and get compensated in the event of a work-related injury.


[https://www.helpadvisor.com/social-security/serious-workplace-injuries-by-state '''Workplace Injuries Report and Benefits Resource Guide'''] {{Dotcom}}

* Direct and intensive guide to workplace injury, such as benefits and compensation that a worker could receive for work-related injuries. This resource also lists out recent statistics on workplace injuries since the onset of the pandemic. 
|}
----

===Episode 5 &quot;A Fair World&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!Episode 5:              
!&quot;A Fair World&quot; (''Pyeongdeung-han Sesang'' 평등한 세상)&lt;ref name=&quot;:0&quot; /&gt;
|-
|Post Traumatic Stress Disorder (PTSD)
|[[Posttraumatic stress disorder (disorder portfolio)|'''Post-traumatic stress disorder''']] {{Dotwiki}}
* Wiki page that provides a comprehensive overview of PTSD


[https://www.ptsd.va.gov/index.asp '''National Center for PTSD'''] {{Dotgov}}

* If you are searching for governmental assistance and/or therapy for PTSD, you can visit this website or call 1-800-273-8255.


[https://www.clinical-partners.co.uk/for-adults/anxiety-disorders/ptsd/ptsd-test '''Clinical Partner online PTSD test''']

* You can take this quick online test to identify if you experience common signs of PTSD. However, this test should not be considered diagnostic, speaking with a professional is encouraged.


[https://www.helpguide.org/articles/ptsd-trauma/helping-someone-with-ptsd.htm '''Helping Someone with PTSD by HelpGuide'''] {{Dotorg}}

* This is a solid article providing tips for helping family members or friends of patients with PTSD.


[[File:Nisha_Iyer_Pediatric_post_traumatic_stress_dISORDER.pdf|780x780px|Nisha Iyer Pediatric post traumatic stress dISORDER]]

|-
|Strike
|[https://www.nlrb.gov/about-nlrb/rights-we-protect/your-rights/nlra-and-the-right-to-strike '''NLRA and the Right to Strike'''] {{Dotgov}}
* The page NLRA and the Right to Strike outlines when it is and is not illegal for workers to strike, with a translation of the page available in Spanish. This is the official site for the National Labor Relations Board, a group consisting of professionals that provide information about the laws and regulations surrounding labor in the United States. 


[https://aflcio.org/ '''The American Federation of Labor and Congress of Industrial Organizations (AFL-CIO)'''] {{Dotorg}}

* An organization that provides resources for joining or establishing a labor union. It provides information on strikes across the country and how to become involved in them. 
|-
|Rape
|'''[[wikipedia:Rape_crisis_center#Typical_services_offered|Rape Crisis Center]] {{Dotwiki}}''' 
'''[https://rainn.org/resources RAINN National Sexual Assault Hotline]'''
* Crisis support service for sexual assault and harassment in the US.

&lt;br /&gt;
[https://www.nsvrc.org/organizations '''National Sexual Violence Resource Center (NSRVC)'''] {{Dotorg}}

* This website offers an easy-to-navigate directory of resources for victims of sexual violence, providing support organizations that can be filtered by organization type or location.

|-
|Incontinence 
|Note: Incontinence is a symptom of advanced Alzheimer’s.


[https://www.nia.nih.gov/health/urinary-incontinence-older-adults '''Urinary Incontinence in Older Adults (National Institute on Aging)'''] {{Dotgov}}
* Article about types of incontinence in older adults and medical treatments.


[https://nafc.org/ '''National Association for Continence'''] {{Dotorg}}

* An organization that provides resources for elderly adults with incontinence and information about the medical conditions that involve incontinence.


[https://www.alz.org/ '''Alzheimer’s Association'''] {{Dotorg}}

* Visit this website or call 1-800-272-3900 for online support groups and resources for diagnosing and treating Alzheimer’s disease.
|}
----

===Episode 6 &quot;Gganbu&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!Episode 6: 
!&quot;Gganbu&quot; (''Kkanbu'' 깐부)&lt;ref name=&quot;:0&quot; /&gt;
|-
|Acculturation Problems
|[[wikipedia:Acculturation|'''What is acculturation?''']] {{Dotwiki}}
* Wiki page on acculturation definition.


[[wikipedia:Interactive_acculturation|'''Interactive acculturation''']] {{Dotwiki}}
* Wiki page on interactive acculturation.


[https://www.joymental.com/therapy-for-acculturation/ '''Joy Mental Fitness'''] {{Dotcom}}

* A therapy site provides information about the definition, categories, and symptoms of acculturation. You can also schedule a teletherapy for acculturation in the website
|-
|Witnessing a Crime
|[https://victimconnect.org/learn/types-of-crime/homicide-and-grief/ '''Victim Connect Resource Center'''] {{Dotorg}}
* Visit the website or call 1-855-4-VICTIM (1-855-484-2846)
* This is a nonprofit organization dedicated to looking out for victims’ rights and aiding witnesses of victims. 
* This page outlines a comprehensive list of ways to address grief and organizations to reach out to after a homicide.


[https://www.compassionatefriends.org/find-support/online-communities/private-facebook-groups/ '''Private Facebook Groups - Compassionate Friends'''] {{Dotorg}}

* A list of private Facebook groups offered by Compassionate Friends, where bereaved people (especially parents, siblings, friends) can find support.
|}
----

===Episode 7 &quot;VIPS&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!Episode 7:
!&quot;VIPS&quot;&lt;ref name=&quot;:0&quot; /&gt;
|-
|Suicide
|'''[https://988lifeline.org/ National Suicide Prevention Lifeline]: Call 1-800-273-8255''' {{Dotorg}}
* This is a national network of local crisis centers that provides 24/7 and free online support.


'''[https://www.crisistextline.org/ Crisis Textline]''' {{Dotorg}}
* Text HOME to 741741
* Connects people who need online counseling with a crisis counselor.


'''Call 911'''

See above (Ep 2: Suicide)


[[File:Warning_Signs_for_Suicidal_Ideation_Infographic_(1).pdf|550x550px|Warning Signs for Suicidal Ideation Infographic (1)]]
|-
|Anxiety/Fear
|[https://www.nimh.nih.gov/health/topics/anxiety-disorders '''Anxiety Disorders on the Nation Institute of Mental Health'''] {{Dotgov}}
* This page provides a brief introduction, symptoms, and treatments, together with comprehensive resources and brochures about Anxiety Disorders.


[https://www.samhsa.gov/find-help/national-helpline '''SAMHSA’s National Helpline'''] {{Dotgov}}

* Anxiety Helpline: 1-800-662-HELP (4357) (in English and Spanish)
* SAMHSA’s National Helpline for anxiety, substance use, and other mental health disorders is a 24/7 confidential resource for individuals facing anxiety and fear. SAMHSA provides callers with access to treatment, support groups, and local organizations for easy-access.
* Note: The helpline does not provide counseling, it is mainly an information center that can transfer people to appropriate state or local services.


[https://www.samhsa.gov/find-help/national-helpline/help4u '''435748 (HELP4U) – Treatment Referrals via Text Message | SAMHSA'''] {{Dotgov}}

* Text your 5-digit ZIP Code to 435748 (HELP4U) (only in English). Reply STOP to cancel or HELP to reach an information specialist.
* This is a text option provided by the SAMHSA’s national helpline

|-
|Sexual Harassment/Assault
|'''National Sexual Assault Hotline: Call 1-800-656-4673'''
* If you need immediate help for sexual assault/rape attempt, please call 1-800-656-4673.


[https://www.med.unc.edu/beacon/get-help/sexual-assault-resources/ '''RAINN (Rape, Abuse, and Incest National Network)'''] {{Dotedu}}

* The nation’s largest anti-sexual violence organization. 
* The organization works with local sexual assault service providers and carries out programs to prevent sexual violence, help victims, and ensure that perpetrators are brought to justice.


[https://www.nsvrc.org/ '''National Sexual Violence Resource Center (NSVRC)'''] {{Dotorg}}

* The NSVRC’s Mission is to provide leadership in preventing and responding to sexual violence through collaboration, sharing and creating resources, and promoting research.


[https://www.endthebacklog.org/backlog/what-rape-kit-backlog '''End the Backlog'''] {{Dotorg}}

* An article by End the Backlog that discusses the Rapekit backlog in addition to providing education on what rapekits are, how to report a rape, and to get involved in the organization.
|-
|Workplace Sexual Harassment/Assault
|[https://iwpr.org/iwpr-publications/briefing-paper/sexual-harassment-and-assault-at-work-understanding-the-costs/ '''Sexual Harassment and Assault At Work by Institute for Women’s Policy Research'''] {{Dotorg}}
* This article is an overview about what qualifies as sexual harassment, when it occurs in the workplace, and what to do when it occurs. 


[https://www.eeoc.gov/harassment '''The US Equal Employment Opportunity Commission (EEOC)'''] {{Dotgov}}
* This page contains the legal definition of harassment and explains what groups are included as protected against harassment under the law. 
* Call 1-800-669-4000 to report an incident of workplace harassment


[https://projectwhen.org/resources/ '''Resources to Fight Harassment in the Workplace by Project WHEN'''] {{Dotorg}}

* This article offers resources for both employers and employees on the topics of workplace harassment, including sexual harassment. 
* You can also find information on how to prevent and report harassment.

|}
----

=== Episode 8 &quot;Front Man&quot; ===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
&lt;!-- starting to add section names so that we can retrieve content from specific topics without repetition --&gt;

|-
!Episode 8:
!&quot;Front Man&quot; (Peuronteumaen 프론트맨)&lt;ref name=&quot;:0&quot; /&gt;
&lt;section begin=Physical_Violence /&gt;
|-
|Physical Violence 
|&lt;u&gt;Note&lt;/u&gt;: Physical Violence is an act that can ultimately affect anyone of any race, gender, sexual orientation, religion. Squid Game episode one sets the precedent for a multitude of physically violent acts that will continue to take place throughout the series. 


&lt;section end=Physical_Violence /&gt;
&lt;section begin=Gun_Violence /&gt;
|-
|Gun Violence
|&lt;u&gt;Note&lt;/u&gt;: Gun violence can be emotionally taxing to not just those directly affected by loss, but by even community members and those from afar. Squid Game has a multitude of depictions of gun violence throughout the show, starting from episode 1.
'''Call [[wikipedia:The_Center_to_Prevent_Youth_Violence#Speak_Up|1-866-SPEAK-UP]]'''{{Dotwiki}} to report threats of violence


[[SCCAP/Resources for Dealing with a School Shooting|'''SCCAP/Resources for Dealing with a School Shooting''']] {{Dotwiki}}

* A Wikiversity page on resources to deal with school shooting.


[https://everytownsupportfund.org/everytown-survivor-network/resources-for-victims-and-survivors-of-gun-violence/finding-help/ '''Everytown Support Fund'''] {{Dotorg}}
* The Everytown Support Fund offers basic resources and information on their website to help victims and survivors of gun violence. Please note that the resources listed are not comprehensive and there may be other resources available to you in your community.
&lt;section end=Gun_Violence /&gt;
&lt;section begin=Trauma /&gt;
|-
|Trauma
|[[Helping Give Away Psychological Science/Coping with traumatic event|'''Helping Give Away Psychological Science/Coping with traumatic event''']] {{Dotwiki}}


[[Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit2020|'''Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit 2020''']] {{Dotwiki}}


[https://www.aaets.org/trauma-information/helpful-information-during-and-after-a-traumatic-event '''Helpful Information During and After a Traumatic Event'''] {{Dotorg}}
* The American Academy of Experts in Traumatic Stress (AAETS) is made up of a committee of professionals who are dedicated to informing the public and providing resources about how to cope with trauma. In collaboration with the National Center for Crisis Management, this page provides detailed information on what to do during and after a traumatic event, including healthy ways to cope with traumatic stress.


[https://www.nctsn.org/ '''National Child Traumatic Stress Network'''] {{Dotorg}}
* The website gathers cumulative information about child trauma (definition, signs, risk factors etc.). It is updated to the latest events, including documents ‘Talking to Children About War’.
&lt;section end=Trauma /&gt;
|}

----

===Episode 9 &quot;One Lucky Day&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!Episode 9:
!&quot;One Lucky Day&quot; (''Unsu Joeun Nal'' 운수 좋은 날)&lt;ref name=&quot;:0&quot; /&gt;
|-
|Loss of a Friend
|[https://www.healthline.com/health/mental-health/disenfranchised-grief '''Disenfranchised Grief: When No One Seems to Understand Your Loss by Healthline'''][[File:HSPolitic.svg|thumb|21x21px]] {{Dotcom}}
* An article focusing specifically on dealing with bereavement of a close friend.


[https://newsinhealth.nih.gov/2017/10/coping-grief '''Coping With Grief by News In Health'''] {{Dotgov}}

* This article discussed methods to relieve complicated griefs triggered by bereavement. 
* It pointed out the importance of a customized therapy system targeting the complicated grief. 
* Meanwhile, the article encourages addressing the ‘prospect of death before the loss happens’.


'''7 Cups website on coping with grief'''

* 7 Cups website is the world's largest emotional support system
* [https://www.7cups.com/qa-grief-33/ Q &amp; A page for grief] {{Dotcom}}
* [https://www.7cups.com/qa-grief-33/how-do-you-or-have-you-gotten-past-losing-your-best-friend-from-childhood-2934/ Q &amp; A page for “How do you (or have you) gotten past losing your best friend from childhood?”] {{Dotcom}}
|-
|Loss of a Family Member (For Children)
|[https://childrengrieve.org/ '''National Alliance for Children’s Grief'''] {{Dotorg}}
* This is a nonprofit organization whose goal is to raise awareness for children and adolescents who are grieving the death of a loved one while also informing a wider audience about these issues and providing resources to help them.


[https://www.dougy.org/resources/audience/kids?how=&amp;who=&amp;type=activities&amp;age= '''Dougy Center: Grief Resources for Kids'''] {{Dotorg}}

* This organization utilizes a humanistic approach to understand and support children who are grieving a loved one. 
* This specific page on their website provides several worksheets with engaging activities for kids to organize their thoughts and emotions towards grief.


[https://sesamestreetincommunities.org/topics/grief/ '''Helping Kids Grieves (Sesame Street in Communities)'''] {{Dotorg}}

* This resource provides several articles, activities, worksheets and videos for kids to use when grieving.
|-
|Loss of a Family Member (For Adults)
|[https://www.hospiceandcommunitycare.org/grief-and-loss/grief-links/ '''Grief Resources by Hospice &amp; Community Care'''] {{Dotorg}}
* This webpage compiles a long list of videos, readings, caregiving suggestions, and general information about grief for adults and teens.


[https://www.aftertalk.com/ '''After Talk'''] {{Dotcom}}

* Online platform where people can write messages to their lost ones to ease the silence of the loss. 
* “It is a place of Comfort, Sharing and Insight for those who have experienced loss or are supporting a Loved One in Hospice Care.”
|-
|Loss of a Family Member (For Widows/Widowers)
|[https://nationalwidowers.org/ '''National Widowers Organization'''] {{Dotorg}}
* This organization provides several resources and virtual support groups for men who are grieving. 
* This website also provides a peer support program to connect with others who are going through similar experiences.


[https://widowedparent.org/ '''Widowed Parents'''] {{Dotorg}}

* This website provides support for widowed parents and children who are experiencing the loss of a loved one. 
* This resource also compiled several virtual and in-person support groups to connect with others.
|-
|Depression
|[https://www.psychiatry.org/patients-families/depression/what-is-depression '''American Psychiatric Association, What is Depression?'''] {{Dotorg}}
* A page from the website for the American Psychiatric Association that provides detailed information about the symptoms of depression.


[https://screening.mhanational.org/screening-tools/depression/ '''Mental Health America’s online test on depression'''] {{Dotorg}}

* A quick online test that helps people better understand their mental situations
* Unofficial test that cannot constitute a diagnosis.


[https://www.healthline.com/health/depression/intervention '''Healtline article on depression intervention: What to Do and What Not to Do'''] {{Dotcom}}


[https://suicidepreventionlifeline.org/ '''National Suicide Prevention Lifeline: 1-800-273-8255'''] {{Dotorg}}
* A national network of local crisis centers; they provide 24/7 and free online support and handle all situations related to suicide and emotional distress.


[https://www.nami.org/home '''National Alliance on Mental Health (NAMH)'''] {{Dotorg}}

* A nationwide mental health organization with affiliates narrowed down to towns. They provide mental health education programs and a help line; useful for people seeking mental health resources.

|-
|Homelessness/Destitution
|'''2-1-1 hotline (Call 2-1-1)'''
* Many states across the US have hotlines for individuals to call 2-1-1 if they are homeless or about to become homeless. 
* Trained staff will help callers find shelter and other resources.


[https://endhomelessness.org/how-to-get-help-experiencing-homelssness/ '''National Alliance to End Homelessness'''] {{Dotorg}}
* This website provides phone numbers and other resources for people to access shelter/housing services, health care, and food if they are experiencing or at risk of experiencing homelessness.


[https://www.hudexchange.info/housing-and-homeless-assistance/ '''HUD Exchange''']
* HUD Exchange is a website run by the US Department of Housing and Urban Development that provides information and access to housing, food, health and safety resources, and job training for people experiencing or at risk for homelessness.
|}
----

== '''Season 2''' ==
Netflix has renewed the series for a second season, with no official release date yet. It is anticipated to release in late 2023 or early 2024.&lt;ref&gt;{{Cite web|url=https://www.tvguide.com/news/squid-game-season-2-release-date-cast-and-everything-to-know/|title=Everything We Know So Far About Squid Game Season 2|website=TVGuide.com|language=en|access-date=2022-12-26}}&lt;/ref&gt; 

=='''Accessing Mental Health Support''' ==
If you are struggling with your mental health, please do not hesitate to seek help. Below are some resources to help you find professional mental health support.

=== Free Self Assessment ===
Helping Give Away Psychological Science ([https://HGAPS.org HGAPS.org]){{Dotorg}} has made free online assessments you can use to check your anxiety, mood, or other concerns and get a free, confidential report and suggestions about where to do for more information or support. These combine some of the best of the free tools to let you check about some of the most common issues with one click. There are versions for teens, college students, and older adults [https://www.hgaps.org/ac.html here]. If you've ever wondered whether focus struggles or restlessness might point to ADHD, you can also take a free ADHD self-assessment [https://adhddegree.co.uk here] to explore whether attention difficulties could be part of the picture.  

Another free online assessments available at [https://missionconnectionhealthcare.com/self-assessments/ Mission Connection Healthcare]. 

=== Ways to Find a Therapist ===
There are many different places to look for support. Below we provide some tips about places to look for a therapist, such as a psychologist, counselor, or other mental-health professional. We focus on ones that are from large organizations (increasing the chances that you may find someone near you, or who better matches what you hope to find in a provider), as well as not charging you to search them. It has become more possible and more common to do therapy by video (&quot;teletherapy&quot;). The rules about teletherapy are changing rapidly. If you want to read more about options with teletherapy, a detailed guide is [[Helping Give Away Psychological Science/Telepsychology Guide for Patients|here]]. 
{| class=&quot;wikitable sortable mw-collapsible&quot;
|-
!Resource
!Description
|-
|[https://locator.apa.org/ '''APA Psychologist Finder'''] {{Dotorg}}
|This service provided by the American Psychological Association (APA) allows you to search for Psychologists in your area. You can also search for a Psychologist by their name or the name of their practice. Your search may yield: 
-the names of local Psychologists

-whether or not they accept insurance as well as which types

-whether or not they are currently accepting new patients

-whether or not Telehealth is available

-the address of their practice
|-
|[https://www.psychologytoday.com/us/psychiatrists '''Psychology Today Psychiatrist Finder'''] {{Dotcom}}
|By typing in your zip code, you can search for psychiatrists in your area using Psychiatrist Finder. The search results will provide a list of psychiatrists and their phone number or website to contact.
|-
|[https://www.findcbt.org/FAT/ '''Find a CBT Specialist'''] {{Dotorg}}
|This ABCT Find-a-Therapist service gives you access to cognitive and behavioral therapists based on your zip code and selected filters.

* The goal of cognitive behavioral therapy is to recognize and change unhealthy patterns in thinking and behavior so develop personal strategies to deal with mental health difficulties.
|-
|[https://www.psychologytoday.com/us/therapists/psychodynamic '''Find a Psychodynamic Specialist'''] {{Dotcom}}
|You can find psychodynamic therapists in your area through Psychology Today's service by searching with your city or zip code.

* Psychodynamic therapy focuses on the unconscious to understand the root of the psychology distress.
|-
|[https://www.psychologytoday.com/us/therapists/humanistic '''Find a Humanistic Specialist'''] {{Dotcom}}
|Humanistic therapists in your city or area code can be easily found using this humanistic specialist finder.

* Humanistic specialists emphasizes developing a strong and healthy sense of self, your true feelings, and meaning to lead your most fulfilling life
|}

=='''Who Can Help Me?''' ==
When seeking mental health support, you may be overwhelmed by the numerous types of mental health professionals you can seek help from. Below are summaries of the primary types of professionals that may be offering mental health services in your area. Please note that availability, finances, or other factors may impact which professionals you can receive support from. 
{| class=&quot;wikitable sortable mw-collapsible&quot;
|-
!Title
!Description
|-
|Clinical Social Worker
|
* Focus on the assessment, diagnosis, treatment, and prevention of mental illnesses and emotional distress
* Licensed or certified at the clinical level in the state of practice
* Work in areas like private practices, hospitals, community mental health, primary care, and agencies
* Advocate for client rights and strong therapeutic connection between client and practitioner
|-
|Mental Health Counselor
|
* Assesses and treats mental and emotional health disorders, relationship issues, and life difficulties
* Provide support and guidance and offer coping strategies for the patient
* License: Must have earned a LMHC (Licensed Mental Health Counselor), LMSW (Licensed Master Social Worker), or LPC (Licensed Professional Counselor)
|-
|Psychologist (Clinical or Counseling)
|
* Assess and treat mental, emotional, and behavioral disorders through observation, interviews, and psychological tests
* License: Must have received a doctoral degree in psychology; requirements vary by state of practice
|-
|Psychiatric Nurse Practitioner
|
* Specially trained nurses that work in the mental health field
* Assess and diagnoses patients, study their medical history, and perform comprehensive mental health tests
* License: Must pass the PMHNP (Psychiatric-Mental Health Nurse Practitioner) board certification exam to obtain the PMHNP license
|-
|Psychiatrist
|
* Medical doctors who specializes in mental health
* Assess, diagnose, and treat mental, emotional, and behavioral disorders
* License: Must be board-certified by the American Board of Psychiatry and Neurology (ABPN). Must be licensed as an MD (Doctor of Medicine) or OD (Optometrist) by the state in which they practice
|}
[[File:Preparing for Your Telepsychology Session Infographic.pdf|alt=Tips for a client getting ready for a telepsychology session|thumb|Tips for your telepsychology session]]


[[File:Is_Telepsychology_Right_for_Your_Clients%3F_Infographic.pdf|750x750px|Is Telepsychology Right for Your Clients? Infographic]]

== See Also ==
&lt;!-- categories below --&gt;
This project was supported by a [[m:Rapid Grant|Rapid Grant]] from the Wikimedia Foundation. The funded proposal is [[m:Grants:Project/Rapid/Hkim243/Promoting dissemination of cross-cultural mental health resources using Squid Game|here]].  
[[Category:HGAPS Numbered Projects]]</text>
      <sha1>6xp8b318g7vi81y9aynay0uoy2jcxlc</sha1>
    </revision>
    <revision>
      <id>2720903</id>
      <parentid>2720902</parentid>
      <timestamp>2025-07-06T11:10:06Z</timestamp>
      <contributor>
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&lt;!--
&lt;div class=&quot;center&quot; style=&quot;width: auto; margin-left: auto; margin-right: auto;&quot;&gt;{{TOC limit|4}}&lt;/div&gt;
--&gt;[[File:Squid Game resources QR Code.svg|alt=QR code that includes a shortened URL to the resource page|thumb|QR code to save or share this page]]

=='''''Squid Game'''''&lt;ref name=&quot;:0&quot;&gt;{{Cite journal|date=2022-02-13|title=Squid Game|url=https://en.wikipedia.org/w/index.php?title=Squid_Game&amp;oldid=1071609561|journal=Wikipedia|language=en}}&lt;/ref&gt;--Mental Health Resources for Triggering Topics==
[[File:Cosplay of Squid Game Guards at Sutera Cosplay Fest 2021.jpg|thumb|left|220x220px|alt=Image depicts a cosplay of one of the guards from Squid Game from the Sutera Cosplay Fest in 2021.|Cosplay of Squid Game Guards at Sutera Cosplay Fest 2021.]]
[[File:Squid Game dalgona cookies.jpg|alt=Image depicts a recreation of &quot;dalgona cookies&quot;, or honeycomb candy-like treats, depicted in Episode 3 of Squid Game in the ppopgi game.|thumb|Recreation of &quot;Dalgona Cookies&quot; depicted in Squid Game]]
[[wikipedia:Squid_Game|Squid Game]] (Hangul: 오징어 게임, Romanization: Ojing-eo Geim) is a South Korean television drama created by [[wikipedia:Hwang_Dong-hyuk|Hwang Dong-hyuk]] for Netflix. Named after a common but often violent South Korean children’s game, Squid Game portrays 456 contestants, all of varying backgrounds but all facing deep financial turmoil, desperately trying to win the significant sum of cash held in a tank above the room in which they sleep&lt;ref name=&quot;:0&quot; /&gt;. Early on, however, the contestants realize they have become involved not in a simple game, but rather in a battle for survival.

Quickly ascending to international fame, the show is popular for its high-stakes, action-packed plot, emotionally compelling moments, and complicated characters. However, the violence displayed and heavy topics covered are likely to leave many viewers rattled, and may even recall to mind personal traumas and negative emotions for some. Many potentially triggering topics, including but not limited to suicide, terminal illness, and physical violence, are portrayed in the drama. Unfortunately, the show does not follow up on the troubling topics shown with education regarding resources or support opportunities.

Passionate about promoting better, more accessible mental health support, our team, a subgroup of the group [https://www.hgaps.org/ Helping Give Away Psychological Science (HGAPS)] {{Dotorg}}, has worked to compile applicable resources to address the various triggering topics incorporated throughout the show. If you have viewed Squid Game or plan to view it in the future and feel affected by the themes included in the drama, please feel free to seek support and resources through the links compiled below.


== '''Season 1''' ==

&lt;strong&gt;Each episode block contains a list of a number of triggering topics displayed in the show. Please note that there may be many triggering topics that were not included on this page. Some themes recur throughout the series, and may therefore be listed in more than one episode. In such cases, the repeat-occurrences of a theme will not have content in the corresponding box, but instead the triggering topic itself will be linked so that you will be redirect to the information corresponding to the first instance.&lt;/strong&gt;

''[[w:Squid Game#Episodes|Here's a link to]] a synopsis of the episodes (major spoilers!).''

==== About the resources: ====
We prefer sites that are not trying to sell a good or service, and that do not have other conflicts of interest. We have added tags so that you can see what type of resource it is without clicking on it. 
{| class=&quot;wikitable&quot;
!Icon
!Description
|-
|{{Dotgov}}
|[[w:.gov|.gov]] links go to pages hosted by government agencies.
|-
|{{Dotorg}}
|[[w:.org|.org]] links to pages that are usually nonprofit organizations. 
|-
|{{Dotnet}}
|[[w:.net|.net]] links to pages that use the .net Internet domain. These originally were mostly technology companies, but now this is a widely used alternative to .com for commercial companies. 
|-
|{{Dotwiki}}
|links to [[w:Wikipedia|Wikipedia]] or [[Wikiversity:Introduction|Wikiversity]] articles.
|-
|{{Dotcom}}
|[[w:.com|.com]] links to pages built by groups with a commercial interest. Some of these are altruistic and well done. We had psychologists review these to see if the material seemed accurate, helpful, and balanced. 
|-
|}
 
{|style=&quot;margin: 0 auto;&quot;
|-
| [[File:Squid Game logo (Korean).png|thumb|right|500px|alt=This is the Korean logo for the popular show Squid Game.|Korean logo for [https://en.wikipedia.org/wiki/Squid%20Game Squid Game].]]
| [[File:Squid Game logo.png|thumb|left|680px|alt=This is the English logo for the popular show Squid Game.|English logo for [https://en.wikipedia.org/wiki/Squid%20Game Squid Game].]]
|}

----

The resources are organized two different ways. Use whichever is more convenient. One is a sortable table, listing more than 30 different topics, and showing which themes occur in each episode. The link goes to the episode section containing helpful resources. It may take some scrolling -- some episodes packed in more than ten different major themes!  You can sort the table by each column, simply by clicking the triangles in the column name. The table may be the easiest way to see the range of topics shown in the series, as well as exploring resources.

The second format has an episode-by-episode structure. If people want to unpack all the themes covered in one installment, they are grouped together here. 

==Table of psychological topics==

{| class=&quot;wikitable sortable mw-collapsible&quot; 
|+ Topic Breakdown Per Episode
|-
!Theme
!Topic
!Ep 1
!Ep 2
!Ep 3
!Ep 4
!Ep 5
!Ep 6
!Ep 7
!Ep 8
!Ep 9
|- style=&quot;text-align: center;&quot;
|Trauma
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Trauma]]
|[[File:Porsa-logo.png|20x20px|link=HGAPS|HGAPS]]
|
|[[File:Porsa-logo.png|20x20px]]
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Gambling Problems]]
|[[File:Porsa-logo.png|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Joblessness/Employment Difficulties]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Financial Trouble]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Physical 
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Physical Violence]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Illness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Terminal Illness]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Physical (or family)
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Domestic Abuse]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Physical
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Physical Abuse]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Witnessing
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Gun Violence]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Witnessing
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 1 &quot;Red Light, Green Light&quot;|Mass Casualty/Trauma]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Financial Distress]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Illness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Chronic Illness]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Living Uninsured]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Medical Expenses]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Housing Instability]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Foster Care/Orphanage]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Separation from Family]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Mental Health
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Suicide]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 2 &quot;Hell&quot;|Divorce/Custody Issues]]
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Food Insecurity]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Organ Trafficking]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Witnessing 
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Mass Violence]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Illness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Memory Impairment/Illness]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Discrimination]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Relational Abuse]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Illness/Injury
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 4 &quot;Stick to the Team&quot;|Workplace Injury]]
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Mental Health
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 5 &quot;A Fair World&quot;|Post Traumatic Stress Disorder (PTSD)]]
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 5 &quot;A Fair World&quot;|Strike]]
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Sexual Violence
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 5 &quot;A Fair World&quot;|Rape]]
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Illness/Injury
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 5 &quot;A Fair World&quot;|Incontinence]]
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 6 &quot;Gganbu&quot;|Acculturation Problems]]
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|- style=&quot;text-align: center;&quot;
|Witnessing
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 6 &quot;Gganbu&quot;|Witnessing a Crime]]
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|
|- style=&quot;text-align: center;&quot;
|Mental Health
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 7 &quot;VIPS&quot;|Anxiety/Fear]]
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|- style=&quot;text-align: center;&quot;
|Sexual Violence
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 7 &quot;VIPS&quot;|Sexual Harassment/Assault]]
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|- style=&quot;text-align: center;&quot;
|Sexual Violence
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 7 &quot;VIPS&quot;|Workplace Sexual Harassment/Assault]]
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Loss of a Friend]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Resources for Children]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Resources for Adults]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Separation/Loss
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Resources for Widows/Widowers]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Mental Health
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Depression]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Financial
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 9 &quot;One Lucky Day&quot;|Homelessness/Destitution]]
|
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|- style=&quot;text-align: center;&quot;
|Illness/Injury
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 8 &quot;Front Man&quot;|Terminal Injury]]
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|- style=&quot;text-align: center;&quot;
|Misc darkness
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 8 &quot;Front Man&quot;|Being hunted down]]
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|- style=&quot;text-align: center;&quot;
|Illness/Injury
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 8 &quot;Front Man&quot;|Significant injury]]
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|- style=&quot;text-align: center;&quot;
|Witnessing
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 8 &quot;Front Man&quot;|Murder (stabbing]]'')''
|
|
|
|
|
|
|
|[[File:Porsa-logo.png|center|20x20px]]
|
|- style=&quot;text-align: center;&quot;
|Witnessing
| style=&quot;text-align: left;&quot; | [[Helping Give Away Psychological Science/Helpful resources for themes in Squid Game#Episode 8 &quot;Front Man&quot;|Shooting]]
|
|
|
|
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|
|[[File:Porsa-logo.png|center|20x20px]]
|
|}

===Episode 1 &quot;Red Light, Green Light&quot;===
{| class=&quot;wikitable sortable mw-collapsible&quot;
&lt;!-- starting to add section names so that we can retrieve content from specific topics without repetition --&gt;

|-
!Episode 1:
!&quot;Red Light, Green Light&quot; (''Mugunghwa Kkoch-i Pideon Nal'' 무궁화 꽃이 피던 날)&lt;ref name=&quot;:0&quot; /&gt;
&lt;section begin=Job_Employment /&gt;
|-
|Joblessness/Employment Difficulties
|[https://www.usa.gov/unemployment '''USA Gov Unemployment Help'''] {{Dotgov}}

* USAGov provides resources for those who face employment difficulties to reach out and apply for unemployment benefits, worker’s compensation, and welfare for families. This website on their page compiles a list of helpful links and webpages depending on the individual’s needs and what situation they may be facing.

[https://www.careeronestop.org/LocalHelp/UnemploymentBenefits/Find-Unemployment-Benefits.aspx '''Career OneStop - Unemployment Benefits'''] {{Dotorg}}

* Sponsored by the U.S. Department of Labor, CareerOneStop is a website dedicated to compiling resources for careers, education, and professional development. This specific page on their website allows users to find unemployment resources based on what state they live in.
[https://www.helpguide.org/articles/stress/job-loss-and-unemployment-stress.htm '''Dealing with Job Loss and Unemployment Stress''']{{Dotorg}}

* This article from HelpGuide provides resources and practical, psychologically-backed tips for coping with the stress of unemployment and job loss.

&lt;section end=Job_Employment /&gt;
&lt;section begin=Financial_Trouble /&gt;
|-
|Financial Trouble
|[https://www.mentalhealth.org.uk/explore-mental-health/a-z-topics/debt-and-mental-health '''Information on Debt and Mental Health'''] {{Dotorg}}

* This article from the UK Mental Health Foundation outlines how debt and financial difficulty can have an impact on people psychologically, and how mental health difficulties contribute to financial problems. It also provides information on how to get help for these issues.
[https://consumer.ftc.gov/articles/how-get-out-debt '''How To Get Out of Debt'''] {{Dotgov}}

* Tip sheet from the Federal Trade Commission about getting out of debt 

[https://www.benefits.gov/categories/Financial%20Assistance '''US Government Financial Assistance Database'''] {{Dotgov}}

* The link provided leads to a database which those who are undergoing financial hardship of many different forms can put in specific search criteria to find assistance specific to the state they live in as well as what they need financial assistance for (Loan Repayment, Tax Assistance, Living Assistance, Insurance, etc.)
&lt;section end=Financial_Trouble /&gt;
&lt;section begin=Gambling_Problems /&gt;
|-
|Gambling Problems 
|'''National Problem Gambling Helpline Network (1-800-522-4700)'''
[[wikipedia:Problem_gambling#Signs_and_symptoms|'''Symptoms of problematic gambling''']] {{Dotwiki}}

'''[https://www.helpguide.org/articles/addictions/gambling-addiction-and-problem-gambling.htm Gambling Problem]''' {{Dotorg}}

* This article provides details on the signs and symptoms of gambling disorder, and it offers self-help tips and treatments.

[[wikipedia:Problem gambling#Treatment|'''Treatment options''']] {{Dotwiki}}

* This page provides a list of treatment options to help with gambling problems.

[https://recovery.org/support-groups/gamblers-anonymous/ '''Gamblers Anonymous'''] {{Dotorg}}

* Gamblers Anonymous is a 12-step recovery program for people with gambling addiction.
&lt;section end=Gambling_Problems /&gt;
&lt;section begin=Physical_Violence /&gt;
|-
|Physical Violence 
|&lt;u&gt;Note&lt;/u&gt;: Physical Violence is an act that can ultimately affect anyone of any race, gender, sexual orientation, religion. Squid Game episode one sets the precedent for a multitude of physically violent acts that will continue to take place throughout the series. 


[https://victimsofcrime.org/ '''National Center for Victims of Crimes'''] {{Dotorg}}
* '''Phone''': 1-202-467-8700
* The National Center for Victims of Crime is a 35 year old nonprofit organization with a plan tailored to fit the needs of those who experience any type of physical violence and also for the families of those victims. 

[http://www.nationalcenterdvtraumamh.org/ '''National Center on Domestic Violence, Trauma &amp; Mental Health'''] {{Dotorg}}

* '''Phone''': 1-312-726-7020, ext. 2011
* The National Center on Domestic Violence, Trauma &amp; Mental Health provides training, support, and consultation to mental health professionals and policymakers in addition to resource education for the general population. 

[https://www.med.unc.edu/beacon/get-help/child-abuse-resources/ '''UNC Hospital's Beacon Program'''] {{Dotedu}}

* UNC Hospital’s Beacon Program lists many resources on their website to aid those affected by all types of abuse. The link attached proivdes specific resources for those affected by child abuse. The Beacon Program provides comprehensive, coordinated care to the UNC System’s patients, families, and employees experiencing a variety of interpersonal abuse.
&lt;section end=Physical_Violence /&gt;
&lt;section begin=Terminal_Illness /&gt;
|-
|Terminal Illness
|'''[[wikipedia:Terminal_illness|Cancer Care]]''' {{Dotwiki}}
* Cancer Care provides resources and expectations for advanced cancer patients, setting expectations, giving advice, and suggesting ways to spend valuable time.

[https://www.cancerresearchuk.org/about-cancer/coping/dying-with-cancer/after-someone-dies/coping-with-grief '''Coping with Grief''']  {{Dotorg}}
* This article, by Cancer Research UK, is directed to someone who has lost a loved one and overviews the stages of grief, different types of grief, and coping skills. Containing many facts and helpful statistics, this article gives insight to all sides of the situation, setting expectations for the future.


[https://www.verywellhealth.com/coping-with-anticipatory-grief-2248856 '''Coping with anticipatory grief'''] {{Dotcom}}
* This website, aimed toward someone who has lost a loved one, focuses on the distinction between anticipatory grief (before someone dies) versus conventional grief (afterwards), utilizing many of the same coping strategies in a more tailored way.
&lt;section end=Terminal_Illness /&gt;
&lt;section begin=Domestic_Abuse /&gt;
|-
|Domestic Abuse
|'''911 Emergency Call'''
* If you are facing an emergent situation regarding domestic abuse, please call 911; it's one of the fastest ways to get help in an emergency situation.

'''National Domestic Violence Hotline: Call 800-799-7233 or Text &quot;START&quot; to 88788'''

* If you need immediate help and/or want to enquire specific information about domestic abuse, you can Call 800-799-7233 or Text &quot;START&quot; to 88788. There are professionals on domestic abuse to give you immediate help.

'''[https://www.americanbar.org/content/dam/aba/administrative/domestic_violence1/Resources/charts/6%2019%202013%20LGBT%20CPO%20statutory%20chart_FINAL.pdf Domestic Violence Civil Protection Orders (Document)]''' {{Dotorg}}

* This chart, provided by Commission on Domestic and Sexual Violence, entails state-by-state information about definition of domestic violence as well as legal rights for domestic violence victims.

[[wikipedia:Domestic_violence#Forms|'''Forms of Domestic Violence''']] {{Dotwiki}}
*This is a wiki page explaining different forms of domestic violence.
&lt;section end=Domestic_Abuse /&gt;
&lt;section begin=Physical_Abuse /&gt;
|-
|Physical Abuse
|'''Call 911'''[https://www.healthyplace.com/abuse/adult-physical-abuse/physically-abused-where-to-get-help-for-physical-abuse '''Where to Get Help for Physical Abuse'''] {{Dotcom}}
* This website lists immediate and additional helping resources for physical abuse victims. There are also resources for teenagers and underrepresented groups.
&lt;section end=Physical_Abuse /&gt;
&lt;section begin=Gun_Violence /&gt;
|-
|Gun Violence
|&lt;u&gt;Note&lt;/u&gt;: Gun violence can be emotionally taxing to not just those directly affected by loss, but by even community members and those from afar. Squid Game has a multitude of depictions of gun violence throughout the show, starting from episode 1.
'''Call [[wikipedia:The_Center_to_Prevent_Youth_Violence#Speak_Up|1-866-SPEAK-UP]]''' {{Dotwiki}} to report threats of violence


[[SCCAP/Resources for Dealing with a School Shooting|'''SCCAP/Resources for Dealing with a School Shooting''']] {{Dotwiki}}

* A Wikiversity page on resources to deal with school shooting.


[https://everytownsupportfund.org/everytown-survivor-network/resources-for-victims-and-survivors-of-gun-violence/finding-help/ '''Everytown Support Fund'''] {{Dotorg}}
* The Everytown Support Fund offers basic resources and information on their website to help victims and survivors of gun violence. Please note that the resources listed are not comprehensive and there may be other resources available to you in your community.
&lt;section end=Gun_Violence /&gt;
&lt;section begin=Mass_Casualty /&gt;
|-
|Mass Casualty/Trauma
|[https://www.ptsd.va.gov/understand/types/resources_disaster_violence.asp '''National Center for PTSD''']  {{Dotgov}}
* This resource specifically provides aids for veterans dealing with PTSD, but also provides great resources for all individuals who face PTSD. This page specifically provides resources on what to expect when faced with mass violence and a virtual PTSD coach.

'''Veterans Crisis Line: Call 1-800-273-8255'''

* Press 1 (available 24/7)
* Chat live
* Text 838255


'''Call 911''' if it is urgent - check '''[https://www.veteranscrisisline.net/signs-of-crisis/ Signs of Crisis]''' {{Dotnet}}


[https://en.m.wikipedia.org/wiki/Mass-casualty_incident '''What is a Mass Casualty Incident?'''] {{Dotwiki}}

* A wiki page one the definition of mass casualty incident and helping resources.
&lt;section end=Mass_Casualty /&gt;
&lt;section begin=Trauma /&gt;
|-
|Trauma
|[[Helping Give Away Psychological Science/Coping with traumatic event|'''Helping Give Away Psychological Science/Coping with traumatic event''']] {{Dotwiki}}


[[Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit2020|'''Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit 2020''']] {{Dotwiki}}

[https://www.aaets.org/trauma-information/helpful-information-during-and-after-a-traumatic-event '''Helpful Information During and After a Traumatic Event'''] {{Dotorg}}
* The American Academy of Experts in Traumatic Stress (AAETS) is made up of a committee of professionals who are dedicated to informing the public and providing resources about how to cope with trauma. In collaboration with the National Center for Crisis Management, this page provides detailed information on what to do during and after a traumatic event, including healthy ways to cope with traumatic stress.

[https://www.nctsn.org/ '''National Child Traumatic Stress Network'''] {{Dotorg}}
* The website gathers cumulative information about child trauma (definition, signs, risk factors etc.). It is updated to the latest events, including documents ‘Talking to Children About War’.
&lt;section end=Trauma /&gt;
|}

----

===Episode 2 &quot;Hell&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!'''Episode 2:'''
!&quot;Hell&quot; (''Ji-ok'' 지옥)&lt;ref name=&quot;:0&quot; /&gt;
|-
|Financial Distress
|&lt;u&gt;Note&lt;/u&gt;: Financial Distress is a dilemma that both companies and individuals might confront. It is the core cause of ‘Squid Game’ and one of the motives that drive participants to perform violence, return the game, and struggle to win.


[https://aamft.org/Consumer_Updates/Financial_Distress.aspx '''The American Association for Marriage and Family Therapy (AAMFT)'''] {{Dotorg}}
* For families, couples encountering mental health issues, joblessness, and parenting problems resulting from financial stress.
* 1. Helps with job seeking, financial management, and mental health issues. 2. Useful LINKS attached at the bottom of the page.
* Financial distress severely influences family life, probably causing depression, alcohol/drug use, panic, etc. The website specifically helps families recognize distress and seek financial help.

[https://financiallit.org/resources/downloadable-forms-and-worksheets/' '''Downloadable Financial Forms and Worksheets'''] {{Dotorg}}

* For you to manage incomes and expenditures.
* Worksheets that help to manage budgets, measure debts, and set financial goals.
* Under ‘Other resources’, there are a bunch of useful docs and website addresses that help to make life more affordable.

'''[https://www.mymoney.gov/ Financial Management Resources]''' {{Dotgov}}

* For anyone who needs financial managing resources.
* Click ‘LIFE EVENTS’ to find appropriate resources targeting specific issues. Click ‘TOOLS’ to access multiple calculators, budgeting worksheets, and checklists.
* Mymoney is a US government website consisting of cumulative finance-related resources that provide various aids to all groups of all ages.

'''[https://studentaid.gov/h/apply-for-aid/fafsa Apply for Student Financial Aid (FAFSA)]''' {{Dotgov}}

* This website provides comprehensive resources about finding financial aid for students.

'''[https://www.usa.gov/unemployment Unemployment Help]''' {{Dotgov}}

* '''Unemployment Help page under the USA government website, where we can find links to health coverage, compensation, temporal assistance, etc.'''

|-
|Chronic Illness
|'''[https://www.cdc.gov/chronic-disease/?CDC_AAref_Val=https://www.cdc.gov/chronicdisease/resources/infographic/chronic-diseases.htm Chronic Diseases in America]''' {{Dotgov}}
* The CDC’s guide to prevention and resources for chronic illness. Includes statistics, study interventions, and funding guides.


[https://www.ncoa.org/article/evidence-based-chronic-disease-self-management-education-programs '''Chronic Disease Self-Management Programs'''] {{Dotorg}}

* This website includes programs that help with managing chronic illness, as well as facts on chronic diseases and recommendations for self-management.
|-
|Living Uninsured
|'''[https://www.healthcare.gov/screener/ See if You Are Eligible for Health Coverage]''' {{Dotgov}}
* HealthCare.Gov provides information on types of federal and state health insurance programs and helps a person see which program would work best for them. Also provides access to local resources so the person can seek assistance closer to them.
* Call 1-800-318-2596 (for questions on healthcare)


[https://www.ruralhealthinfo.org/topics/rural-health-clinics#overview '''Rural Health Clinic Program'''] {{Dotorg}}

* This program is designed to increase healthcare access to those living in rural communities, and it covers treatment from doctors and nurses. 


[https://nhchc.org/directory/ '''National Health Care for the Homeless Council'''] {{Dotorg}}

* This is a great resource that could help homeless or displaced individuals get health care coverage as it connects them to local services and helps provide them with potential coverage options.


[https://khealth.com/urgent-care/ '''Cash pay out and out of pocket options'''] {{Dotcom}}

* For those who necessarily do not have the means to pay for health insurance, this resource can help people get the healthcare that they need without having to pay the extra costs that come with not having insurance. K health is essentially virtual urgent care, where you use an app that connects with a healthcare provider without the additional cost. 


[https://www.medicare.gov/basics/get-started-with-medicare '''Medicare'''] {{Dotgov}}
* Medicare is a federally sanctioned health insurance program that offers coverage for prescription medication, hospital visits, doctor’s visits, etc. It is for people who are 65 years or older and for those who are younger than 65 who have health conditions or disabilities. 


[https://www.kff.org/uninsured/issue-brief/key-facts-about-the-uninsured-population/ '''Facts about the Uninsured Population'''] {{Dotorg}}

* This website provides information on the uninsured population living in the US to educate more people on the implications of living uninsured.


[https://en.m.wikipedia.org/wiki/Health_insurance_coverage_in_the_United_States '''Health Insurance Coverage in the United States'''] {{Dotwiki}}

* A wiki page on health insurance coverage in the U.S.
|-
|Medical Expenses
|[https://www.ssa.gov/benefits/medicare/prescriptionhelp.html '''Extra Help with Medicare Prescription Drug Plan Costs'''] {{Dotgov}}
* &quot;MeMedicare beneficiaries can qualify for Extra Help paying for their monthly premiums, annual deductibles, and co-payments related to Medicare prescription drug coverage.
* We estimate the Extra Help is worth about $5,100 per year. To qualify for Extra Help, you must be receiving Medicare and have limited resources and income.”
* Apply online, over the phone: 1-800-772-1213, request a paper application, or apply at your local Social Security Office.


'''[https://www.healthwellfoundation.org/ Health Well Foundation]''' {{Dotorg}}
* Health Well is an organization that provides financial assistance by assisting with copays, premiums, deductibles and out-of-pocket expenses when health insurance is not enough.


[https://www.panfoundation.org/ '''Patient Access Network Foundation'''] {{Dotorg}}
* PAN Foundation helps underinsured individuals with diseases with out-of-pocket costs, allowing them to get the medications and treatments they need and advocating for improved access and affordability.


'''[https://nafcclinics.org/ National Association of Free and Charitable Clinics]''' {{Dotorg}}

* The National Association of Free &amp; Charitable Clinics (NAFCC) focuses on connecting economically disadvantaged individuals to free and charitable clinics. NAFCC has a goal in mind of making healthcare more accessible to individuals based on location.


'''[https://www.cancercare.org/copayfoundation CancerCare Co-Payment Assistance Program]''' {{Dotorg}}

* This program helps people with cancer overcome financial stress and treatment barriers by assisting them with co-payments for treatments.


[https://en.m.wikipedia.org/wiki/Medical_debt '''Medical Debt'''] {{Dotwiki}}

* A wiki page on medical debt.
|-
|Housing Instability 
|'''[https://www.coabode.org/ Home Sharing Program for Single Mothers]''' {{Dotorg}}
* This is a homes sharing program designed to help single mothers connect and find a home to share together. This decreases the chance of housing instability and helps support single mothers in raising their children.


[https://www.rd.usda.gov/about-rd/agencies/rural-housing-service '''Rural Housing Services'''] {{Dotgov}}
* This resource offers housing assistance to those in rural communities. They also help improve housing and essential community facilities through the offering of loans and grants. 


'''[https://www.habitat.org/housing-help/apply Habitat for Humanity]''' {{Dotorg}}

* This is a program where people with housing instability can apply to live in a home of another homeowner’s construction. For example a person will buy a home or construct a home for another person to live in. This is called sweat equity.


[https://www.hud.gov/program_offices/public_indian_housing/pha/contacts '''Public Housing Agency Plan'''] {{Dotgov}}
* This provides information on housing instability along with a place where someone can apply for housing assistance. This resource specifically allows people to apply for an emergency housing voucher.


[https://www.consumerfinance.gov/coronavirus/mortgage-and-housing-assistance/renter-protections/find-help-with-rent-and-utilities/ '''Consumer Financial Protection Bureau'''] {{Dotgov}}
* This website allows people to find rental assistance in their area to help with housing costs.
|-
|Foster Care/Orphanage
|'''Foster Parent Advice Line: +1 800-829-3777'''
* Call the hotline to get advice with issues such as navigating the foster care system, probate court and legal guardianship, understanding child development.


'''[https://kidsmatterinc.org/for-youth/how-to-help-a-younger-sibling/ How to Help a Younger Sibling in Foster Care]''' {{Dotorg}}

* This website provides information about requirements, guidelines and assistance hotline for older siblings/relatives who wish to foster or adopt younger siblings or relatives.


[https://nfpaonline.org/ '''National Foster Parent Association'''] {{Dotorg}}

* This program provides foster families with opportunities for advocacy, networking, and education. Resources include adoption information, foster parents training and education, etc.


'''[https://www.familylawselfhelpcenter.org/self-help/custody-paternity-child-support Family Law Self-Help Center]''' {{Dotorg}}
* This is a self-help center for foster parents to access common Q&amp;A about legal issues regarding custody and child support.


[https://en.m.wikipedia.org/wiki/Foster_care_in_the_United_States '''Foster care in the US'''] {{Dotwiki}}

* A wiki page on foster care system in the U.S.

|-
|Separation from Family
|'''[https://www.therecoveryvillage.com/mental-health/self-harm/how-to-help-a-friend-with-separation-anxiety/ How to Help a Friend with Separation Anxiety]''' {{Dotcom}}
* Call: 877-782-7659
* The Recovery Village is a website focused on providing resources for a wide variety of mental health concerns, including separation anxiety. This particular article on their website lists ways to help a friend who is facing separation anxiety as well as methods to cope with it.


'''[https://raisingchildren.net.au/for-professionals/mental-health-resources/parent-mental-health-and-wellbeing/separation-and-divorce Support During Separation &amp; Divorce] 🇦🇺''' {{Dotnet}}

* This site provides support for parents after a separation or divorce, including how to help children in various age groups facing the same conflicts. This resource provides support for single parents, children living in two separate homes, teenagers, and conflict management between parents.

|-
|Suicide
|'''[https://988lifeline.org/ National Suicide Prevention Lifeline]: Call 1-800-273-8255''' {{Dotorg}}
* This is a national network of local crisis centers that provides 24/7 and free online support.


'''[https://www.crisistextline.org/ Crisis Textline]''' {{Dotorg}}
* Text HOME to 741741
* Connects people who need online counseling with a crisis counselor.


'''[https://988lifeline.org/ 988 Suicide &amp; Crisis Lifeline] {{Dotorg}}'''

* National network of local crisis centers in the US that provide free and confidential support to people in suicidal crisis or emotional distress at any time.


'''Wikipeadia pages on suicide help resources:'''

[[wikipedia:Suicide#Risk_factors|'''Risk Factors of Suicide''']] {{Dotwiki}}

[[wikipedia:Suicide#Prevention|'''Suicide Prevention''']] {{Dotwiki}}

[[wikipedia:Suicide_prevention#Interventions|'''Suicide Interventions''']] {{Dotwiki}}

[[wikipedia:Suicide_prevention#Risk_assessment|'''Suicide Risk Assessment''']] {{Dotwiki}}

[[wikipedia:Suicide_prevention#Support_organizations|'''Support Organizations''']] {{Dotwiki}}
|-
|Divorce/Custody Issues
|[https://www.divorcecare.org/healing '''Divorce Care'''] {{Dotorg}}
* This is an organization that offers divorce recovery and support services that help people heal from the pain of divorce.


[https://www.helpguide.org/articles/parenting-family/children-and-divorce.htm '''Children in Divorce'''] {{Dotorg}}
* This website provides tips to communicate with kids about divorce and ways to work with experts to help kids cope with parents’ divorce.


[https://www.womansdivorce.com/state-divorce-resources.html '''State Divorce Resource Directory'''] {{Dotcom}}
* Click the link to the directory that provides access to state-specific divorce laws and guidelines, along with divorce lawyers in the surrounding area.


[[wikipedia:Child_custody#Physical_custody|'''Forms of Domestic Violence''']] {{Dotwiki}}


[https://simple.wikipedia.org/wiki/Children%27s_rights '''Children's Rights'''] {{Dotwiki}}


[[wikipedia:Alimony#By_country|'''Alimony in Different Countries''']] {{Dotwiki}}
|}

----

=== Episode 3 &quot;The Man with the Umbrella&quot; ===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
&lt;!-- starting to add section names so that we can retrieve content from specific topics without repetition --&gt;

|-
!Episode 3:
!&quot;The Man with the Umbrella&quot; (Usan-eul Sseun Namja 우산을 쓴 남자)&lt;ref name=&quot;:0&quot; /&gt;
&lt;section begin=Physical_Violence /&gt;
|-
|Physical Violence 
|&lt;u&gt;Note&lt;/u&gt;: Physical Violence is an act that can ultimately affect anyone of any race, gender, sexual orientation, religion. Squid Game episode one sets the precedent for a multitude of physically violent acts that will continue to take place throughout the series. 


&lt;section end=Physical_Violence /&gt;
&lt;section begin=Gun_Violence /&gt;
|-
|Gun Violence
|&lt;u&gt;Note&lt;/u&gt;: Gun violence can be emotionally taxing to not just those directly affected by loss, but by even community members and those from afar. Squid Game has a multitude of depictions of gun violence throughout the show, starting from episode 1.
'''Call [[wikipedia:The_Center_to_Prevent_Youth_Violence#Speak_Up|1-866-SPEAK-UP]]''' {{Dotwiki}} to report threats of violence


[[SCCAP/Resources for Dealing with a School Shooting|'''SCCAP/Resources for Dealing with a School Shooting''']] {{Dotwiki}}

* A Wikiversity page on resources to deal with school shooting.


[https://everytownsupportfund.org/everytown-survivor-network/resources-for-victims-and-survivors-of-gun-violence/finding-help/ '''Everytown Support Fund'''] {{Dotorg}}
* The Everytown Support Fund offers basic resources and information on their website to help victims and survivors of gun violence. Please note that the resources listed are not comprehensive and there may be other resources available to you in your community.
&lt;section end=Gun_Violence /&gt;
&lt;section begin=Trauma /&gt;
|-
|Trauma
|[[Helping Give Away Psychological Science/Coping with traumatic event|'''Helping Give Away Psychological Science/Coping with traumatic event''']] {{Dotwiki}}


[[Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit2020|'''Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit 2020''']] {{Dotwiki}}


[https://www.aaets.org/trauma-information/helpful-information-during-and-after-a-traumatic-event '''Helpful Information During and After a Traumatic Event'''] {{Dotorg}}
* The American Academy of Experts in Traumatic Stress (AAETS) is made up of a committee of professionals who are dedicated to informing the public and providing resources about how to cope with trauma. In collaboration with the National Center for Crisis Management, this page provides detailed information on what to do during and after a traumatic event, including healthy ways to cope with traumatic stress.


[https://www.nctsn.org/ '''National Child Traumatic Stress Network'''] {{Dotorg}}
* The website gathers cumulative information about child trauma (definition, signs, risk factors etc.). It is updated to the latest events, including documents ‘Talking to Children About War’.
&lt;section end=Trauma /&gt;
|}

----

===Episode 4 &quot;Stick to the Team&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!Episode 4:
!&quot;Stick to the Team&quot; (''Jjollyeodo Pyeonmeokgi''쫄려도 편먹기)&lt;ref name=&quot;:0&quot; /&gt;
|-
|Food Insecurity
|[[wikipedia:Food_security|'''Food security''']] {{Dotwiki}}
* Wiki page for food security definition.


[https://www.fns.usda.gov/contacts/contact-map?f%5B0%5D=program%3A27 '''Food Distribution Programs Map (click on state for more programs)'''] {{Dotgov}}

* Provide a list of programs on food and nutrition services by state.


[https://www.fns.usda.gov/snap/supplemental-nutrition-assistance-program '''Supplemental Nutrition Assistance Program (SNAP)'''] {{Dotgov}}

* SNAP provides nutrition benefits to add to the food budget of families in need so they can buy healthy food and move towards being self-sufficient.


[https://www.fns.usda.gov/wic '''Special Supplemental Nutrition Program for Women, Infants, and Children (WIC)'''] {{Dotgov}}

* “The Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) provides federal grants to states for supplemental foods, health care referrals, and nutrition education for low-income pregnant, breastfeeding, and non-breastfeeding postpartum women, and to infants and children up to age 5 who are found to be at nutritional risk.”


[https://www.fns.usda.gov/sfmnp/senior-farmers-market-nutrition-program '''Senior Farmers' Market Nutrition Program'''] {{Dotgov}}

* This program provides low-income seniors with access to locally grown fruits, vegetables, honey and herbs. 


'''[https://uwcf.org/8-ways-to-help-people-who-are-food-insecure/ 8 Ways to Help People Who are Food Insecure] {{Dotorg}}'''

* United Way of Central Florida's tips for mutual aid and helping people who are food insecure.

|-
|Organ Trafficking
|[https://humantraffickinghotline.org/resources '''National Human Trafficking Hotline'''] {{Dotorg}}
* Instant Help Number: 1-800-373-7888 or Text: 233733
* An organization for those who have been a survivor of human trafficking to seek out support or a way to alert authorities of a potential trafficking situation. 
* It is also a useful source if you want to learn more about the signs of trafficking and the story of the victims.  


[https://en.m.wikipedia.org/wiki/United_Nations_Voluntary_Trust_Fund_for_Victims_of_Trafficking_in_Persons '''Trust Fund for Victims of Trafficking in Persons'''] {{Dotwiki}}

* Background on organ trafficking in the global context. Links to United Nations Trust Fund webpage provides the latest news on organ trafficking and fundraising events. 


[https://en.m.wikipedia.org/wiki/United_Nations_Voluntary_Trust_Fund_for_Victims_of_Trafficking_in_Persons '''United Nations Voluntary'''] {{Dotwiki}}
|-
|Mass Violence
|[https://www.ptsd.va.gov/professional/treat/type/violence_trauma_effects.asp '''The Impact of Disaster and Mass Violence Events on Mental Health'''] {{Dotgov}}
* This article from the US Department of Veterans Affairs details information about survivors’ reactions to disasters and mass violence events, and it distinguishes the pathology of PTSD (post-traumatic stress disorder) from an expected reaction to such traumas.


[https://www.samhsa.gov/find-help/disaster-distress-helpline/disaster-types/incidents-mass-violence '''Incidents of mass violence'''] {{Dotgov}}

* This article from the Substance Abuse and Mental Health Services Administration describes common reactions to incidents of mass violence and how to get help for those experiencing distress due to these events.

|-
|Memory Impairment/Illness
|[https://www.healthline.com/health/memory-loss '''Heathline article on memory loss'''] {{Dotcom}}
* Learn about causes and coping skills of memory loss.


[https://alzheimersprevention.org/alzheimers-info/memory-quiz/ '''The Alzheimer’s Research and Prevention Foundation Memory Quiz'''] {{Dotorg}}
* Visit this website for a quiz to quickly assess the degree of memory loss (*should not be considered diagnostic).


[https://www.alz.org/ '''The Alzheimer Association'''] {{Dotorg}}
* Visit this website or call 1-800-272-3900 if you need dementia services and support groups for memory loss due to Alzheimer disease.
|-
|Discrimination
|[[wikipedia:Caste_discrimination_in_the_United_States|'''Caste discrimination in the United States''']] {{Dotwiki}}

* Overview of caste discrimination and social hirearchy in the US.
[https://en.m.wikipedia.org/wiki/Economic_discrimination '''Economic Discrimination'''] {{Dotwiki}}


[https://www.eeoc.gov/laws/guidance/facts-about-racecolor-discrimination '''Workplace Racial/Color Discrimination'''] {{Dotgov}} (U.S. Equal Employment Opportunity Commission)

* In-depth facts about race/color discrimination in the workforce, gives informations about Title VII of the Civil Rights Act of 1964 (Act which protects people from being discriminated because of gender, religion, sexuality, race, or color of their skin) and includes examples of how Title VII can protect people from being discriminated in workplace settings.

[https://www.dol.gov/general/migrantworker/rights '''Migrant Worker Rights and Combating Migrant Worker Discrimination'''] {{Dotgov}}

* Resources from the U.S. Department of Labor describing the rights afforded to migrant workers. 


[https://myusf.usfca.edu/caps/self-help-resources/discrimination '''USF Discrimination and Racism Resources''']{{Dotedu}}

* List of resources compiled by the University of San Francisco. 

|-
|Relational Abuse
|'''National Dating Abuse Helpline''': 1-866-331-9474

* If you need immediate help and/or want to enquire specific information about relational abuse, you can call this hotline. There are professionals on relational abuse to help you immediately.


'''[https://kidshealth.org/en/teens/abuse.html Abusive Relationships (TeensHealth)]''' {{Dotorg}}

* This provides information on definitions/signs of abusive relationships,  tips for getting out of an abusive relationship, and how to deal with the mental and emotional struggles. 
|-
|Workplace Injury
|[https://www.wilg.org/ '''Workers’ Injury Law &amp; Advocacy Group (WILG)'''] {{Dotorg}}
* A national non-profit membership organization dedicated to help workers and their families who suffer the consequences of work-related injuries or occupational illnesses and who need expert legal assistance to obtain medical care and other relief under workers’ compensation programs.


[https://www.osha.gov/workers '''OSHA Worker Rights and Protections'''] {{Dotgov}}

* Visit website or call 1-800-321-6742 about health and safety issues at work. The website provides good information on worker’s rights such as how to file a claim and get compensated in the event of a work-related injury.


[https://www.helpadvisor.com/social-security/serious-workplace-injuries-by-state '''Workplace Injuries Report and Benefits Resource Guide'''] {{Dotcom}}

* Direct and intensive guide to workplace injury, such as benefits and compensation that a worker could receive for work-related injuries. This resource also lists out recent statistics on workplace injuries since the onset of the pandemic. 
|}
----

===Episode 5 &quot;A Fair World&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!Episode 5:              
!&quot;A Fair World&quot; (''Pyeongdeung-han Sesang'' 평등한 세상)&lt;ref name=&quot;:0&quot; /&gt;
|-
|Post Traumatic Stress Disorder (PTSD)
|[[Posttraumatic stress disorder (disorder portfolio)|'''Post-traumatic stress disorder''']] {{Dotwiki}}
* Wiki page that provides a comprehensive overview of PTSD


[https://www.ptsd.va.gov/index.asp '''National Center for PTSD'''] {{Dotgov}}

* If you are searching for governmental assistance and/or therapy for PTSD, you can visit this website or call 1-800-273-8255.


[https://www.clinical-partners.co.uk/for-adults/anxiety-disorders/ptsd/ptsd-test '''Clinical Partner online PTSD test''']

* You can take this quick online test to identify if you experience common signs of PTSD. However, this test should not be considered diagnostic, speaking with a professional is encouraged.


[https://www.helpguide.org/articles/ptsd-trauma/helping-someone-with-ptsd.htm '''Helping Someone with PTSD by HelpGuide'''] {{Dotorg}}

* This is a solid article providing tips for helping family members or friends of patients with PTSD.


[[File:Nisha_Iyer_Pediatric_post_traumatic_stress_dISORDER.pdf|780x780px|Nisha Iyer Pediatric post traumatic stress dISORDER]]

|-
|Strike
|[https://www.nlrb.gov/about-nlrb/rights-we-protect/your-rights/nlra-and-the-right-to-strike '''NLRA and the Right to Strike'''] {{Dotgov}}
* The page NLRA and the Right to Strike outlines when it is and is not illegal for workers to strike, with a translation of the page available in Spanish. This is the official site for the National Labor Relations Board, a group consisting of professionals that provide information about the laws and regulations surrounding labor in the United States. 


[https://aflcio.org/ '''The American Federation of Labor and Congress of Industrial Organizations (AFL-CIO)'''] {{Dotorg}}

* An organization that provides resources for joining or establishing a labor union. It provides information on strikes across the country and how to become involved in them. 
|-
|Rape
|'''[[wikipedia:Rape_crisis_center#Typical_services_offered|Rape Crisis Center]] {{Dotwiki}}''' 
'''[https://rainn.org/resources RAINN National Sexual Assault Hotline]'''
* Crisis support service for sexual assault and harassment in the US.

&lt;br /&gt;
[https://www.nsvrc.org/organizations '''National Sexual Violence Resource Center (NSRVC)'''] {{Dotorg}}

* This website offers an easy-to-navigate directory of resources for victims of sexual violence, providing support organizations that can be filtered by organization type or location.

|-
|Incontinence 
|Note: Incontinence is a symptom of advanced Alzheimer’s.


[https://www.nia.nih.gov/health/urinary-incontinence-older-adults '''Urinary Incontinence in Older Adults (National Institute on Aging)'''] {{Dotgov}}
* Article about types of incontinence in older adults and medical treatments.


[https://nafc.org/ '''National Association for Continence'''] {{Dotorg}}

* An organization that provides resources for elderly adults with incontinence and information about the medical conditions that involve incontinence.


[https://www.alz.org/ '''Alzheimer’s Association'''] {{Dotorg}}

* Visit this website or call 1-800-272-3900 for online support groups and resources for diagnosing and treating Alzheimer’s disease.
|}
----

===Episode 6 &quot;Gganbu&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!Episode 6: 
!&quot;Gganbu&quot; (''Kkanbu'' 깐부)&lt;ref name=&quot;:0&quot; /&gt;
|-
|Acculturation Problems
|[[wikipedia:Acculturation|'''What is acculturation?''']] {{Dotwiki}}
* Wiki page on acculturation definition.


[[wikipedia:Interactive_acculturation|'''Interactive acculturation''']] {{Dotwiki}}
* Wiki page on interactive acculturation.


[https://www.joymental.com/therapy-for-acculturation/ '''Joy Mental Fitness'''] {{Dotcom}}

* A therapy site provides information about the definition, categories, and symptoms of acculturation. You can also schedule a teletherapy for acculturation in the website
|-
|Witnessing a Crime
|[https://victimconnect.org/learn/types-of-crime/homicide-and-grief/ '''Victim Connect Resource Center'''] {{Dotorg}}
* Visit the website or call 1-855-4-VICTIM (1-855-484-2846)
* This is a nonprofit organization dedicated to looking out for victims’ rights and aiding witnesses of victims. 
* This page outlines a comprehensive list of ways to address grief and organizations to reach out to after a homicide.


[https://www.compassionatefriends.org/find-support/online-communities/private-facebook-groups/ '''Private Facebook Groups - Compassionate Friends'''] {{Dotorg}}

* A list of private Facebook groups offered by Compassionate Friends, where bereaved people (especially parents, siblings, friends) can find support.
|}
----

===Episode 7 &quot;VIPS&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!Episode 7:
!&quot;VIPS&quot;&lt;ref name=&quot;:0&quot; /&gt;
|-
|Suicide
|'''[https://988lifeline.org/ National Suicide Prevention Lifeline]: Call 1-800-273-8255''' {{Dotorg}}
* This is a national network of local crisis centers that provides 24/7 and free online support.


'''[https://www.crisistextline.org/ Crisis Textline]''' {{Dotorg}}
* Text HOME to 741741
* Connects people who need online counseling with a crisis counselor.


'''Call 911'''

See above (Ep 2: Suicide)


[[File:Warning_Signs_for_Suicidal_Ideation_Infographic_(1).pdf|550x550px|Warning Signs for Suicidal Ideation Infographic (1)]]
|-
|Anxiety/Fear
|[https://www.nimh.nih.gov/health/topics/anxiety-disorders '''Anxiety Disorders on the Nation Institute of Mental Health'''] {{Dotgov}}
* This page provides a brief introduction, symptoms, and treatments, together with comprehensive resources and brochures about Anxiety Disorders.


[https://www.samhsa.gov/find-help/national-helpline '''SAMHSA’s National Helpline'''] {{Dotgov}}

* Anxiety Helpline: 1-800-662-HELP (4357) (in English and Spanish)
* SAMHSA’s National Helpline for anxiety, substance use, and other mental health disorders is a 24/7 confidential resource for individuals facing anxiety and fear. SAMHSA provides callers with access to treatment, support groups, and local organizations for easy-access.
* Note: The helpline does not provide counseling, it is mainly an information center that can transfer people to appropriate state or local services.


[https://www.samhsa.gov/find-help/national-helpline/help4u '''435748 (HELP4U) – Treatment Referrals via Text Message | SAMHSA'''] {{Dotgov}}

* Text your 5-digit ZIP Code to 435748 (HELP4U) (only in English). Reply STOP to cancel or HELP to reach an information specialist.
* This is a text option provided by the SAMHSA’s national helpline

|-
|Sexual Harassment/Assault
|'''National Sexual Assault Hotline: Call 1-800-656-4673'''
* If you need immediate help for sexual assault/rape attempt, please call 1-800-656-4673.


[https://www.med.unc.edu/beacon/get-help/sexual-assault-resources/ '''RAINN (Rape, Abuse, and Incest National Network)'''] {{Dotedu}}

* The nation’s largest anti-sexual violence organization. 
* The organization works with local sexual assault service providers and carries out programs to prevent sexual violence, help victims, and ensure that perpetrators are brought to justice.


[https://www.nsvrc.org/ '''National Sexual Violence Resource Center (NSVRC)'''] {{Dotorg}}

* The NSVRC’s Mission is to provide leadership in preventing and responding to sexual violence through collaboration, sharing and creating resources, and promoting research.


[https://www.endthebacklog.org/backlog/what-rape-kit-backlog '''End the Backlog'''] {{Dotorg}}

* An article by End the Backlog that discusses the Rapekit backlog in addition to providing education on what rapekits are, how to report a rape, and to get involved in the organization.
|-
|Workplace Sexual Harassment/Assault
|[https://iwpr.org/iwpr-publications/briefing-paper/sexual-harassment-and-assault-at-work-understanding-the-costs/ '''Sexual Harassment and Assault At Work by Institute for Women’s Policy Research'''] {{Dotorg}}
* This article is an overview about what qualifies as sexual harassment, when it occurs in the workplace, and what to do when it occurs. 


[https://www.eeoc.gov/harassment '''The US Equal Employment Opportunity Commission (EEOC)'''] {{Dotgov}}
* This page contains the legal definition of harassment and explains what groups are included as protected against harassment under the law. 
* Call 1-800-669-4000 to report an incident of workplace harassment


[https://projectwhen.org/resources/ '''Resources to Fight Harassment in the Workplace by Project WHEN'''] {{Dotorg}}

* This article offers resources for both employers and employees on the topics of workplace harassment, including sexual harassment. 
* You can also find information on how to prevent and report harassment.

|}
----

=== Episode 8 &quot;Front Man&quot; ===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
&lt;!-- starting to add section names so that we can retrieve content from specific topics without repetition --&gt;

|-
!Episode 8:
!&quot;Front Man&quot; (Peuronteumaen 프론트맨)&lt;ref name=&quot;:0&quot; /&gt;
&lt;section begin=Physical_Violence /&gt;
|-
|Physical Violence 
|&lt;u&gt;Note&lt;/u&gt;: Physical Violence is an act that can ultimately affect anyone of any race, gender, sexual orientation, religion. Squid Game episode one sets the precedent for a multitude of physically violent acts that will continue to take place throughout the series. 


&lt;section end=Physical_Violence /&gt;
&lt;section begin=Gun_Violence /&gt;
|-
|Gun Violence
|&lt;u&gt;Note&lt;/u&gt;: Gun violence can be emotionally taxing to not just those directly affected by loss, but by even community members and those from afar. Squid Game has a multitude of depictions of gun violence throughout the show, starting from episode 1.
'''Call [[wikipedia:The_Center_to_Prevent_Youth_Violence#Speak_Up|1-866-SPEAK-UP]]'''{{Dotwiki}} to report threats of violence


[[SCCAP/Resources for Dealing with a School Shooting|'''SCCAP/Resources for Dealing with a School Shooting''']] {{Dotwiki}}

* A Wikiversity page on resources to deal with school shooting.


[https://everytownsupportfund.org/everytown-survivor-network/resources-for-victims-and-survivors-of-gun-violence/finding-help/ '''Everytown Support Fund'''] {{Dotorg}}
* The Everytown Support Fund offers basic resources and information on their website to help victims and survivors of gun violence. Please note that the resources listed are not comprehensive and there may be other resources available to you in your community.
&lt;section end=Gun_Violence /&gt;
&lt;section begin=Trauma /&gt;
|-
|Trauma
|[[Helping Give Away Psychological Science/Coping with traumatic event|'''Helping Give Away Psychological Science/Coping with traumatic event''']] {{Dotwiki}}


[[Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit2020|'''Helping Give Away Psychological Science/draft:Coping with traumatic events Beruit 2020''']] {{Dotwiki}}


[https://www.aaets.org/trauma-information/helpful-information-during-and-after-a-traumatic-event '''Helpful Information During and After a Traumatic Event'''] {{Dotorg}}
* The American Academy of Experts in Traumatic Stress (AAETS) is made up of a committee of professionals who are dedicated to informing the public and providing resources about how to cope with trauma. In collaboration with the National Center for Crisis Management, this page provides detailed information on what to do during and after a traumatic event, including healthy ways to cope with traumatic stress.


[https://www.nctsn.org/ '''National Child Traumatic Stress Network'''] {{Dotorg}}
* The website gathers cumulative information about child trauma (definition, signs, risk factors etc.). It is updated to the latest events, including documents ‘Talking to Children About War’.
&lt;section end=Trauma /&gt;
|}

----

===Episode 9 &quot;One Lucky Day&quot;===
{| class=&quot;wikitable sortable mw-collapsible mw-collapsed&quot;
|-
!Episode 9:
!&quot;One Lucky Day&quot; (''Unsu Joeun Nal'' 운수 좋은 날)&lt;ref name=&quot;:0&quot; /&gt;
|-
|Loss of a Friend
|[https://www.healthline.com/health/mental-health/disenfranchised-grief '''Disenfranchised Grief: When No One Seems to Understand Your Loss by Healthline'''][[File:HSPolitic.svg|thumb|21x21px]] {{Dotcom}}
* An article focusing specifically on dealing with bereavement of a close friend.


[https://newsinhealth.nih.gov/2017/10/coping-grief '''Coping With Grief by News In Health'''] {{Dotgov}}

* This article discussed methods to relieve complicated griefs triggered by bereavement. 
* It pointed out the importance of a customized therapy system targeting the complicated grief. 
* Meanwhile, the article encourages addressing the ‘prospect of death before the loss happens’.


'''7 Cups website on coping with grief'''

* 7 Cups website is the world's largest emotional support system
* [https://www.7cups.com/qa-grief-33/ Q &amp; A page for grief] {{Dotcom}}
* [https://www.7cups.com/qa-grief-33/how-do-you-or-have-you-gotten-past-losing-your-best-friend-from-childhood-2934/ Q &amp; A page for “How do you (or have you) gotten past losing your best friend from childhood?”] {{Dotcom}}
|-
|Loss of a Family Member (For Children)
|[https://childrengrieve.org/ '''National Alliance for Children’s Grief'''] {{Dotorg}}
* This is a nonprofit organization whose goal is to raise awareness for children and adolescents who are grieving the death of a loved one while also informing a wider audience about these issues and providing resources to help them.


[https://www.dougy.org/resources/audience/kids?how=&amp;who=&amp;type=activities&amp;age= '''Dougy Center: Grief Resources for Kids'''] {{Dotorg}}

* This organization utilizes a humanistic approach to understand and support children who are grieving a loved one. 
* This specific page on their website provides several worksheets with engaging activities for kids to organize their thoughts and emotions towards grief.


[https://sesamestreetincommunities.org/topics/grief/ '''Helping Kids Grieves (Sesame Street in Communities)'''] {{Dotorg}}

* This resource provides several articles, activities, worksheets and videos for kids to use when grieving.
|-
|Loss of a Family Member (For Adults)
|[https://www.hospiceandcommunitycare.org/grief-and-loss/grief-links/ '''Grief Resources by Hospice &amp; Community Care'''] {{Dotorg}}
* This webpage compiles a long list of videos, readings, caregiving suggestions, and general information about grief for adults and teens.


[https://www.aftertalk.com/ '''After Talk'''] {{Dotcom}}

* Online platform where people can write messages to their lost ones to ease the silence of the loss. 
* “It is a place of Comfort, Sharing and Insight for those who have experienced loss or are supporting a Loved One in Hospice Care.”
|-
|Loss of a Family Member (For Widows/Widowers)
|[https://nationalwidowers.org/ '''National Widowers Organization'''] {{Dotorg}}
* This organization provides several resources and virtual support groups for men who are grieving. 
* This website also provides a peer support program to connect with others who are going through similar experiences.


[https://widowedparent.org/ '''Widowed Parents'''] {{Dotorg}}

* This website provides support for widowed parents and children who are experiencing the loss of a loved one. 
* This resource also compiled several virtual and in-person support groups to connect with others.
|-
|Depression
|[https://www.psychiatry.org/patients-families/depression/what-is-depression '''American Psychiatric Association, What is Depression?'''] {{Dotorg}}
* A page from the website for the American Psychiatric Association that provides detailed information about the symptoms of depression.


[https://screening.mhanational.org/screening-tools/depression/ '''Mental Health America’s online test on depression'''] {{Dotorg}}

* A quick online test that helps people better understand their mental situations
* Unofficial test that cannot constitute a diagnosis.


[https://www.healthline.com/health/depression/intervention '''Healtline article on depression intervention: What to Do and What Not to Do'''] {{Dotcom}}


[https://suicidepreventionlifeline.org/ '''National Suicide Prevention Lifeline: 1-800-273-8255'''] {{Dotorg}}
* A national network of local crisis centers; they provide 24/7 and free online support and handle all situations related to suicide and emotional distress.


[https://www.nami.org/home '''National Alliance on Mental Health (NAMH)'''] {{Dotorg}}

* A nationwide mental health organization with affiliates narrowed down to towns. They provide mental health education programs and a help line; useful for people seeking mental health resources.

|-
|Homelessness/Destitution
|'''2-1-1 hotline (Call 2-1-1)'''
* Many states across the US have hotlines for individuals to call 2-1-1 if they are homeless or about to become homeless. 
* Trained staff will help callers find shelter and other resources.


[https://endhomelessness.org/how-to-get-help-experiencing-homelssness/ '''National Alliance to End Homelessness'''] {{Dotorg}}
* This website provides phone numbers and other resources for people to access shelter/housing services, health care, and food if they are experiencing or at risk of experiencing homelessness.


[https://www.hudexchange.info/housing-and-homeless-assistance/ '''HUD Exchange''']
* HUD Exchange is a website run by the US Department of Housing and Urban Development that provides information and access to housing, food, health and safety resources, and job training for people experiencing or at risk for homelessness.
|}
----

== '''Season 2''' ==
Netflix has renewed the series for a second season, with no official release date yet. It is anticipated to release in late 2023 or early 2024.&lt;ref&gt;{{Cite web|url=https://www.tvguide.com/news/squid-game-season-2-release-date-cast-and-everything-to-know/|title=Everything We Know So Far About Squid Game Season 2|website=TVGuide.com|language=en|access-date=2022-12-26}}&lt;/ref&gt; 

=='''Accessing Mental Health Support''' ==
If you are struggling with your mental health, please do not hesitate to seek help. Below are some resources to help you find professional mental health support.

=== Free Self Assessment ===
Helping Give Away Psychological Science ([https://HGAPS.org HGAPS.org]){{Dotorg}} has made free online assessments you can use to check your anxiety, mood, or other concerns and get a free, confidential report and suggestions about where to do for more information or support. These combine some of the best of the free tools to let you check about some of the most common issues with one click. There are versions for teens, college students, and older adults [https://www.hgaps.org/ac.html here]. If you've ever wondered whether focus struggles or restlessness might point to ADHD, you can also take a free ADHD self-assessment [https://adhddegree.co.uk here] to explore whether attention difficulties could be part of the picture.  

Another free online assessments available at [https://missionconnectionhealthcare.com/self-assessments/ Mission Connection Healthcare]. 

=== Ways to Find a Therapist ===
There are many different places to look for support. Below we provide some tips about places to look for a therapist, such as a psychologist, counselor, or other mental-health professional. We focus on ones that are from large organizations (increasing the chances that you may find someone near you, or who better matches what you hope to find in a provider), as well as not charging you to search them. It has become more possible and more common to do therapy by video (&quot;teletherapy&quot;). The rules about teletherapy are changing rapidly. If you want to read more about options with teletherapy, a detailed guide is [[Helping Give Away Psychological Science/Telepsychology Guide for Patients|here]]. 
{| class=&quot;wikitable sortable mw-collapsible&quot;
|-
!Resource
!Description
|-
|[https://locator.apa.org/ '''APA Psychologist Finder'''] {{Dotorg}}
|This service provided by the American Psychological Association (APA) allows you to search for Psychologists in your area. You can also search for a Psychologist by their name or the name of their practice. Your search may yield: 
-the names of local Psychologists

-whether or not they accept insurance as well as which types

-whether or not they are currently accepting new patients

-whether or not Telehealth is available

-the address of their practice
|-
|[https://www.psychologytoday.com/us/psychiatrists '''Psychology Today Psychiatrist Finder'''] {{Dotcom}}
|By typing in your zip code, you can search for psychiatrists in your area using Psychiatrist Finder. The search results will provide a list of psychiatrists and their phone number or website to contact.
|-
|[https://www.findcbt.org/FAT/ '''Find a CBT Specialist'''] {{Dotorg}}
|This ABCT Find-a-Therapist service gives you access to cognitive and behavioral therapists based on your zip code and selected filters.

* The goal of cognitive behavioral therapy is to recognize and change unhealthy patterns in thinking and behavior so develop personal strategies to deal with mental health difficulties.
|-
|[https://www.psychologytoday.com/us/therapists/psychodynamic '''Find a Psychodynamic Specialist'''] {{Dotcom}}
|You can find psychodynamic therapists in your area through Psychology Today's service by searching with your city or zip code.

* Psychodynamic therapy focuses on the unconscious to understand the root of the psychology distress.
|-
|[https://www.psychologytoday.com/us/therapists/humanistic '''Find a Humanistic Specialist'''] {{Dotcom}}
|Humanistic therapists in your city or area code can be easily found using this humanistic specialist finder.

* Humanistic specialists emphasizes developing a strong and healthy sense of self, your true feelings, and meaning to lead your most fulfilling life
|}

=='''Who Can Help Me?''' ==
When seeking mental health support, you may be overwhelmed by the numerous types of mental health professionals you can seek help from. Below are summaries of the primary types of professionals that may be offering mental health services in your area. Please note that availability, finances, or other factors may impact which professionals you can receive support from. 
{| class=&quot;wikitable sortable mw-collapsible&quot;
|-
!Title
!Description
|-
|Clinical Social Worker
|
* Focus on the assessment, diagnosis, treatment, and prevention of mental illnesses and emotional distress
* Licensed or certified at the clinical level in the state of practice
* Work in areas like private practices, hospitals, community mental health, primary care, and agencies
* Advocate for client rights and strong therapeutic connection between client and practitioner
|-
|Mental Health Counselor
|
* Assesses and treats mental and emotional health disorders, relationship issues, and life difficulties
* Provide support and guidance and offer coping strategies for the patient
* License: Must have earned a LMHC (Licensed Mental Health Counselor), LMSW (Licensed Master Social Worker), or LPC (Licensed Professional Counselor)
|-
|Psychologist (Clinical or Counseling)
|
* Assess and treat mental, emotional, and behavioral disorders through observation, interviews, and psychological tests
* License: Must have received a doctoral degree in psychology; requirements vary by state of practice
|-
|Psychiatric Nurse Practitioner
|
* Specially trained nurses that work in the mental health field
* Assess and diagnoses patients, study their medical history, and perform comprehensive mental health tests
* License: Must pass the PMHNP (Psychiatric-Mental Health Nurse Practitioner) board certification exam to obtain the PMHNP license
|-
|Psychiatrist
|
* Medical doctors who specializes in mental health
* Assess, diagnose, and treat mental, emotional, and behavioral disorders
* License: Must be board-certified by the American Board of Psychiatry and Neurology (ABPN). Must be licensed as an MD (Doctor of Medicine) or OD (Optometrist) by the state in which they practice
|}
[[File:Preparing for Your Telepsychology Session Infographic.pdf|alt=Tips for a client getting ready for a telepsychology session|thumb|Tips for your telepsychology session]]


[[File:Is_Telepsychology_Right_for_Your_Clients%3F_Infographic.pdf|750x750px|Is Telepsychology Right for Your Clients? Infographic]]

== See Also ==
&lt;!-- categories below --&gt;
This project was supported by a [[m:Rapid Grant|Rapid Grant]] from the Wikimedia Foundation. The funded proposal is [[m:Grants:Project/Rapid/Hkim243/Promoting dissemination of cross-cultural mental health resources using Squid Game|here]].  
[[Category:HGAPS Numbered Projects]]</text>
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      <text bytes="108592" sha1="3n0qipjujiaotquikpat1t8myr4bml7" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|June 2023 - June 2025}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. A typical galaxy such as ours is a hollow [[w:3-sphere|4-dimensional 3-sphere]] with these objects distributed on its 3-dimensional surface. The black hole at the galaxy's center is nothing: the 4-ball of empty space they surround. Objects in our galaxy occupy this thin 3-dimensional surface, forming a filmy 4-dimensional soap-bubble of galactic size, thicker than an atom only in the interior of stars. Mass is confined to this 3-dimensional manifold by its inertia, also called gravity, the property of its ceaseless motion at a constant, universal velocity &lt;math&gt;c&lt;/math&gt;, the rate of causality at which the universe evolves. Atoms are always internally in inertial rotational motion, and externally in inertial translational motion through 4-space, at this universal rate of transformation. The observed universe appears to be a 3-sphere expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light through 3-space as measured by all observers. All objects with mass move through 4-space at velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c^\prime = 2c&lt;/math&gt;, so we can see in 4 dimensions, even though we are physically confined to a moving 3-dimensional manifold, where our direction of motion through 4-space is our proper time dimension. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at velocity &lt;math&gt;c&lt;/math&gt;. This model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries.&lt;/blockquote&gt;

== Symmetries ==
It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway|Burgiel|Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter group]] theory did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups and obey the principle of relativity. As I understand Coxeter theory (which is not mathematically),{{Efn|Coxeter's formulation of the motions (congruent transformations) possible in an ''n''-dimensional Euclidean space:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let Q denote a rotation, R a reflection, T a translation, and let Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T denote a product of several such transformations, all commutative with one another. Then RT is a glide-reflection (in two or three dimensions), QR is a rotary-reflection, QT is a screw-displacement, and Q&lt;sup&gt;2&lt;/sup&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
{{spaces|10}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt;&lt;br&gt;
where 2''q'' + ''r'' ≤ ''n'', the number of dimensions.&lt;br&gt;
Transformations involving a translation are expressible as:&lt;br&gt;
{{spaces|10}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T&lt;br&gt;
where 2''q'' + ''r'' + 1 ≤ ''n''.&lt;br&gt;
For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q&lt;sup&gt;2&lt;/sup&gt;, or a screw-displacement QT (where the rotation component Q is a simple rotation). Every enantiomorphous transformation in 4-space (reversing chirality) is a QRT.&lt;/blockquote&gt;
If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a Q&lt;sup&gt;2&lt;/sup&gt; or a QT, because we can view any QT as a Q&lt;sup&gt;2&lt;/sup&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q&lt;sup&gt;2&lt;/sup&gt;. By the same principle, we can view any QT or Q&lt;sup&gt;2&lt;/sup&gt; as an isoclinic (equi-angled) Q&lt;sup&gt;2&lt;/sup&gt; by appropriate choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]]. The distinct symmetry groups of the regular polytopes each correspond to their characteristic isoclinic rotations. These isoclinic rotations are distinguished in geometry, relativity, and quantum mechanics.|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to relativity, in that we can only exchange the translation (T) for ''one'' of the two rotations (Q). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation up to uncertainty, and can always distinguish the direction of his own proper time arrow.|name=transformations}} the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic rather than algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional objects, and nature can be understood in terms of their [[W:group action|group actions]], including centrally [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]].

== Special relativity describes Euclidean 4-dimensional space ==
&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.{{Sfn|Goldberg|2013|loc=§10. Hidden Symmetries: Why some symmetries but not others?|p=264}}&lt;/blockquote&gt;

...cite Yamashita{{Sfn|Yamashita|2023}}

=== Minkowski spacetime and Euclidean 4-space in relativity ===
...

Is there a configuration in Euclidean space where every observer, and every observed object, is moving at velocity &lt;math&gt;c&lt;/math&gt;? Yes, there is one such configuration, in 4-dimensional Euclidean space. This configuration must be like the one described above, in our ''Abstract''.

== The rate of atomic symmetry operations ==
...

== General relativity describes a curved 3-dimensional manifold embedded in Euclidean 4-dimensional space ==
...

== The geometry of the atomic nucleus ==

In [[W:Euclidean 4-space|Euclidean four dimensional space]], an [[W:atomic nucleus|atomic nucleus]] is a one or more concentric 4-polytopes of increasing radius. Each concentric shell is a single or compound [[24-cell]], the regular 4-polytope with [[W:Coxeter group#Symmetry groups of regular polytopes|𝔽&lt;sub&gt;4&lt;/sub&gt; symmetry]]. Nuclear shells are concentric [[W:3-sphere|3-sphere]]s occupied (fully or partially) by the orbits of this 24-point [[#The 6 regular convex 4-polytopes|regular convex 4-polytope]]. An actual atomic nucleus is a rotating four dimensional object. It is not a ''rigid'' rotating object, it is a kinematic one, because the nucleus of an actual atom of a distinct [[W:nucleon number|nucleon number]] contains a distinct number of orbiting 24-cell vertices which may be in different isoclinic rotational orbits. These moving vertices never describe a compound of static 24-cells at any single instant in time, though their orbits do all the time. The physical configuration of a nucleus as concentric 24-cells can be reduced to the [[W:kinematics|kinematics]] of the orbits of its constituent protons and neutrons. The geometry of the atomic nucleus is therefore strictly [[W:Euclidean geometry#19th century|Euclidean]] in four dimensional space.

=== Rotations ===
The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out.

This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a precise [[24-cell|detailed description]] enabling the reader to properly visualize it runs to many pages and illustrations, with many accompanying pages of explanatory notes on basic phenomena that arise only in 4-dimensional space: [[24-cell#Squares|completely orthogonal planes]], [[24-cell#Hexagons|Clifford parallelism]] and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Helical hexagrams and their isoclines|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a surprise. [[#The 6 regular convex 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120, and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (generally), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It is much harder for us to visualize, because the only way we can experience it is in our imaginations; we have no body of sensory experience in 4-dimensional space to draw upon.

For that reason, descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than a single rigid 24-cell. 

To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with any other at any time.

That is still an example of a rigid object in a single distinct isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing the characteristic rotation of the 24-cell. But we can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same shell without collisions? In adjacent shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore questions of this kind of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[W:kinetics|kinetics]].

=== Isospin ===
A [[W:Nucleon|nucleon]] is a [[W:proton|proton]] or a [[W:neutron|neutron]]. The proton carries a positive net [[W:Electric charge|charge]], and the neutron carries a zero net charge. The proton's [[W:Mass|mass]] is only about 0.13% less than the neutron's, and since they are observed to be identical in other respects, they can be viewed as two states of the same nucleon, together forming an isospin doublet ({{nowrap|''I'' {{=}} {{sfrac|1|2}}}}). In isospin space, neutrons can be transformed into protons and conversely by actions of the [[W:SU(2)|SU(2)]] symmetry group. In nature, protons are very stable (the most stable particle known); a proton and a neutron are a stable nuclide; but free neutrons decay into protons in about 10 or 15 seconds.

According to the [[W:Noether theorem|Noether theorem]], [[W:Isospin|isospin]] is conserved with respect to the [[W:strong interaction|strong interaction]].&lt;ref name=Griffiths2008&gt;{{cite book |author=Griffiths, David J. |title=Introduction to Elementary Particles |edition=2nd revised |publisher=WILEY-VCH |year=2008 |isbn=978-3-527-40601-2}}&lt;/ref&gt;{{rp|129–130}} Nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space.

Isospin was introduced as a concept in 1932 by [[W:Werner Heisenberg|Werner Heisenberg]],&lt;ref&gt;
{{cite journal
 |last=Heisenberg |first=W. |author-link=W:Werner Heisenberg
 |year=1932
 |title=Über den Bau der Atomkerne
 |journal=[[W:Zeitschrift für Physik|Zeitschrift für Physik]]
 |volume=77 |issue=1–2 |pages=1–11
 |doi=10.1007/BF01342433
 |bibcode = 1932ZPhy...77....1H
 |s2cid=186218053
 |language=de}}&lt;/ref&gt; well before the 1960s development of the [[W:quark model|quark model]], to explain the symmetry of the proton and the then newly discovered neutron. Heisenberg introduced the concept of another conserved quantity that would cause the proton to turn into a neutron and vice versa. In 1937, [[W:Eugene Wigner|Eugene Wigner]] introduced the term &quot;isospin&quot; to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.&lt;ref&gt;
{{cite journal
 |last=Wigner |first=E. |author-link=W:Eugene Wigner
 |year=1937
 |title=On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei
 |journal=[[W:Physical Review|Physical Review]]
 |volume=51
 |pages=106–119
 |doi=10.1103/PhysRev.51.106
 |bibcode = 1937PhRv...51..106W
 |issue=2
}}&lt;/ref&gt; Similar to a spin-1/2 particle, which has two states, protons and neutrons were said to be of isospin 1/2. The proton and neutron were then associated with different isospin projections ''I''&lt;sub&gt;3&lt;/sub&gt;&amp;nbsp;=&amp;nbsp;+1/2 and −1/2 respectively.

Isospin is a different kind of rotation entirely than the ordinary spin which objects undergo when they rotate in three-dimensional space. Isospin does not correspond to a [[W:Rotations in 4-dimensional Euclidean space#Simple rotations|simple rotation]] in any space (of any number of dimensions). However, it does seem to correspond exactly to an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]] in a Euclidean space of four dimensions. Isospin space resembles the [[W:3-sphere|3-sphere]], the [[W:Elliptical space#Elliptic space (the 3D case)|curved 3-dimensional space]] that is the surface of a [[W:4-ball (mathematics)#In Euclidean space|4-dimensional ball]].

=== Spinors ===
[[File:Spinor on the circle.png|thumb|upright=1.5|A spinor visualized as a vector pointing along the [[W:Möbius band|Möbius band]], exhibiting a sign inversion when the circle (the &quot;physical system&quot;) is continuously rotated through a full turn of 360°.]][[W:Spinors|Spinors]] are [[W:representation of a Lie group|representations]] of a [[W:spin group|spin group]], which are [[W:Double covering group|double cover]]s of the [[W:special orthogonal group|special orthogonal groups]]. The spin group Spin(4) is the double cover of [[W:SO(4)|SO(4)]], the group of rotations in 4-dimensional Euclidean space. [[600-cell#Fibrations of isocline polygrams|Isoclines]], the helical geodesic paths followed by points under isoclinic rotation, correspond to spinors representing Spin(4).

Spinors can be viewed as the &quot;square roots&quot; of [[W:Section (fiber bundle)|cross sections]] of [[W:vector bundle|vector bundle]]s; in this correspondence, a fiber bundle of isoclines (of a distinct isoclinic rotation) is a cross section (inverse bundle) of a fibration of great circles (in the invariant planes of that rotation).

A spinor can be visualized as a moving vector on a Möbius strip which transforms to its negative when continuously rotated through 360°, just as [[24-cell#Helical hexagrams and their isoclines|an isocline can be visualized as a Möbius strip]] winding twice around the 3-sphere, during which [[24-cell#Isoclinic rotations|720° isoclinic rotation]] the rigid 4-polytope turns itself inside-out twice.{{Sfn|Goucher|2019|loc=Spin Groups}} Under isoclinic rotation, a rigid 4-polytope is an isospin-1/2 object with two states.

=== Isoclinic rotations in the nucleus ===
Isospin is regarded as a symmetry of the strong interaction under the [[W:Group action (mathematics)|action]] of the [[W:Lie group|Lie group]] [[W:SU(2)|SU(2)]], the two [[W:eigenstate|states]] being the [[W:Up quark|up flavour]] and [[W:Down quark|down flavour]]. A 360° isoclinic rotation of a rigid [[W:nuclide|nuclide]] would transform its protons into neutrons and vice versa, exchanging the up and down flavours of their constituent [[W:quarks|quarks]], by turning the nuclide and all its parts inside-out (or perhaps we should say upside-down). Because we never observe this, we know that the nucleus is not a ''rigid'' polytope undergoing isoclinic rotation.

If the nucleus ''were'' a rigid object, nuclides that were isospin-rotated 360° would be isoclinic mirror images of each other, isospin +1/2 and isospin −1/2 states of the whole nucleus. We don't see whole nuclides rotating as a rigid object, but considering what would happen if they ''were'' rigid tells us something about the geometry we must expect inside the nucleons. One way that an isospin-rotated neutron could become a proton would be if the up quark and down quark were a left and right mirror-image pair of the same object; exchanging them in place would turn each down-down-up neutron into an up-up-down proton. But the case cannot be quite that simple, because the up quark and the down quark are not mirror-images of the same object: they have very different mass and other incongruities.

Another way an isospin-rotated neutron could be a proton would be if the up and down quarks were asymmetrical kinematic polytopes (not indirectly congruent mirror-images, and not rigid polytopes), rotating within the nucleus in different ''hybrid'' orbits. By that we mean that they may have vertices orbiting in rotations characteristic of more than one 4-polytope, so they may change shape as they rotate. In that case their composites (protons and neutrons) could have a symmetry not manifest in their components, but emerging from their combination.

....

=== Hybrid isoclinic rotations ===
The 24-cell has [[24-cell#Isoclinic rotations|its own characteristic isoclinic rotations]] in 4 Clifford parallel hexagonal planes (each intersecting 6 vertices), and also inherits the [[16-cell#Rotations|characteristic isoclinic rotations of its 3 Clifford parallel constituent 16-cells]] in 6 Clifford parallel square planes (each intersecting 4 vertices). The twisted circular paths followed by vertices in these two different kinds of rotation have entirely different geometries. Vertices rotating in hexagonal invariant planes follow [[24-cell#Helical hexagrams and their isoclines|helical geodesic curves whose chords form hexagrams]], and vertices rotating in square invariant planes follow [[24-cell#Helical octagrams and their isoclines|helical geodesic curves whose chords form octagrams]].

In a rigid isoclinic rotation, ''all'' the [[24-cell#Geodesics|great circle polygons]] move, in any kind of rotation. What distinguishes the hexagonal and square isoclinic rotations is the invariant planes of rotation the vertices stay in. The rotation described [[#Rotations|above]] (of 8 vertices rotating in 4 Clifford parallel hexagonal planes) is a single hexagonal isoclinic rotation, not a kinematic or hybrid rotation.

A ''kinematic'' isoclinic rotation in the 24-cell is any subset of the 24 vertices rotating through the same angle in the same time, but independently with respect to the choice of a Clifford parallel set of invariant planes of rotation and the chirality (left or right) of the rotation. A ''hybrid'' isoclinic rotation combines moving vertices from different kinds of isoclinic rotations, characteristic of different regular 4-polytopes. For example, if at least one vertex rotates in a square plane and at least one vertex rotates in a hexagonal plane, the kinematic rotation is a hybrid rotation, combining rotations characteristic of the 16-cell and characteristic of the 24-cell.

As an example of the simplest hybrid isoclinic rotation, consider a 24-cell vertex rotating in a square plane, and a second vertex, initially one 24-cell edge-length distant, rotating in a hexagonal plane. Rotating isoclinically at the same rate, the two moving vertices will never collide where their paths intersect, so this is a ''valid'' hybrid rotation.

To understand hybrid rotations in the 24-cell more generally, visualize the relationship between great squares and great hexagons. The [[24-cell#Squares|18 great squares]] occur as three sets of 6 orthogonal great squares,{{Efn|name=six orthogonal planes of the Cartesian basis}} each [[16-cell#Coordinates|forming a 16-cell]]. The three 16-cells are completely disjoint{{Efn|name=completely disjoint}} and [[24-cell#Clifford parallel polytopes|Clifford parallel]]: each has its own 8 vertices (on 4 orthogonal axes) and its own 24 edges (of length {{radic|2}}).{{Efn|name=three isoclinic 16-cells}} The 18 square great circles are crossed by 16 hexagonal great circles; each [[24-cell#Hexagons|hexagon]] has one axis (2 vertices) in each 16-cell.{{Efn|name=non-orthogonal hexagons}} The two [[24-cell#Triangles|great triangles]] inscribed in each great hexagon (occupying its alternate vertices, with edges that are its {{radic|3}} chords) have one vertex in each 16-cell. Thus ''each great triangle is a ring linking three completely disjoint great squares, one from each of the three completely disjoint 16-cells''.{{Efn|There are four different ways (four different ''fibrations'' of the 24-cell) in which the 8 vertices of the 16-cells correspond by being triangles of vertices {{radic|3}} apart: there are 32 distinct linking triangles. Each ''pair'' of 16-cells forms a tesseract (8-cell).{{Efn|name=three 16-cells form three tesseracts}} Each great triangle has one {{radic|3}} edge in each tesseract, so it is also a ring linking the three tesseracts.|name=great linking triangles}} Isoclinic rotations take the elements of the 4-polytope to congruent [[24-cell#Clifford parallel polytopes|Clifford parallel elements]] elsewhere in the 4-polytope. The square rotations do this ''locally'', confined within each 16-cell: for example, they take great squares to other great squares within the same 16-cell. The hexagonal rotations act ''globally'' within the entire 24-cell: for example, they take great squares to other great squares in ''different'' 16-cells. The [[16-cell#Helical construction|chords of the square rotations]] bind the 16-cells together internally, and the [[24-cell#Helical hexagrams and their isoclines|chords of the hexagonal rotations]] bind the three 16-cells together.

....

=== Color ===
When the existence of quarks was suspected in 1964, [[W:Oscar W. Greenberg|Greenberg]] introduced the notion of color charge to explain how quarks could coexist inside some [[W:hadron|hadron]]s in [[W:quark model#The discovery of color|otherwise identical quantum states]] without violating the [[W:Pauli exclusion principle|Pauli exclusion principle]]. The modern concept of [[W:color charge|color charge]] completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [[W:William A. Bardeen|William Bardeen]], [[W:de:Harald Fritzsch|Harald Fritzsch]], and [[W:Murray Gell-Mann|Murray Gell-Mann]].&lt;ref&gt;{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''&lt;sup&gt;0&lt;/sup&gt; decay, and ''e''&lt;sup&gt;+&lt;/sup&gt; ''e''&lt;sup&gt;&amp;minus;&lt;/sup&gt; annihilation |arxiv=hep-ph/0211388 |editor=Gatto, R. |book-title=Scale and conformal symmetry in hadron physics |page=[https://archive.org/details/scaleconformalsy0000unse/page/139 139] |publisher=[[W:John Wiley &amp; Sons|John Wiley &amp; Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}&lt;/ref&gt;&lt;ref&gt;{{cite journal |title=Advantages of the color octet gluon picture |journal=[[W:Physics Letters B|Physics Letters B]] |volume=47 |issue=4 |page=365 |year=1973 |last1=Fritzsch |first1=H. |last2=Gell-Mann |first2=M. |last3=Leutwyler |first3=H. |doi=10.1016/0370-2693(73)90625-4 |bibcode=1973PhLB...47..365F |citeseerx=10.1.1.453.4712}}&lt;/ref&gt;

Color charge is not [[W:electric charge|electric charge]]; the whole point of it is that it is a quantum of something different. But it is related to electric charge, through the way in which the three different-colored quarks combine to contribute fractional quantities of electric charge to a nucleon. As we shall see, color is not really a separate kind of charge at all, but a partitioning of the electric charge into [[24-cell#Clifford parallel polytopes|Clifford parallel subspaces]].

The [[W:Color charge#Red, green, and blue|three different colors]] of quark charge might correspond to three different 16-cells, such as the three disjoint 16-cells inscribed in the 24-cell. Each color might be a disjoint domain in isospin space (the space of points on the 3-sphere).{{Efn|The 8 vertices of each disjoint 16-cell constitute an independent [[16-cell#Coordinates|orthonormal basis for a coordinate reference frame]].}} Alternatively, the three colors might correspond to three different fibrations of the same isospin space: three different ''sequences'' of the same total set of discrete points on the 3-sphere. These alternative possibilities constrain possible representations of the nuclides themselves, for example if we try to represent nuclides as particular rotating 4-polytopes. If the neutron is a (8-point) 16-cell, either of the two color possibilities might somehow make sense as far as the neutron is concerned. But if the proton is a (5-point) 5-cell, only the latter color possibility makes sense, because fibrations (which correspond to distinct isoclinic left-and-right rigid rotations) are the ''only'' thing the 5-cell has three of. Both the 5-cell and the 16-cell have three discrete rotational fibrations. Moreover, in the case of a rigid, isoclinically rotating 4-polytope, those three fibrations always come one-of-a-kind and two-of-a-kind, in at least two different ways. First, one fibration is the set of invariant planes currently being rotated through, and the other two are not. Second, when one considers the three fibrations of each of these 4-polytopes, in each fibration two isoclines carry the left and right rotations respectively, and the third isocline acts simply as a Petrie polygon, the difference between the fibrations being the role assigned to each isocline.

If we associate each quark with one or more isoclinic rotations in which the moving vertices belong to different 16-cells of the 24-cell, and the sign (plus or minus) of the electric charge with the chirality (right or left) of isoclinic rotations generally, we can configure nucleons of three quarks, two performing rotations of one chirality and one performing rotations of the other chirality. The configuration will be a valid kinematic rotation because the completely disjoint 16-cells can rotate independently; their vertices would never collide even if the 16-cells were performing different rigid square isoclinic rotations (all 8 vertices rotating in unison). But we need not associate a quark with a [[16-cell#Rotations|rigidly rotating 16-cell]], or with a single distinct square rotation.

Minimally, we must associate each quark with at least one moving vertex in each of three different 16-cells, following the twisted geodesic isocline of an isoclinic rotation. In the up quark, that could be the isocline of a right rotation; and in the down quark, the isocline of a left rotation. The chirality accounts for the sign of the electric charge (we have said conventionally as +right, −left), but we must also account for the quantity of charge: +{{sfrac|2|3}} in an up quark, and −{{sfrac|1|3}} in a down quark. One way to do that would be to give the three distinct quarks moving vertices of {{sfrac|1|3}} charge in different 16-cells, but provide up quarks with twice as many vertices moving on +right isoclines as down quarks have vertices moving on −left isoclines (assuming the correct chiral pairing is up+right, down−left).

Minimally, an up quark requires two moving vertices (of the up+right chirality).{{Efn|Two moving vertices in one quark could belong to the same 16-cell. A 16-cell may have two vertices moving in the same isoclinic square (octagram) orbit, such as an antipodal pair (a rotating dipole), or two vertices moving in different square orbits of the same up+right chirality.{{Efn|There is only one [[16-cell#Helical construction|octagram orbit]] of each chirality in each fibration of the 16-cell, so two octagram orbits of the same chirality cannot be Clifford parallel (part of the same distinct rotation). Two vertices right-moving on different octagram isoclines in the same 16-cell is a combination of two distinct rotations, whose isoclines will intersect: a kinematic rotation. It can be a valid kinematic rotation if the moving vertices will never pass through a point of intersection at the same time. Octagram isoclines pass through all 8 vertices of the 16-cell, and all eight isoclines (the left and right isoclines of four different fibrations) intersect at ''every'' vertex.}} However, the theory of [[W:Color confinement|color confinement]] may not require that two moving vertices in one quark belong to the same 16-cell; like the moving vertices of different quarks, they could be drawn from the disjoint vertex sets of two different 16-cells.}} Minimally, a down quark requires one moving vertex (of the down−left chirality). In these minimal quark configurations, a proton would have 5 moving vertices and a neutron would have 4.

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=== Nucleons ===
[[File:Symmetrical_5-set_Venn_diagram.svg|thumb|[[W:Branko Grünbaum|Grünbaum's]] rotationally symmetrical 5-set Venn diagram, 1975. It is the [[5-cell]]. Think of it as an [[W:Nuclear magnetic resonance|NMR image]] of the 4-dimensional proton in projection to the plane.]]
The proton is a very stable mass particle. Is there a stable orbit of 5 moving vertices in 4-dimensional Euclidean space? There are few known solutions to the 5-body problem, and fewer still to the [[W:n-body problem|{{mvar|n}}-body problem]], but one is known: the ''central configuration'' of {{mvar|n}} bodies in a space of dimension {{mvar|n}}-1. A [[W:Central configuration|central configuration]] is a system of [[W:Point particle|point masses]] with the property that each mass is pulled by the combined attractive force of the system directly towards the [[W:Center of mass|center of mass]], with acceleration proportional to its distance from the center. Placing three masses in an equilateral triangle, four at the vertices of a regular [[W:Tetrahedron|tetrahedron]], five at the vertices of a regular [[5-cell]], or more generally {{mvar|n}} masses at the vertices of a regular [[W:Simplex|simplex]] produces a central configuration [[W:Central configuration#Examples|even when the masses are not equal]]. In an isoclinic rotation, all the moving vertices orbit at the same radius and the same speed. Therefore if any 5 bodies are orbiting as an isoclinically rotating regular 5-cell (a rigid 4-simplex figure undergoing isoclinic rotation), they maintain a central configuration, describing 5 mutually stable orbits.

Unlike the proton, the neutron is not always a stable particle; a free neutron will decay into a proton. A deficiency of the minimal configurations is that there is no way for this [[W:beta minus decay|beta minus decay]] to occur. The minimal neutron of 4 moving vertices described [[#Color|above]] cannot possibly decay into a proton by losing moving vertices, because it does not possess the four up+right moving vertices required in a proton. This deficiency could be remedied by giving the neutron configuration 8 moving vertices instead of 4: four down−left and four up+right moving vertices. Then by losing 3 down−left moving vertices the neutron could decay into the 5 vertex up-down-up proton configuration.{{Efn|Although protons are very stable, during [[W:stellar nucleosynthesis|stellar nucleosynthesis]] two H&lt;sub&gt;1&lt;/sub&gt; protons are fused into an H&lt;sub&gt;2&lt;/sub&gt; nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus &quot;decay&quot;]] of a proton into a neutron is actually the result of a rare high-energy collision between the two protons, in which a neutron is constructed. With respect to our nucleon configurations of moving vertices, it has to be explained as the conversion of two 5-point 5-cells into a 5-point 5-cell and an 8-point 16-cell, emitting two decay products of at least 1-point each. Thus it must involve the creation of moving vertices, by the conversion of kinetic energy to point-masses.}} A neutron configuration of 8 moving vertices could occur as the 8-point 16-cell, the second-smallest regular 4-polytope after the 5-point 5-cell (the hypothesized proton configuration).

It is possible to double the neutron configuration in this way, without destroying the charge balance that defines the nucleons, by giving down quarks three moving vertices instead of just one: two −left vertices and one +right vertex. The net charge on the down quark remains −{{sfrac|1|3}}, but the down quark becomes heavier (at least in vertex count) than the up quark, as in fact its mass is measured to be.

A nucleon's quark configuration is only a partial specification of its properties. There is much more to a nucleon than what is contained within its three quarks, which contribute only about 1% of the nucleon's energy. The additional 99% of the nucleon mass is said to be associated with the force that binds the three quarks together, rather than being intrinsic to the individual quarks separately. In the case of the proton, 5 moving vertices in the stable orbits of a central configuration (in one of the [[5-cell#Geodesics and rotations|isoclinic rotations characteristic of the regular 5-cell]]) might be sufficient to account for the stability of the proton, but not to account for most of the proton's energy. It is not the point-masses of the moving vertices themselves which constitute most of the mass of the nucleon; if mass is a consequence of geometry, we must look to the larger geometric elements of these polytopes as their major mass contributors. The quark configurations are thus incomplete specifications of the geometry of the nucleons, predictive of only some of the nucleon's properties, such as charge.{{Efn|Notice that by giving the down quark three moving vertices, we seem to have changed the quark model's prediction of the proton's number of moving vertices from 5 to 7, which would be incompatible with our theory that the proton configuration is a rotating regular 5-cell in a central configuration of 5 stable orbits. Fortunately, the actual quark model has nothing at all to say about moving vertices, so we may choose to regard that number as one of the geometric properties the quark model does not specify.}} In particular, they do not account for the forces binding the nucleon together. Moreover, if the rotating regular 5-cell is the proton configuration and the rotating regular 16-cell is the neutron configuration, then a nucleus is a complex of rotating 5-cells and 16-cells, and we must look to the geometric relationship between those two very different regular 4-polytopes for an understanding of the nuclear force binding them together.

The most direct [[120-cell#Relationships among interior polytopes|geometric relationship among stationary regular 4-polytopes]] is the way they occupy a common 3-sphere together. Multiple 16-cells of equal radius can be compounded to form each of the larger regular 4-polytopes, the 8-cell, 24-cell, 600-cell, and 120-cell, but it is noteworthy that multiple regular 5-cells of equal radius cannot be compounded to form any of the other 4-polytopes except the largest, the 120-cell. The 120-cell is the unique intersection of the regular 5-cell and 16-cell: it is a compound of 120 regular 5-cells, and also a compound of 75 16-cells. All regular 4-polytopes except the 5-cell are compounds of 16-cells, but none of them except the largest, the 120-cell, contains any regular 5-cells. So in any compound of equal-radius 16-cells which also contains a regular 5-cell, whether that compound forms some single larger regular 4-polytope or does not, no two of the regular 5-cell's five vertices ever lie in the same 16-cell. So the geometric relationship between the regular 5-cell (our proton candidate) and the regular 16-cell (our neutron candidate) is quite a distant one: they are much more exclusive of each other's elements than they are distantly related, despite their complementary three-quark configurations and other similarities as nucleons. The relationship between a regular 5-cell and a regular 16-cell of equal radius is manifest only in the 120-cell, the most complex regular 4-polytope, which [[120-cell#Geometry|uniquely embodies all the containment relationships]] among all the regular 4-polytopes and their elements.

If the nucleus is a complex of 5-cells (protons) and 16-cells (neutrons) rotating isoclinically around a common center, then its overall motion is a hybrid isoclinic rotation, because the 5-cell and the 16-cell have different characteristic isoclinic rotations, and they have no isoclinic rotation in common.{{Efn|The regular 5-cell does not occur inscribed in any other regular 4-polytope except one, the 600-vertex 120-cell. No two of the 5 vertices of a regular 5-cell can be vertices of the same 16-cell, 8-cell, 24-cell, or 600-cell. The isoclinic rotations characteristic of the regular 5-cell maintain the separation of its 5 moving vertices in 5 disjoint Clifford-parallel subspaces at all times. The [[16-cell#Rotations|isoclinic rotation characteristic of the 16-cell]] maintains the separation of its 8 moving vertices in 2 disjoint Clifford-parallel subspaces (completely orthogonal great square planes) at all times. Therefore, in any hybrid rotation of a concentric 5-cell and 16-cell, at most one 5-cell subspace (containing 1 vertex) might be synchronized with one 16-cell subspace (containing 4 vertices), such that the 1 + 4 vertices they jointly contain occupy the same moving subspace continually, forming a rigid 5-vertex polytope undergoing some kind of rotation. If in fact it existed, this 5-vertex rotating rigid polytope would not be [[5-cell#Geometry|not a 5-cell, since 4 of its vertices are coplanar]]; it is not a 4-polytope but merely a polyhedron, a [[W:square pyramid|square pyramid]].}}

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=== Nuclides ===

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=== Quantum phenomena ===

The Bell-Kochen-Specker (BKS) theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a space of three or more dimensions can be given by exhibiting a finite set of lines through the origin that cannot each be colored black or white in such a way that (i) no two orthogonal lines are both black, and (ii) not all members of a set of ''d'' mutually orthogonal lines are white.{{Efn|&quot;The Bell-Kochen-Specker theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a Hilbert space of dimension d ≥ 3 can be given by exhibiting a finite set of rays [9] that cannot each be assigned the value 0 or 1 in such a way that (i) no two orthogonal rays are both assigned the value 1, and (ii) not all members of a set of d mutually orthogonal rays are assigned the value 0.&quot;{{Sfn|Waegell|Aravind|2009|loc=2. The Bell-Kochen-Specker (BKS) theorem}}|name=BKS theorem}}

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=== Motion ===
What does it mean to say that an object moves through space? Coxeter group theory provides precise answers to questions of this kind. A rigid object (polytope) moves by distinct transformations, changing itself in each discrete step into a congruent object in a different orientation and position.{{Efn|name=transformations}}

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== Galilean relativity in a space of four orthogonal dimensions ==

Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions.

General relativity is just Galilean relativity in a general space of four orthogonal dimensions, e.g. Euclidean 4-space &lt;math&gt;R^4&lt;/math&gt;, spherical 4-space &lt;math&gt;S^4&lt;/math&gt;, or any orthogonal 4-manifold.

Light is just reflection. Gravity (and all force) is just rotation. Both motions are just group actions, expressions of intrinsic symmetries. That is all of physics.

Every observer properly sees himself as stationary and the universe as a sphere with himself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and it can be measured by the observer as the speed of light.

=== Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions ===
Perspective effects occur because each observer's ordinary 3-dimensional space is only a curved manifold embedded in 4-dimensional Euclidean space, and its curvature complicates the calculations for him (e.g., he sometimes requires Lorentz transformations). But if  all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) except when you want to calculate a projection, or a shadow, that is, how things will appear from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} The universe really has four spatial dimensions, and space and time behave just as they do in classical 3-vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a spacetime to explain 4-dimensional perspective effects at high velocities, because 4-space is already spatially 4-dimensional, and those perspective effects fall out of the 4-dimensional Pythagorean theorem naturally, just as perspective does in three dimensions. The universe is only strange in the ways the Euclidean fourth dimension is strange; but that does hold many surprises for us. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way that 3-space is much more interesting than 2-space. But all Euclidean spaces are dimensionally analogous. Dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries.

=== General relativity is just Galilean relativity in a general space of four orthogonal dimensions ===
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=== Physics ===
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=== Thoreau's spherical relativity ===
Every observer may properly see himself as stationary and the universe as a 4-sphere with himself at the center observing it, perceptually equidistant from all points on its surface, including his own ''physical'' location which is one of those surface points, distinguished to him but not the center of anything. This statement of the principle of relativity is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's relativity of orthogonal group actions in Euclidean spaces of any number of dimensions.{{Efn|name=transformations}} It should be known as Thoreau's spherical relativity, since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polytopes in any number of dimensions.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassman and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}}]}}

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== Conclusions==

=== Spherical relativity ===

We began our inquiry by wondering why physical space should be limited to just three dimensions (why ''three''). By visualizing the universe as a Euclidian space of four dimensions, we recognize that relativistic and quantum phenomena are natural consequences of symmetry group operations (including reflections and rotations) in four orthogonal dimensions. We should not then be surprised to see that the universe does not have just four dimensions, either. Physical space must bear as many dimensions as we need to ascribe to it, though the distinct phenomena for which we find a need to do so, in order to explain them, seem to be fewer and fewer as we consider higher and higher dimensions. To laws of physics generally, such as the principle of relativity in particular, we should always append the phrase &quot;in Euclidean spaces of any number of dimensions&quot;. Laws of physics should operate in any flat Euclidean space &lt;math&gt;R^n&lt;/math&gt; and in its corresponding spherical space &lt;math&gt;S^n&lt;/math&gt;.

The first and simplest sense in which we are forced to contemplate a fifth dimension is to accommodate our normal idea of time. Just as Einstein was forced to admit time as a dimension, in his four-dimensional spacetime of three spatial dimensions plus time, for some purposes we require a fifth time dimension to accompany our four spatial dimensions, when our purpose is orthogonal to (in the sense of independent of) the four spatial dimensions. For example, if we theorize that we observe a finite homogeneous universe, and that it is a Euclidean 4-space overall, we may prefer not to have to identify any distinct place within that 4-space as the center where the universe began in a big bang. To avoid having to pick a distinct place as the center of the universe, our model of it must be expanded, at least to be a ''spherical'' 4-dimensional space with the fifth radial dimension as time. Essentially, we require the fifth dimension in order to make our homogeneous 4-space finite, by wrapping it around into a 4-sphere. But perhaps we can still resist admitting the fifth radial dimension as a full-fledged Euclidean spatial dimension, at least so long as we have not observed how any naturally occurring object configurations are best described as 5-polytopes.

One phenomenon which resists explanation in a space of just four dimensions is the propagation of light in a vacuum. The propagation of mass-carrying particles is explained as the consequence of their rotations in closed, curved spaces (3-spheres) of finite size, moving through four-dimensional Euclidean space at a universal constant speed, the speed of light. But an apparent paradox remains that light must seemingly propagate through four-dimensional Euclidean space at more than the speed of light. From an ''n''-dimensional viewpoint, this apparent paradox can be resolved, and in retrospect it is clear how massless particles can translate through four-dimensional space at twice the speed constant, since they are not simultaneously rotating.

Another phenomenon justifying a five-dimensional view of space is the relation between the the 5-cell proton and the 16-cell neutron (the 4-simplex and 4-orthoplex polytopes). Their indirect relationship can be observed in the 4-600-point polytope (the 120-cell), and in its 11-cells,{{Sfn|Christie|2025|loc=&quot;A symmetrical arrangement of eleven 11-cells&quot;}} but it is only directly observed (absent a 120-cell) in a five-dimensional reference frame.

=== Nuclear geometry ===
We have seen how isoclinic rotations (Clifford displacements) relate the orbits in the atomic nucleus to each other, just as they relate the regular convex 4-polytopes to each other, in a sequence of nested objects of increasing complexity. We have identified the proton as a  5-point, 5-cell 4-simplex 𝜶&lt;sub&gt;4&lt;/sub&gt;, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽&lt;sub&gt;4&lt;/sub&gt;, and the shell of the atomic nucleus as a 24-point 24-cell. As Coxeter noted, that unique 24-point object stands quite alone in four dimensions, having no analogue above or below.

=== Atomic geometry ===
I'm on a plane flying to Eugene to visit Catalin, we'll talk after I arrive. I've been working on both my unpublished papers, the one going put for pre-publication review soon about 4D geometry, and the big one not going out soon about the 4D sun, 4D atoms, and 4D galaxies and n-D universe. I'vd just added the following paragraph to that big paper:

Atomic geometry

The force binding the protons and neutrons of the nucleus together into a distinct element is specifically an expression of the 11-cell 4-polytope, itself an expression of the pyritohedral symmetry, which binds the distinct 4-polytopes to each other, and relates the n-polytopes to their neighbors of different n by dimensional analogy.


flying over mt shasta out my right-side window at the moment, that last text showing &quot;not delivered&quot; yet because there's no wifi on this plane, gazing at that great peak of the world and feeling as if i've just made the first ascent of it

=== Molecular geometry ===
Molecules are 3-dimensional structures that live in the thin film of 3-membrane only one atom thick in most places that is our ordinary space, but since that is a significantly curved 3-dimensional space at the scale of a molecule, the way the molecule's covalent bonds form is influenced by the local curvature in 4-dimensions at that point.

In the water molecule, there is a reason why the hydrogen atoms are attached to the oxygen atom at an angle of 104.45° in 3-dimensional space, and at root it must be the same symmetry that locates any two of the hydrogen proton's five vertices 104.45° apart on a great circle arc of its tiny 3-sphere.

=== Cosmology ===

==== Solar systems ====

===== Stars =====
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===== The Kepler problem =====
In the proper reference frame of some hypothetical observer in 4-dimensional Euclidean space, the Kepler problem has a solution in which all the planetary orbits are circles. This occurs because all bodies are always orbiting, each in some distinct isoclinic (equi-angled double) rotation. All atoms are rotating isoclinically at (double) the velocity &lt;math&gt;c&lt;/math&gt;. In the observer's proper reference frame, the isoclinic double rotation of each of his own atoms is most conveniently represented as an equivalent screw displacement: a linear translation at velocity &lt;math&gt;c&lt;/math&gt; (along the observer's proper time axis through 4-space), combined with a simple rotation at velocity &lt;math&gt;c&lt;/math&gt; (of the atom internally). 

This representation, though proper, is subject to the over-simplification of special relativity, because it ignores the fact that the observer is himself moving on some circular orbit; he is not linearly translating through 4-space. When the observer's own orbit is also represented, the screw displacement becomes an elliptical double rotation, with a very slow, very large-radius simple circular orbit (almost a linear translation), combined with a very fast, very small-radius simple circular orbit of each atom internally. This is the observer's proper reference frame according to general relativity.

An observer moving differently will perceive the motion of the observer and his atoms to be a different elliptical double rotation. We can find a proper reference frame, of some hypothetical observer moving hypothetically, in which the ratio of the radii of the two orthogonal rotations of the atom becomes any value we choose between 1 and &lt;math&gt;c&lt;/math&gt;. In particular there exists, conceptually accessible to all observers independent of their motion, a distinct reference frame in which an atom is stationary, rotating isoclinically at (double) the velocity &lt;math&gt;c&lt;/math&gt;. That is simply the stationary reference frame of the atom itself, such as the stationary reference frame of any observer and his own atoms. In 3-dimensional physics, it is known as the observer's proper inertial reference frame. But in 4-dimensional physics, that is ''not'' the most convenient or sensible reference frame in which to consider objects moving differently, in different proper reference frames. In 4-dimensional physics, a reference frame in which an observer and his atoms are translating linearly at velocity &lt;math&gt;c&lt;/math&gt; is known as the observer's proper inertial reference frame. Any such proper reference frame makes a great deal more sense for the purpose of considering the motion of objects moving differently in 4-space, just as a heliocentric solar system makes a great deal more sense than a geocentric solar system for the purpose of considering the motion of the planets.

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==== Galaxies ====

The spacetime of general relativity is often illustrated as a projection to a curved 2D surface in which large gravitational objects make gravity wells or dimples in the surface. In the Euclidean 4D view of the universe the 3D surface of a large cosmic object such as a galaxy surrounds an empty 4D space, and large gravitational objects within the galaxy must make dimples in its surface. But should we see them as dimples exactly? Would they dimple inwards or outwards? In the spacetime illustrations they are naturally always shown as dimpling downwards, which is somewhat disingenuous, strongly suggesting to the viewer that the reason for gravity is that it flows downhill - the original tautology we are trying to surmount! In the Euclidean 4D galaxy the dimple, if it is one, must be either inward or outward, and which it is matters since the dimple is flying outward at velocity {{mvar|c}}. The galaxy is not collapsing inward. Is a large gravitational mass (such as a star) ''ahead'' of the smaller masses orbiting around it (such as its planets), or is it ''behind'' them, as they fly through 4-space on their Clifford parallel trajectories? The answer is ''both'' of course, because a star is not a dimple, it is a 4-ball, and it dimples the 3D surface both inwards and outwards. It is a thick place in the 3D surface. We should view it as having its gravitational center precisely at the surface of the expanding 3-sphere. 

What is a black hole? It is the hollow four-dimensional space that a galaxy is the three-dimensional surface of.

When we view another galaxy, such as Andromeda, we are seeing that whole galaxy from a distance, the way the moon astronauts looked back at the whole earth. We see our own milky way galaxy from where we are on its surface, the way we see the earth from its surface, except that the earth is solid, but the galaxy is hollow and transparent. We can look across its empty center and see all the other stars also on its surface, including those opposite ours on the far side of its 3-sphere. The thicker band of stars we see in our night sky and identify as the milky way is not our whole galaxy; the majority of the other visible stars also lie in our galaxy. That dense band is not thicker and brighter than other parts of our galaxy because it lies toward a dense galactic center (our galaxy has an empty center), but for exactly the opposite reason: those apparently more thickly clustered stars lie all around us on the galaxy's surface, in the nearest region of space surrounding us. They appear to be densely packed only because we are looking at them &quot;edge on&quot;. Actually, we are looking into this nearby apparently dense region ''face on'', not edge on, because we are looking at a round sphere of space surrounding us, not a disk. In contrast, stars in our galaxy outside that bright band lie farther off from us, across the empty center of the galaxy, and we see them spread out as they actually are, instead of &quot;edge on&quot; so they appear to be densely clustered. The &quot;dense band&quot; covers only an equatorial band of the night sky instead of all the sky, because when we look out into the four-dimensional space around us, we can see stars above and below our three-dimensional hyperplane in our four-dimensional space. Everything in our solar system lies in our hyperplane, and the nearby stars around us in our galaxy are near our hyperplane (just slightly below it). All the other, more distant stars in our galaxy are also below our hyperplane. We can see objects outside our galaxy, such as other galaxies, both above and below our hyperplane. We can see all around us above our hyperplane (looking up from the galactic surface into the fourth dimension), and all around us below our hyperplane (looking down through our transparent galaxy and out the other side).

== Revolutions ==
The original Copernican revolution displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the stars remaining on a fixed sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

In such fashion the Euclidean four-dimensional viewpoint initially lends itself to a big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the stars need not be equidistant from a single origin in time, any more than they all lie in the same galaxy, equidistant from its center in space. The expanding sphere of matter on the surface of which we find ourselves living might be one of many such spheres, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe.

When we look up at the heavens, we have no obvious way of knowing whether the space we are looking into is a curved 3-spherical one or a flat 4-space. In this work we suggest a theory of how light travels that says we can see into all four dimensions, and so when we look up at night we see cosmological objects distributed in 4-dimensional space, and not all located on our own 3-spherical membrane. The view from our solar system suggests that our galaxy is its own hollow 3-sphere, and that galaxies generally are single roughly spherical 3-membranes, with the smaller objects within them all lying on that same 3-spherical surface, equidistant from the galaxy center in 4-space. 

The Euclidean four-dimensional viewpoint requires that all mass-carrying objects are in motion at constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Since their paths away from their origin are not straight lines but various helical isoclines, their 3-sphere will be expanding radially at slightly less than the constant velocity &lt;math&gt;c&lt;/math&gt;. The view from our solar system does ''not'' suggest that each galaxy is its own distinct 3-sphere expanding at this great rate; rather, the standard theory has been that the entire observable universe is expanding from a single big bang origin in time. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also allows theories which require no single origin point in space and time.

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and we have not slowed down since.

== Origins of the theory ==
Einstein himself was one of the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean sphere, in what was narrowly the first written articulation of the principle of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below). Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from his perspective; the forthshortenings, clock desynchronizations and other perceptual effects it predicts are exact calculations of actual perspective effects; but space is actually a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean 4-dimensional theory differs from the standard theory in being a description of the physical universe in terms of a geometry of four or more orthogonal spatial dimensions, rather than in the standard theory's terms of the [[w:Minkowski spacetime|Minkowski spacetime]] geometry (in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions). The invention of geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years. It was first worked out by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] around 1850. Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''polyscheme'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he discovered all the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the six convex regular polyschemes which can be constructed in a Euclidean space of four dimensions (a set analogous to the five [[w:Platonic solid|Platonic solids]] in three dimensional space). Thus he was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover all its astonishing regular objects. Because most of his work remained almost completely unknown until it was published posthumously in 1901, other researchers had more than fifty years to rediscover the regular polyschemes, and competing terms were coined; today [[W:Alicia Boole Stott|Alicia Boole Stott]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme''.{{Efn|Today Schläfli's original ''polyscheme'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}}

== Boundaries ==
&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schlafli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it, is that there ''is'' a boundary between three and four dimensions. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our world apparently only three dimensional? Why would it have ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schlafli mapped? What is the nature of the boundary which confines us to just three? 

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way by receiving light signals that traveled to us on straight lines through it. The reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creates, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not surprise us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schlafli discovered something else: all the astonishing regular objects that exist in higher dimensions. So this conception now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and not a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation?

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that our universe is properly a Euclidean space of four orthogonal spatial dimensions. Others will have to work out the physics and do the math, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are 4-dimensionally circular, but not all isoclines on 3-manifolds in 4-space are perfectly circular.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point.{{Sfn|Tyrrell|Semple|1971|loc=§3. Clifford's original definition of parallelism|pp=5-6}} A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the 2-sphere will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect; various sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. Perhaps the simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles.{{Efn|name=six orthogonal planes of the Cartesian basis}} Each completely orthogonal pair is Clifford parallel. The two circles cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 3-sphere.{{Efn|name=only some Clifford parallels are orthogonal}} Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]].|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Notelist|40em}}

== Citations ==
{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

{{Reflist|40em}}

== References ==
{{Refbegin}}
* {{Cite book | last=Kepler | first=Johannes | author-link=W:Johannes Kepler | title=Harmonices Mundi (The Harmony of the World) | title-link=W:Harmonices Mundi | publisher=Johann Planck | year=1619}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston}}
* {{Cite book | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1973 | orig-year=1948 | title=Regular Polytopes | publisher=Dover | place=New York | edition=3rd | title-link=W:Regular Polytopes (book) }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1991 | title=Regular Complex Polytopes | place=Cambridge | publisher=Cambridge University Press | edition=2nd }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1995 | title=Kaleidoscopes: Selected Writings of H.S.M. Coxeter | publisher=Wiley-Interscience Publication | edition=2nd | isbn=978-0-471-01003-6 | url=https://archive.org/details/kaleidoscopessel0000coxe | editor1-last=Sherk | editor1-first=F. Arthur | editor2-last=McMullen | editor2-first=Peter | editor3-last=Thompson | editor3-first=Anthony C. | editor4-last=Weiss | editor4-first=Asia Ivic | url-access=registration }}
** (Paper 3) H.S.M. Coxeter, ''Two aspects of the regular 24-cell in four dimensions''
** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10]
** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', [Math. Zeit. 188 (1985) 559-591]
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
* {{Cite journal | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1989 | title=Trisecting an Orthoscheme | journal=Computers Math. Applic. | volume=17 | issue=1-3 | pp=59-71 }}
* {{Cite journal|last=Stillwell|first=John|author-link=W:John Colin Stillwell|date=January 2001|title=The Story of the 120-Cell|url=https://www.ams.org/notices/200101/fea-stillwell.pdf|journal=Notices of the AMS|volume=48|issue=1|pages=17–25}}
* {{Cite book | last1=Conway | first1=John H. | author-link1=W:John Horton Conway | last2=Burgiel | first2=Heidi | last3=Goodman-Strauss | first3=Chaim | author-link3=W:Chaim Goodman-Strauss | year=2008 | title=The Symmetries of Things | publisher=A K Peters | place=Wellesley, MA | title-link=W:The Symmetries of Things }}
* {{Cite journal|last1=Perez-Gracia|first1=Alba|last2=Thomas|first2=Federico|date=2017|title=On Cayley's Factorization of 4D Rotations and Applications|url=https://upcommons.upc.edu/bitstream/handle/2117/113067/1749-ON-CAYLEYS-FACTORIZATION-OF-4D-ROTATIONS-AND-APPLICATIONS.pdf|journal=Adv. Appl. Clifford Algebras|volume=27|pages=523–538|doi=10.1007/s00006-016-0683-9|hdl=2117/113067|s2cid=12350382|hdl-access=free}}
* {{Cite arXiv | eprint=1903.06971 | last=Copher | first=Jessica | year=2019 | title=Sums and Products of Regular Polytopes' Squared Chord Lengths | class=math.MG }}
* {{Cite thesis|url= http://resolver.tudelft.nl/uuid:dcffce5a-0b47-404e-8a67-9a3845774d89 |title=Symmetry groups of regular polytopes in three and four dimensions|last=van Ittersum |first=Clara|year=2020|publisher=[[W:Delft University of Technology|Delft University of Technology]]}}
* {{cite arXiv|last1=Kim|first1=Heuna|last2=Rote|first2=G.|date=2016|title=Congruence Testing of Point Sets in 4 Dimensions|class=cs.CG|eprint=1603.07269}}
* {{cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|year=2013|publisher=DUTTON Penguin Group|isbn=978-0-525-95366-1}}
* {{Cite journal|last1=Waegell|first1=Mordecai|last2=Aravind|first2=P. K.|date=2009-11-12|title=Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem|journal=Journal of Physics A: Mathematical and Theoretical|volume=43|issue=10|page=105304|language=en|doi=10.1088/1751-8113/43/10/105304|arxiv=0911.2289|s2cid=118501180}}
* {{Cite book|title=Generalized Clifford parallelism|last1=Tyrrell|first1=J. A.|last2=Semple|first2=J.G.|year=1971|publisher=[[W:Cambridge University Press|Cambridge University Press]]|url=https://archive.org/details/generalizedcliff0000tyrr|isbn=0-521-08042-8}}
* {{Cite journal | last1=Mamone|first1=Salvatore | last2=Pileio|first2=Giuseppe | last3=Levitt|first3=Malcolm H. | year=2010 | title=Orientational Sampling Schemes Based on Four Dimensional Polytopes | journal=Symmetry | volume=2 | pages=1423-1449 | doi=10.3390/sym2031423 }}
* {{Cite journal|last=Dorst|first=Leo|title=Conformal Villarceau Rotors|year=2019|journal=Advances in Applied Clifford Algebras|volume=29|issue=44|url=https://doi.org/10.1007/s00006-019-0960-5}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}}
*{{Citation | last=Goucher | first=A.P. | title=Spin groups | date=19 November 2019 | journal=Complex Projective 4-Space | url=https://cp4space.hatsya.com/2012/11/19/spin-groups/ }}
* {{Citation|last=Christie|first=David Brooks|author-link=User:Dc.samizdat|year=2025|title=A symmetrical arrangement of eleven 11-cells|title-link=User:Dc.samizdat/A symmetrical arrangement of eleven 11-cells|journal=Wikiversity}}
{{Refend}}</text>
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      <text bytes="108597" sha1="arl4hsepineay8izkvpydwvju12mrbt" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|June 2023 - June 2025}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. A typical galaxy such as ours is a hollow [[w:3-sphere|4-dimensional 3-sphere]] with these objects distributed on its 3-dimensional surface. The black hole at the galaxy's center is nothing: the 4-ball of empty space they surround. Objects in our galaxy occupy this thin 3-dimensional surface, forming a filmy 4-dimensional soap-bubble of galactic size, thicker than an atom only in the interior of stars. Mass is confined to this 3-dimensional manifold by its inertia, also called gravity, the property of its ceaseless motion at a constant, universal velocity &lt;math&gt;c&lt;/math&gt;, the rate of causality at which the universe evolves. Atoms are always internally in inertial rotational motion, and externally in inertial translational motion through 4-space, at this universal rate of transformation. The observed universe appears to be a 3-sphere expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light through 3-space as measured by all observers. All objects with mass move through 4-space at velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c^\prime = 2c&lt;/math&gt;, so we can see in 4 dimensions, even though we are physically confined to a moving 3-dimensional manifold, where our direction of motion through 4-space is our proper time dimension. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at velocity &lt;math&gt;c&lt;/math&gt;. This model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries.&lt;/blockquote&gt;

== Symmetries ==
It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway|Burgiel|Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter group]] theory did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups and obey the principle of relativity. As I understand Coxeter theory (which is not mathematically),{{Efn|Coxeter's formulation of the motions (congruent transformations) possible in an ''n''-dimensional Euclidean space:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let Q denote a rotation, R a reflection, T a translation, and let Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T denote a product of several such transformations, all commutative with one another. Then RT is a glide-reflection (in two or three dimensions), QR is a rotary-reflection, QT is a screw-displacement, and Q&lt;sup&gt;2&lt;/sup&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
{{spaces|10}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt;&lt;br&gt;
where 2''q'' + ''r'' ≤ ''n'', the number of dimensions.&lt;br&gt;
Transformations involving a translation are expressible as:&lt;br&gt;
{{spaces|10}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T&lt;br&gt;
where 2''q'' + ''r'' + 1 ≤ ''n''.&lt;br&gt;
For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q&lt;sup&gt;2&lt;/sup&gt;, or a screw-displacement QT (where the rotation component Q is a simple rotation). Every enantiomorphous transformation in 4-space (reversing chirality) is a QRT.&lt;/blockquote&gt;
If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a Q&lt;sup&gt;2&lt;/sup&gt; or a QT, because we can view any QT as a Q&lt;sup&gt;2&lt;/sup&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q&lt;sup&gt;2&lt;/sup&gt;. By the same principle, we can view any QT or Q&lt;sup&gt;2&lt;/sup&gt; as an isoclinic (equi-angled) Q&lt;sup&gt;2&lt;/sup&gt; by appropriate choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]]. The distinct symmetry groups of the regular polytopes each correspond to their characteristic isoclinic rotations. These isoclinic rotations are distinguished in geometry, relativity, and quantum mechanics.|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to relativity, in that we can only exchange the translation (T) for ''one'' of the two rotations (Q). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation up to uncertainty, and can always distinguish the direction of his own proper time arrow.|name=transformations}} the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic rather than algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional objects, and nature can be understood in terms of their [[W:group action|group actions]], including centrally [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]].

== Special relativity describes Euclidean 4-dimensional space ==
&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.{{Sfn|Goldberg|2013|loc=§10. Hidden Symmetries: Why some symmetries but not others?|p=264}}&lt;/blockquote&gt;

...cite Yamashita{{Sfn|Yamashita|2023}}

=== Minkowski spacetime and Euclidean 4-space in relativity ===
...

Is there a configuration in Euclidean space where every observer, and every observed object, is moving at velocity &lt;math&gt;c&lt;/math&gt;? Yes, there is one such configuration, in 4-dimensional Euclidean space. This configuration must be like the one described above, in our ''Abstract''.

== The rate of atomic symmetry operations ==
...

== General relativity describes a curved 3-dimensional manifold embedded in Euclidean 4-dimensional space ==
...

== The geometry of the atomic nucleus ==

In [[W:Euclidean 4-space|Euclidean four dimensional space]], an [[W:atomic nucleus|atomic nucleus]] is a one or more concentric 4-polytopes of increasing radius. Each concentric shell is a single or compound [[24-cell]], the regular 4-polytope with [[W:Coxeter group#Symmetry groups of regular polytopes|𝔽&lt;sub&gt;4&lt;/sub&gt; symmetry]]. Nuclear shells are concentric [[W:3-sphere|3-sphere]]s occupied (fully or partially) by the orbits of this 24-point [[#The 6 regular convex 4-polytopes|regular convex 4-polytope]]. An actual atomic nucleus is a rotating four dimensional object. It is not a ''rigid'' rotating object, it is a kinematic one, because the nucleus of an actual atom of a distinct [[W:nucleon number|nucleon number]] contains a distinct number of orbiting 24-cell vertices which may be in different isoclinic rotational orbits. These moving vertices never describe a compound of static 24-cells at any single instant in time, though their orbits do all the time. The physical configuration of a nucleus as concentric 24-cells can be reduced to the [[W:kinematics|kinematics]] of the orbits of its constituent protons and neutrons. The geometry of the atomic nucleus is therefore strictly [[W:Euclidean geometry#19th century|Euclidean]] in four dimensional space.

=== Rotations ===
The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out.

This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a precise [[24-cell|detailed description]] enabling the reader to properly visualize it runs to many pages and illustrations, with many accompanying pages of explanatory notes on basic phenomena that arise only in 4-dimensional space: [[24-cell#Squares|completely orthogonal planes]], [[24-cell#Hexagons|Clifford parallelism]] and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Helical hexagrams and their isoclines|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a surprise. [[#The 6 regular convex 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120, and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (generally), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It is much harder for us to visualize, because the only way we can experience it is in our imaginations; we have no body of sensory experience in 4-dimensional space to draw upon.

For that reason, descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than a single rigid 24-cell. 

To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with any other at any time.

That is still an example of a rigid object in a single distinct isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing the characteristic rotation of the 24-cell. But we can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same shell without collisions? In adjacent shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore questions of this kind of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[W:kinetics|kinetics]].

=== Isospin ===
A [[W:Nucleon|nucleon]] is a [[W:proton|proton]] or a [[W:neutron|neutron]]. The proton carries a positive net [[W:Electric charge|charge]], and the neutron carries a zero net charge. The proton's [[W:Mass|mass]] is only about 0.13% less than the neutron's, and since they are observed to be identical in other respects, they can be viewed as two states of the same nucleon, together forming an isospin doublet ({{nowrap|''I'' {{=}} {{sfrac|1|2}}}}). In isospin space, neutrons can be transformed into protons and conversely by actions of the [[W:SU(2)|SU(2)]] symmetry group. In nature, protons are very stable (the most stable particle known); a proton and a neutron are a stable nuclide; but free neutrons decay into protons in about 10 or 15 seconds.

According to the [[W:Noether theorem|Noether theorem]], [[W:Isospin|isospin]] is conserved with respect to the [[W:strong interaction|strong interaction]].&lt;ref name=Griffiths2008&gt;{{cite book |author=Griffiths, David J. |title=Introduction to Elementary Particles |edition=2nd revised |publisher=WILEY-VCH |year=2008 |isbn=978-3-527-40601-2}}&lt;/ref&gt;{{rp|129–130}} Nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space.

Isospin was introduced as a concept in 1932 by [[W:Werner Heisenberg|Werner Heisenberg]],&lt;ref&gt;
{{cite journal
 |last=Heisenberg |first=W. |author-link=W:Werner Heisenberg
 |year=1932
 |title=Über den Bau der Atomkerne
 |journal=[[W:Zeitschrift für Physik|Zeitschrift für Physik]]
 |volume=77 |issue=1–2 |pages=1–11
 |doi=10.1007/BF01342433
 |bibcode = 1932ZPhy...77....1H
 |s2cid=186218053
 |language=de}}&lt;/ref&gt; well before the 1960s development of the [[W:quark model|quark model]], to explain the symmetry of the proton and the then newly discovered neutron. Heisenberg introduced the concept of another conserved quantity that would cause the proton to turn into a neutron and vice versa. In 1937, [[W:Eugene Wigner|Eugene Wigner]] introduced the term &quot;isospin&quot; to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.&lt;ref&gt;
{{cite journal
 |last=Wigner |first=E. |author-link=W:Eugene Wigner
 |year=1937
 |title=On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei
 |journal=[[W:Physical Review|Physical Review]]
 |volume=51
 |pages=106–119
 |doi=10.1103/PhysRev.51.106
 |bibcode = 1937PhRv...51..106W
 |issue=2
}}&lt;/ref&gt; Similar to a spin-1/2 particle, which has two states, protons and neutrons were said to be of isospin 1/2. The proton and neutron were then associated with different isospin projections ''I''&lt;sub&gt;3&lt;/sub&gt;&amp;nbsp;=&amp;nbsp;+1/2 and −1/2 respectively.

Isospin is a different kind of rotation entirely than the ordinary spin which objects undergo when they rotate in three-dimensional space. Isospin does not correspond to a [[W:Rotations in 4-dimensional Euclidean space#Simple rotations|simple rotation]] in any space (of any number of dimensions). However, it does seem to correspond exactly to an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]] in a Euclidean space of four dimensions. Isospin space resembles the [[W:3-sphere|3-sphere]], the [[W:Elliptical space#Elliptic space (the 3D case)|curved 3-dimensional space]] that is the surface of a [[W:4-ball (mathematics)#In Euclidean space|4-dimensional ball]].

=== Spinors ===
[[File:Spinor on the circle.png|thumb|upright=1.5|A spinor visualized as a vector pointing along the [[W:Möbius band|Möbius band]], exhibiting a sign inversion when the circle (the &quot;physical system&quot;) is continuously rotated through a full turn of 360°.]][[W:Spinors|Spinors]] are [[W:representation of a Lie group|representations]] of a [[W:spin group|spin group]], which are [[W:Double covering group|double cover]]s of the [[W:special orthogonal group|special orthogonal groups]]. The spin group Spin(4) is the double cover of [[W:SO(4)|SO(4)]], the group of rotations in 4-dimensional Euclidean space. [[600-cell#Fibrations of isocline polygrams|Isoclines]], the helical geodesic paths followed by points under isoclinic rotation, correspond to spinors representing Spin(4).

Spinors can be viewed as the &quot;square roots&quot; of [[W:Section (fiber bundle)|cross sections]] of [[W:vector bundle|vector bundle]]s; in this correspondence, a fiber bundle of isoclines (of a distinct isoclinic rotation) is a cross section (inverse bundle) of a fibration of great circles (in the invariant planes of that rotation).

A spinor can be visualized as a moving vector on a Möbius strip which transforms to its negative when continuously rotated through 360°, just as [[24-cell#Helical hexagrams and their isoclines|an isocline can be visualized as a Möbius strip]] winding twice around the 3-sphere, during which [[24-cell#Isoclinic rotations|720° isoclinic rotation]] the rigid 4-polytope turns itself inside-out twice.{{Sfn|Goucher|2019|loc=Spin Groups}} Under isoclinic rotation, a rigid 4-polytope is an isospin-1/2 object with two states.

=== Isoclinic rotations in the nucleus ===
Isospin is regarded as a symmetry of the strong interaction under the [[W:Group action (mathematics)|action]] of the [[W:Lie group|Lie group]] [[W:SU(2)|SU(2)]], the two [[W:eigenstate|states]] being the [[W:Up quark|up flavour]] and [[W:Down quark|down flavour]]. A 360° isoclinic rotation of a rigid [[W:nuclide|nuclide]] would transform its protons into neutrons and vice versa, exchanging the up and down flavours of their constituent [[W:quarks|quarks]], by turning the nuclide and all its parts inside-out (or perhaps we should say upside-down). Because we never observe this, we know that the nucleus is not a ''rigid'' polytope undergoing isoclinic rotation.

If the nucleus ''were'' a rigid object, nuclides that were isospin-rotated 360° would be isoclinic mirror images of each other, isospin +1/2 and isospin −1/2 states of the whole nucleus. We don't see whole nuclides rotating as a rigid object, but considering what would happen if they ''were'' rigid tells us something about the geometry we must expect inside the nucleons. One way that an isospin-rotated neutron could become a proton would be if the up quark and down quark were a left and right mirror-image pair of the same object; exchanging them in place would turn each down-down-up neutron into an up-up-down proton. But the case cannot be quite that simple, because the up quark and the down quark are not mirror-images of the same object: they have very different mass and other incongruities.

Another way an isospin-rotated neutron could be a proton would be if the up and down quarks were asymmetrical kinematic polytopes (not indirectly congruent mirror-images, and not rigid polytopes), rotating within the nucleus in different ''hybrid'' orbits. By that we mean that they may have vertices orbiting in rotations characteristic of more than one 4-polytope, so they may change shape as they rotate. In that case their composites (protons and neutrons) could have a symmetry not manifest in their components, but emerging from their combination.

....

=== Hybrid isoclinic rotations ===
The 24-cell has [[24-cell#Isoclinic rotations|its own characteristic isoclinic rotations]] in 4 Clifford parallel hexagonal planes (each intersecting 6 vertices), and also inherits the [[16-cell#Rotations|characteristic isoclinic rotations of its 3 Clifford parallel constituent 16-cells]] in 6 Clifford parallel square planes (each intersecting 4 vertices). The twisted circular paths followed by vertices in these two different kinds of rotation have entirely different geometries. Vertices rotating in hexagonal invariant planes follow [[24-cell#Helical hexagrams and their isoclines|helical geodesic curves whose chords form hexagrams]], and vertices rotating in square invariant planes follow [[24-cell#Helical octagrams and their isoclines|helical geodesic curves whose chords form octagrams]].

In a rigid isoclinic rotation, ''all'' the [[24-cell#Geodesics|great circle polygons]] move, in any kind of rotation. What distinguishes the hexagonal and square isoclinic rotations is the invariant planes of rotation the vertices stay in. The rotation described [[#Rotations|above]] (of 8 vertices rotating in 4 Clifford parallel hexagonal planes) is a single hexagonal isoclinic rotation, not a kinematic or hybrid rotation.

A ''kinematic'' isoclinic rotation in the 24-cell is any subset of the 24 vertices rotating through the same angle in the same time, but independently with respect to the choice of a Clifford parallel set of invariant planes of rotation and the chirality (left or right) of the rotation. A ''hybrid'' isoclinic rotation combines moving vertices from different kinds of isoclinic rotations, characteristic of different regular 4-polytopes. For example, if at least one vertex rotates in a square plane and at least one vertex rotates in a hexagonal plane, the kinematic rotation is a hybrid rotation, combining rotations characteristic of the 16-cell and characteristic of the 24-cell.

As an example of the simplest hybrid isoclinic rotation, consider a 24-cell vertex rotating in a square plane, and a second vertex, initially one 24-cell edge-length distant, rotating in a hexagonal plane. Rotating isoclinically at the same rate, the two moving vertices will never collide where their paths intersect, so this is a ''valid'' hybrid rotation.

To understand hybrid rotations in the 24-cell more generally, visualize the relationship between great squares and great hexagons. The [[24-cell#Squares|18 great squares]] occur as three sets of 6 orthogonal great squares,{{Efn|name=six orthogonal planes of the Cartesian basis}} each [[16-cell#Coordinates|forming a 16-cell]]. The three 16-cells are completely disjoint{{Efn|name=completely disjoint}} and [[24-cell#Clifford parallel polytopes|Clifford parallel]]: each has its own 8 vertices (on 4 orthogonal axes) and its own 24 edges (of length {{radic|2}}).{{Efn|name=three isoclinic 16-cells}} The 18 square great circles are crossed by 16 hexagonal great circles; each [[24-cell#Hexagons|hexagon]] has one axis (2 vertices) in each 16-cell.{{Efn|name=non-orthogonal hexagons}} The two [[24-cell#Triangles|great triangles]] inscribed in each great hexagon (occupying its alternate vertices, with edges that are its {{radic|3}} chords) have one vertex in each 16-cell. Thus ''each great triangle is a ring linking three completely disjoint great squares, one from each of the three completely disjoint 16-cells''.{{Efn|There are four different ways (four different ''fibrations'' of the 24-cell) in which the 8 vertices of the 16-cells correspond by being triangles of vertices {{radic|3}} apart: there are 32 distinct linking triangles. Each ''pair'' of 16-cells forms a tesseract (8-cell).{{Efn|name=three 16-cells form three tesseracts}} Each great triangle has one {{radic|3}} edge in each tesseract, so it is also a ring linking the three tesseracts.|name=great linking triangles}} Isoclinic rotations take the elements of the 4-polytope to congruent [[24-cell#Clifford parallel polytopes|Clifford parallel elements]] elsewhere in the 4-polytope. The square rotations do this ''locally'', confined within each 16-cell: for example, they take great squares to other great squares within the same 16-cell. The hexagonal rotations act ''globally'' within the entire 24-cell: for example, they take great squares to other great squares in ''different'' 16-cells. The [[16-cell#Helical construction|chords of the square rotations]] bind the 16-cells together internally, and the [[24-cell#Helical hexagrams and their isoclines|chords of the hexagonal rotations]] bind the three 16-cells together.

....

=== Color ===
When the existence of quarks was suspected in 1964, [[W:Oscar W. Greenberg|Greenberg]] introduced the notion of color charge to explain how quarks could coexist inside some [[W:hadron|hadron]]s in [[W:quark model#The discovery of color|otherwise identical quantum states]] without violating the [[W:Pauli exclusion principle|Pauli exclusion principle]]. The modern concept of [[W:color charge|color charge]] completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [[W:William A. Bardeen|William Bardeen]], [[W:de:Harald Fritzsch|Harald Fritzsch]], and [[W:Murray Gell-Mann|Murray Gell-Mann]].&lt;ref&gt;{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''&lt;sup&gt;0&lt;/sup&gt; decay, and ''e''&lt;sup&gt;+&lt;/sup&gt; ''e''&lt;sup&gt;&amp;minus;&lt;/sup&gt; annihilation |arxiv=hep-ph/0211388 |editor=Gatto, R. |book-title=Scale and conformal symmetry in hadron physics |page=[https://archive.org/details/scaleconformalsy0000unse/page/139 139] |publisher=[[W:John Wiley &amp; Sons|John Wiley &amp; Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}&lt;/ref&gt;&lt;ref&gt;{{cite journal |title=Advantages of the color octet gluon picture |journal=[[W:Physics Letters B|Physics Letters B]] |volume=47 |issue=4 |page=365 |year=1973 |last1=Fritzsch |first1=H. |last2=Gell-Mann |first2=M. |last3=Leutwyler |first3=H. |doi=10.1016/0370-2693(73)90625-4 |bibcode=1973PhLB...47..365F |citeseerx=10.1.1.453.4712}}&lt;/ref&gt;

Color charge is not [[W:electric charge|electric charge]]; the whole point of it is that it is a quantum of something different. But it is related to electric charge, through the way in which the three different-colored quarks combine to contribute fractional quantities of electric charge to a nucleon. As we shall see, color is not really a separate kind of charge at all, but a partitioning of the electric charge into [[24-cell#Clifford parallel polytopes|Clifford parallel subspaces]].

The [[W:Color charge#Red, green, and blue|three different colors]] of quark charge might correspond to three different 16-cells, such as the three disjoint 16-cells inscribed in the 24-cell. Each color might be a disjoint domain in isospin space (the space of points on the 3-sphere).{{Efn|The 8 vertices of each disjoint 16-cell constitute an independent [[16-cell#Coordinates|orthonormal basis for a coordinate reference frame]].}} Alternatively, the three colors might correspond to three different fibrations of the same isospin space: three different ''sequences'' of the same total set of discrete points on the 3-sphere. These alternative possibilities constrain possible representations of the nuclides themselves, for example if we try to represent nuclides as particular rotating 4-polytopes. If the neutron is a (8-point) 16-cell, either of the two color possibilities might somehow make sense as far as the neutron is concerned. But if the proton is a (5-point) 5-cell, only the latter color possibility makes sense, because fibrations (which correspond to distinct isoclinic left-and-right rigid rotations) are the ''only'' thing the 5-cell has three of. Both the 5-cell and the 16-cell have three discrete rotational fibrations. Moreover, in the case of a rigid, isoclinically rotating 4-polytope, those three fibrations always come one-of-a-kind and two-of-a-kind, in at least two different ways. First, one fibration is the set of invariant planes currently being rotated through, and the other two are not. Second, when one considers the three fibrations of each of these 4-polytopes, in each fibration two isoclines carry the left and right rotations respectively, and the third isocline acts simply as a Petrie polygon, the difference between the fibrations being the role assigned to each isocline.

If we associate each quark with one or more isoclinic rotations in which the moving vertices belong to different 16-cells of the 24-cell, and the sign (plus or minus) of the electric charge with the chirality (right or left) of isoclinic rotations generally, we can configure nucleons of three quarks, two performing rotations of one chirality and one performing rotations of the other chirality. The configuration will be a valid kinematic rotation because the completely disjoint 16-cells can rotate independently; their vertices would never collide even if the 16-cells were performing different rigid square isoclinic rotations (all 8 vertices rotating in unison). But we need not associate a quark with a [[16-cell#Rotations|rigidly rotating 16-cell]], or with a single distinct square rotation.

Minimally, we must associate each quark with at least one moving vertex in each of three different 16-cells, following the twisted geodesic isocline of an isoclinic rotation. In the up quark, that could be the isocline of a right rotation; and in the down quark, the isocline of a left rotation. The chirality accounts for the sign of the electric charge (we have said conventionally as +right, −left), but we must also account for the quantity of charge: +{{sfrac|2|3}} in an up quark, and −{{sfrac|1|3}} in a down quark. One way to do that would be to give the three distinct quarks moving vertices of {{sfrac|1|3}} charge in different 16-cells, but provide up quarks with twice as many vertices moving on +right isoclines as down quarks have vertices moving on −left isoclines (assuming the correct chiral pairing is up+right, down−left).

Minimally, an up quark requires two moving vertices (of the up+right chirality).{{Efn|Two moving vertices in one quark could belong to the same 16-cell. A 16-cell may have two vertices moving in the same isoclinic square (octagram) orbit, such as an antipodal pair (a rotating dipole), or two vertices moving in different square orbits of the same up+right chirality.{{Efn|There is only one [[16-cell#Helical construction|octagram orbit]] of each chirality in each fibration of the 16-cell, so two octagram orbits of the same chirality cannot be Clifford parallel (part of the same distinct rotation). Two vertices right-moving on different octagram isoclines in the same 16-cell is a combination of two distinct rotations, whose isoclines will intersect: a kinematic rotation. It can be a valid kinematic rotation if the moving vertices will never pass through a point of intersection at the same time. Octagram isoclines pass through all 8 vertices of the 16-cell, and all eight isoclines (the left and right isoclines of four different fibrations) intersect at ''every'' vertex.}} However, the theory of [[W:Color confinement|color confinement]] may not require that two moving vertices in one quark belong to the same 16-cell; like the moving vertices of different quarks, they could be drawn from the disjoint vertex sets of two different 16-cells.}} Minimally, a down quark requires one moving vertex (of the down−left chirality). In these minimal quark configurations, a proton would have 5 moving vertices and a neutron would have 4.

....

=== Nucleons ===
[[File:Symmetrical_5-set_Venn_diagram.svg|thumb|[[W:Branko Grünbaum|Grünbaum's]] rotationally symmetrical 5-set Venn diagram, 1975. It is the [[5-cell]]. Think of it as an [[W:Nuclear magnetic resonance|NMR image]] of the 4-dimensional proton in projection to the plane.]]
The proton is a very stable mass particle. Is there a stable orbit of 5 moving vertices in 4-dimensional Euclidean space? There are few known solutions to the 5-body problem, and fewer still to the [[W:n-body problem|{{mvar|n}}-body problem]], but one is known: the ''central configuration'' of {{mvar|n}} bodies in a space of dimension {{mvar|n}}-1. A [[W:Central configuration|central configuration]] is a system of [[W:Point particle|point masses]] with the property that each mass is pulled by the combined attractive force of the system directly towards the [[W:Center of mass|center of mass]], with acceleration proportional to its distance from the center. Placing three masses in an equilateral triangle, four at the vertices of a regular [[W:Tetrahedron|tetrahedron]], five at the vertices of a regular [[5-cell]], or more generally {{mvar|n}} masses at the vertices of a regular [[W:Simplex|simplex]] produces a central configuration [[W:Central configuration#Examples|even when the masses are not equal]]. In an isoclinic rotation, all the moving vertices orbit at the same radius and the same speed. Therefore if any 5 bodies are orbiting as an isoclinically rotating regular 5-cell (a rigid 4-simplex figure undergoing isoclinic rotation), they maintain a central configuration, describing 5 mutually stable orbits.

Unlike the proton, the neutron is not always a stable particle; a free neutron will decay into a proton. A deficiency of the minimal configurations is that there is no way for this [[W:beta minus decay|beta minus decay]] to occur. The minimal neutron of 4 moving vertices described [[#Color|above]] cannot possibly decay into a proton by losing moving vertices, because it does not possess the four up+right moving vertices required in a proton. This deficiency could be remedied by giving the neutron configuration 8 moving vertices instead of 4: four down−left and four up+right moving vertices. Then by losing 3 down−left moving vertices the neutron could decay into the 5 vertex up-down-up proton configuration.{{Efn|Although protons are very stable, during [[W:stellar nucleosynthesis|stellar nucleosynthesis]] two H&lt;sub&gt;1&lt;/sub&gt; protons are fused into an H&lt;sub&gt;2&lt;/sub&gt; nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus &quot;decay&quot;]] of a proton into a neutron is actually the result of a rare high-energy collision between the two protons, in which a neutron is constructed. With respect to our nucleon configurations of moving vertices, it has to be explained as the conversion of two 5-point 5-cells into a 5-point 5-cell and an 8-point 16-cell, emitting two decay products of at least 1-point each. Thus it must involve the creation of moving vertices, by the conversion of kinetic energy to point-masses.}} A neutron configuration of 8 moving vertices could occur as the 8-point 16-cell, the second-smallest regular 4-polytope after the 5-point 5-cell (the hypothesized proton configuration).

It is possible to double the neutron configuration in this way, without destroying the charge balance that defines the nucleons, by giving down quarks three moving vertices instead of just one: two −left vertices and one +right vertex. The net charge on the down quark remains −{{sfrac|1|3}}, but the down quark becomes heavier (at least in vertex count) than the up quark, as in fact its mass is measured to be.

A nucleon's quark configuration is only a partial specification of its properties. There is much more to a nucleon than what is contained within its three quarks, which contribute only about 1% of the nucleon's energy. The additional 99% of the nucleon mass is said to be associated with the force that binds the three quarks together, rather than being intrinsic to the individual quarks separately. In the case of the proton, 5 moving vertices in the stable orbits of a central configuration (in one of the [[5-cell#Geodesics and rotations|isoclinic rotations characteristic of the regular 5-cell]]) might be sufficient to account for the stability of the proton, but not to account for most of the proton's energy. It is not the point-masses of the moving vertices themselves which constitute most of the mass of the nucleon; if mass is a consequence of geometry, we must look to the larger geometric elements of these polytopes as their major mass contributors. The quark configurations are thus incomplete specifications of the geometry of the nucleons, predictive of only some of the nucleon's properties, such as charge.{{Efn|Notice that by giving the down quark three moving vertices, we seem to have changed the quark model's prediction of the proton's number of moving vertices from 5 to 7, which would be incompatible with our theory that the proton configuration is a rotating regular 5-cell in a central configuration of 5 stable orbits. Fortunately, the actual quark model has nothing at all to say about moving vertices, so we may choose to regard that number as one of the geometric properties the quark model does not specify.}} In particular, they do not account for the forces binding the nucleon together. Moreover, if the rotating regular 5-cell is the proton configuration and the rotating regular 16-cell is the neutron configuration, then a nucleus is a complex of rotating 5-cells and 16-cells, and we must look to the geometric relationship between those two very different regular 4-polytopes for an understanding of the nuclear force binding them together.

The most direct [[120-cell#Relationships among interior polytopes|geometric relationship among stationary regular 4-polytopes]] is the way they occupy a common 3-sphere together. Multiple 16-cells of equal radius can be compounded to form each of the larger regular 4-polytopes, the 8-cell, 24-cell, 600-cell, and 120-cell, but it is noteworthy that multiple regular 5-cells of equal radius cannot be compounded to form any of the other 4-polytopes except the largest, the 120-cell. The 120-cell is the unique intersection of the regular 5-cell and 16-cell: it is a compound of 120 regular 5-cells, and also a compound of 75 16-cells. All regular 4-polytopes except the 5-cell are compounds of 16-cells, but none of them except the largest, the 120-cell, contains any regular 5-cells. So in any compound of equal-radius 16-cells which also contains a regular 5-cell, whether that compound forms some single larger regular 4-polytope or does not, no two of the regular 5-cell's five vertices ever lie in the same 16-cell. So the geometric relationship between the regular 5-cell (our proton candidate) and the regular 16-cell (our neutron candidate) is quite a distant one: they are much more exclusive of each other's elements than they are distantly related, despite their complementary three-quark configurations and other similarities as nucleons. The relationship between a regular 5-cell and a regular 16-cell of equal radius is manifest only in the 120-cell, the most complex regular 4-polytope, which [[120-cell#Geometry|uniquely embodies all the containment relationships]] among all the regular 4-polytopes and their elements.

If the nucleus is a complex of 5-cells (protons) and 16-cells (neutrons) rotating isoclinically around a common center, then its overall motion is a hybrid isoclinic rotation, because the 5-cell and the 16-cell have different characteristic isoclinic rotations, and they have no isoclinic rotation in common.{{Efn|The regular 5-cell does not occur inscribed in any other regular 4-polytope except one, the 600-vertex 120-cell. No two of the 5 vertices of a regular 5-cell can be vertices of the same 16-cell, 8-cell, 24-cell, or 600-cell. The isoclinic rotations characteristic of the regular 5-cell maintain the separation of its 5 moving vertices in 5 disjoint Clifford-parallel subspaces at all times. The [[16-cell#Rotations|isoclinic rotation characteristic of the 16-cell]] maintains the separation of its 8 moving vertices in 2 disjoint Clifford-parallel subspaces (completely orthogonal great square planes) at all times. Therefore, in any hybrid rotation of a concentric 5-cell and 16-cell, at most one 5-cell subspace (containing 1 vertex) might be synchronized with one 16-cell subspace (containing 4 vertices), such that the 1 + 4 vertices they jointly contain occupy the same moving subspace continually, forming a rigid 5-vertex polytope undergoing some kind of rotation. If in fact it existed, this 5-vertex rotating rigid polytope would not be [[5-cell#Geometry|not a 5-cell, since 4 of its vertices are coplanar]]; it is not a 4-polytope but merely a polyhedron, a [[W:square pyramid|square pyramid]].}}

....

=== Nuclides ===

...

=== Quantum phenomena ===

The Bell-Kochen-Specker (BKS) theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a space of three or more dimensions can be given by exhibiting a finite set of lines through the origin that cannot each be colored black or white in such a way that (i) no two orthogonal lines are both black, and (ii) not all members of a set of ''d'' mutually orthogonal lines are white.{{Efn|&quot;The Bell-Kochen-Specker theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a Hilbert space of dimension d ≥ 3 can be given by exhibiting a finite set of rays [9] that cannot each be assigned the value 0 or 1 in such a way that (i) no two orthogonal rays are both assigned the value 1, and (ii) not all members of a set of d mutually orthogonal rays are assigned the value 0.&quot;{{Sfn|Waegell|Aravind|2009|loc=2. The Bell-Kochen-Specker (BKS) theorem}}|name=BKS theorem}}

....

=== Motion ===
What does it mean to say that an object moves through space? Coxeter group theory provides precise answers to questions of this kind. A rigid object (polytope) moves by distinct transformations, changing itself in each discrete step into a congruent object in a different orientation and position.{{Efn|name=transformations}}

....

== Galilean relativity in a space of four orthogonal dimensions ==

Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions.

General relativity is just Galilean relativity in a general space of four orthogonal dimensions, e.g. Euclidean 4-space &lt;math&gt;R^4&lt;/math&gt;, spherical 4-space &lt;math&gt;S^4&lt;/math&gt;, or any orthogonal 4-manifold.

Light is just reflection. Gravity (and all force) is just rotation. Both motions are just group actions, expressions of intrinsic symmetries. That is all of physics.

Every observer properly sees himself as stationary and the universe as a sphere with himself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and it can be measured by the observer as the speed of light.

=== Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions ===
Perspective effects occur because each observer's ordinary 3-dimensional space is only a curved manifold embedded in 4-dimensional Euclidean space, and its curvature complicates the calculations for him (e.g., he sometimes requires Lorentz transformations). But if  all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) except when you want to calculate a projection, or a shadow, that is, how things will appear from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} The universe really has four spatial dimensions, and space and time behave just as they do in classical 3-vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a spacetime to explain 4-dimensional perspective effects at high velocities, because 4-space is already spatially 4-dimensional, and those perspective effects fall out of the 4-dimensional Pythagorean theorem naturally, just as perspective does in three dimensions. The universe is only strange in the ways the Euclidean fourth dimension is strange; but that does hold many surprises for us. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way that 3-space is much more interesting than 2-space. But all Euclidean spaces are dimensionally analogous. Dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries.

=== General relativity is just Galilean relativity in a general space of four orthogonal dimensions ===
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=== Physics ===
....

=== Thoreau's spherical relativity ===
Every observer may properly see himself as stationary and the universe as a 4-sphere with himself at the center observing it, perceptually equidistant from all points on its surface, including his own ''physical'' location which is one of those surface points, distinguished to him but not the center of anything. This statement of the principle of relativity is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's relativity of orthogonal group actions in Euclidean spaces of any number of dimensions.{{Efn|name=transformations}} It should be known as Thoreau's spherical relativity, since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polytopes in any number of dimensions.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassman and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}}]}}

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== Conclusions==

=== Spherical relativity ===

We began our inquiry by wondering why physical space should be limited to just three dimensions (why ''three''). By visualizing the universe as a Euclidian space of four dimensions, we recognize that relativistic and quantum phenomena are natural consequences of symmetry group operations (including reflections and rotations) in four orthogonal dimensions. We should not then be surprised to see that the universe does not have just four dimensions, either. Physical space must bear as many dimensions as we need to ascribe to it, though the distinct phenomena for which we find a need to do so, in order to explain them, seem to be fewer and fewer as we consider higher and higher dimensions. To laws of physics generally, such as the principle of relativity in particular, we should always append the phrase &quot;in Euclidean spaces of any number of dimensions&quot;. Laws of physics should operate in any flat Euclidean space &lt;math&gt;R^n&lt;/math&gt; and in its corresponding spherical space &lt;math&gt;S^n&lt;/math&gt;.

The first and simplest sense in which we are forced to contemplate a fifth dimension is to accommodate our normal idea of time. Just as Einstein was forced to admit time as a dimension, in his four-dimensional spacetime of three spatial dimensions plus time, for some purposes we require a fifth time dimension to accompany our four spatial dimensions, when our purpose is orthogonal to (in the sense of independent of) the four spatial dimensions. For example, if we theorize that we observe a finite homogeneous universe, and that it is a Euclidean 4-space overall, we may prefer not to have to identify any distinct place within that 4-space as the center where the universe began in a big bang. To avoid having to pick a distinct place as the center of the universe, our model of it must be expanded, at least to be a ''spherical'' 4-dimensional space with the fifth radial dimension as time. Essentially, we require the fifth dimension in order to make our homogeneous 4-space finite, by wrapping it around into a 4-sphere. But perhaps we can still resist admitting the fifth radial dimension as a full-fledged Euclidean spatial dimension, at least so long as we have not observed how any naturally occurring object configurations are best described as 5-polytopes.

One phenomenon which resists explanation in a space of just four dimensions is the propagation of light in a vacuum. The propagation of mass-carrying particles is explained as the consequence of their rotations in closed, curved spaces (3-spheres) of finite size, moving through four-dimensional Euclidean space at a universal constant speed, the speed of light. But an apparent paradox remains that light must seemingly propagate through four-dimensional Euclidean space at more than the speed of light. From an ''n''-dimensional viewpoint, this apparent paradox can be resolved, and in retrospect it is clear how massless particles can translate through four-dimensional space at twice the speed constant, since they are not simultaneously rotating.

Another phenomenon justifying a five-dimensional view of space is the relation between the the 5-cell proton and the 16-cell neutron (the 4-simplex and 4-orthoplex polytopes). Their indirect relationship can be observed in the 4-600-point polytope (the 120-cell), and in its 11-cells,{{Sfn|Christie|2025|loc=&quot;A symmetrical arrangement of eleven 11-cells&quot;}} but it is only directly observed (absent a 120-cell) in a five-dimensional reference frame.

=== Nuclear geometry ===
We have seen how isoclinic rotations (Clifford displacements) relate the orbits in the atomic nucleus to each other, just as they relate the regular convex 4-polytopes to each other, in a sequence of nested objects of increasing complexity. We have identified the proton as a  5-point, 5-cell 4-simplex 𝜶&lt;sub&gt;4&lt;/sub&gt;, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽&lt;sub&gt;4&lt;/sub&gt;, and the shell of the atomic nucleus as a 24-point 24-cell. As Coxeter noted, that unique 24-point object stands quite alone in four dimensions, having no analogue above or below.

=== Atomic geometry ===
I'm on a plane flying to Eugene to visit Catalin, we'll talk after I arrive. I've been working on both my unpublished papers, the one going put for pre-publication review soon about 4D geometry, and the big one not going out soon about the 4D sun, 4D atoms, and 4D galaxies and n-D universe. I'vd just added the following paragraph to that big paper:

Atomic geometry

The force binding the protons and neutrons of the nucleus together into a distinct element is specifically an expression of the 11-cell 4-polytope, itself an expression of the pyritohedral symmetry, which binds the distinct 4-polytopes to each other, and relates the n-polytopes to their neighbors of different n by dimensional analogy.


flying over mt shasta out my right-side window at the moment, that last text showing &quot;not delivered&quot; yet because there's no wifi on this plane, gazing at that great peak of the world and feeling as if i've just made the first ascent of it

=== Molecular geometry ===
Molecules are 3-dimensional structures that live in the thin film of 3-membrane only one atom thick in most places that is our ordinary space, but since that is a significantly curved 3-dimensional space at the scale of a molecule, the way the molecule's covalent bonds form is influenced by the local curvature in 4-dimensions at that point.

In the water molecule, there is a reason why the hydrogen atoms are attached to the oxygen atom at an angle of 104.45° in 3-dimensional space, and at root it must be the same symmetry that locates any two of the hydrogen proton's five vertices 104.45° apart on a great circle arc of its tiny 3-sphere.

=== Cosmology ===

==== Solar systems ====

===== Stars =====
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===== The Kepler problem =====
In the proper reference frame of some hypothetical observer in 4-dimensional Euclidean space, the Kepler problem has a solution in which all the planetary orbits are circles. This occurs because all bodies are always orbiting, each in some distinct isoclinic (equi-angled double) rotation. All atoms are rotating isoclinically at (double) the velocity &lt;math&gt;c&lt;/math&gt;. In the observer's proper reference frame, the isoclinic double rotation of each of his own atoms is most conveniently represented as an equivalent screw displacement: a linear translation at velocity &lt;math&gt;c&lt;/math&gt; (along the observer's proper time axis through 4-space), combined with a simple rotation at velocity &lt;math&gt;c&lt;/math&gt; (of the atom internally). 

This representation, though proper, is subject to the over-simplification of special relativity, because it ignores the fact that the observer is himself moving on some circular orbit; he is not linearly translating through 4-space. When the observer's own orbit is also represented, the screw displacement becomes an elliptical double rotation, with a very slow, very large-radius simple circular orbit (almost a linear translation), combined with a very fast, very small-radius simple circular orbit of each atom internally. This is the observer's proper reference frame according to general relativity.

An observer moving differently will perceive the motion of the observer and his atoms to be a different elliptical double rotation. We can find a proper reference frame, of some hypothetical observer moving hypothetically, in which the ratio of the radii of the two orthogonal rotations of the atom becomes any value we choose between 1 and &lt;math&gt;c&lt;/math&gt;. In particular there exists, conceptually accessible to all observers independent of their motion, a distinct reference frame in which an atom is stationary, rotating isoclinically at (double) the velocity &lt;math&gt;c&lt;/math&gt;. That is simply the stationary reference frame of the atom itself, such as the stationary reference frame of any observer and his own atoms. In 3-dimensional physics, it is known as the observer's proper inertial reference frame. But in 4-dimensional physics, that is ''not'' the most convenient or sensible reference frame in which to consider objects moving differently, in different proper reference frames. In 4-dimensional physics, a reference frame in which an observer and his atoms are translating linearly at velocity &lt;math&gt;c&lt;/math&gt; is known as the observer's proper inertial reference frame. Any such proper reference frame makes a great deal more sense for the purpose of considering the motion of objects moving differently in 4-space, just as a heliocentric solar system makes a great deal more sense than a geocentric solar system for the purpose of considering the motion of the planets.

...

==== Galaxies ====

The spacetime of general relativity is often illustrated as a projection to a curved 2D surface in which large gravitational objects make gravity wells or dimples in the surface. In the Euclidean 4D view of the universe the 3D surface of a large cosmic object such as a galaxy surrounds an empty 4D space, and large gravitational objects within the galaxy must make dimples in its surface. But should we see them as dimples exactly? Would they dimple inwards or outwards? In the spacetime illustrations they are naturally always shown as dimpling downwards, which is somewhat disingenuous, strongly suggesting to the viewer that the reason for gravity is that it flows downhill - the original tautology we are trying to surmount! In the Euclidean 4D galaxy the dimple, if it is one, must be either inward or outward, and which it is matters since the dimple is flying outward at velocity {{mvar|c}}. The galaxy is not collapsing inward. Is a large gravitational mass (such as a star) ''ahead'' of the smaller masses orbiting around it (such as its planets), or is it ''behind'' them, as they fly through 4-space on their Clifford parallel trajectories? The answer is ''both'' of course, because a star is not a dimple, it is a 4-ball, and it dimples the 3D surface both inwards and outwards. It is a thick place in the 3D surface. We should view it as having its gravitational center precisely at the surface of the expanding 3-sphere. 

What is a black hole? It is the hollow four-dimensional space that a galaxy is the three-dimensional surface of.

When we view another galaxy, such as Andromeda, we are seeing that whole galaxy from a distance, the way the moon astronauts looked back at the whole earth. We see our own milky way galaxy from where we are on its surface, the way we see the earth from its surface, except that the earth is solid, but the galaxy is hollow and transparent. We can look across its empty center and see all the other stars also on its surface, including those opposite ours on the far side of its 3-sphere. The thicker band of stars we see in our night sky and identify as the milky way is not our whole galaxy; the majority of the other visible stars also lie in our galaxy. That dense band is not thicker and brighter than other parts of our galaxy because it lies toward a dense galactic center (our galaxy has an empty center), but for exactly the opposite reason: those apparently more thickly clustered stars lie all around us on the galaxy's surface, in the nearest region of space surrounding us. They appear to be densely packed only because we are looking at them &quot;edge on&quot;. Actually, we are looking into this nearby apparently dense region ''face on'', not edge on, because we are looking at a round sphere of space surrounding us, not a disk. In contrast, stars in our galaxy outside that bright band lie farther off from us, across the empty center of the galaxy, and we see them spread out as they actually are, instead of &quot;edge on&quot; so they appear to be densely clustered. The &quot;dense band&quot; covers only an equatorial band of the night sky instead of all the sky, because when we look out into the four-dimensional space around us, we can see stars above and below our three-dimensional hyperplane in our four-dimensional space. Everything in our solar system lies in our hyperplane, and the nearby stars around us in our galaxy are near our hyperplane (just slightly below it). All the other, more distant stars in our galaxy are also below our hyperplane. We can see objects outside our galaxy, such as other galaxies, both above and below our hyperplane. We can see all around us above our hyperplane (looking up from the galactic surface into the fourth dimension), and all around us below our hyperplane (looking down through our transparent galaxy and out the other side).

== Revolutions ==
The original Copernican revolution displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the stars remaining on a fixed sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

In such fashion the Euclidean four-dimensional viewpoint initially lends itself to a big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the stars need not be equidistant from a single origin in time, any more than they all lie in the same galaxy, equidistant from its center in space. The expanding sphere of matter on the surface of which we find ourselves living might be one of many such spheres, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe.

When we look up at the heavens, we have no obvious way of knowing whether the space we are looking into is a curved 3-spherical one or a flat 4-space. In this work we suggest a theory of how light travels that says we can see into all four dimensions, and so when we look up at night we see cosmological objects distributed in 4-dimensional space, and not all located on our own 3-spherical membrane. The view from our solar system suggests that our galaxy is its own hollow 3-sphere, and that galaxies generally are single roughly spherical 3-membranes, with the smaller objects within them all lying on that same 3-spherical surface, equidistant from the galaxy center in 4-space. 

The Euclidean four-dimensional viewpoint requires that all mass-carrying objects are in motion at constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Since their paths away from their origin are not straight lines but various helical isoclines, their 3-sphere will be expanding radially at slightly less than the constant velocity &lt;math&gt;c&lt;/math&gt;. The view from our solar system does ''not'' suggest that each galaxy is its own distinct 3-sphere expanding at this great rate; rather, the standard theory has been that the entire observable universe is expanding from a single big bang origin in time. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also allows theories which require no single origin point in space and time.

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and we have not slowed down since.

== Origins of the theory ==
Einstein himself was one of the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean sphere, in what was narrowly the first written articulation of the principle of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below). Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from his perspective; the forthshortenings, clock desynchronizations and other Lorentz transformations it predicts are exact calculations of actual perspective effects; but space is actually a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean 4-dimensional theory differs from the standard theory in being a description of the physical universe in terms of a geometry of four or more orthogonal spatial dimensions, rather than in the standard theory's terms of the [[w:Minkowski spacetime|Minkowski spacetime]] geometry (in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions). The invention of geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years. It was first worked out by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] around 1850. Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''polyscheme'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he discovered all the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the six convex regular polyschemes which can be constructed in a Euclidean space of four dimensions (a set analogous to the five [[w:Platonic solid|Platonic solids]] in three dimensional space). Thus he was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover all its astonishing regular objects. Because most of his work remained almost completely unknown until it was published posthumously in 1901, other researchers had more than fifty years to rediscover the regular polyschemes, and competing terms were coined; today [[W:Alicia Boole Stott|Alicia Boole Stott]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme''.{{Efn|Today Schläfli's original ''polyscheme'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}}

== Boundaries ==
&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schlafli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it, is that there ''is'' a boundary between three and four dimensions. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our world apparently only three dimensional? Why would it have ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schlafli mapped? What is the nature of the boundary which confines us to just three? 

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way by receiving light signals that traveled to us on straight lines through it. The reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creates, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not surprise us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schlafli discovered something else: all the astonishing regular objects that exist in higher dimensions. So this conception now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and not a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation?

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that our universe is properly a Euclidean space of four orthogonal spatial dimensions. Others will have to work out the physics and do the math, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are 4-dimensionally circular, but not all isoclines on 3-manifolds in 4-space are perfectly circular.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point.{{Sfn|Tyrrell|Semple|1971|loc=§3. Clifford's original definition of parallelism|pp=5-6}} A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the 2-sphere will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect; various sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. Perhaps the simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles.{{Efn|name=six orthogonal planes of the Cartesian basis}} Each completely orthogonal pair is Clifford parallel. The two circles cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 3-sphere.{{Efn|name=only some Clifford parallels are orthogonal}} Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]].|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Notelist|40em}}

== Citations ==
{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

{{Reflist|40em}}

== References ==
{{Refbegin}}
* {{Cite book | last=Kepler | first=Johannes | author-link=W:Johannes Kepler | title=Harmonices Mundi (The Harmony of the World) | title-link=W:Harmonices Mundi | publisher=Johann Planck | year=1619}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston}}
* {{Cite book | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1973 | orig-year=1948 | title=Regular Polytopes | publisher=Dover | place=New York | edition=3rd | title-link=W:Regular Polytopes (book) }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1991 | title=Regular Complex Polytopes | place=Cambridge | publisher=Cambridge University Press | edition=2nd }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1995 | title=Kaleidoscopes: Selected Writings of H.S.M. Coxeter | publisher=Wiley-Interscience Publication | edition=2nd | isbn=978-0-471-01003-6 | url=https://archive.org/details/kaleidoscopessel0000coxe | editor1-last=Sherk | editor1-first=F. Arthur | editor2-last=McMullen | editor2-first=Peter | editor3-last=Thompson | editor3-first=Anthony C. | editor4-last=Weiss | editor4-first=Asia Ivic | url-access=registration }}
** (Paper 3) H.S.M. Coxeter, ''Two aspects of the regular 24-cell in four dimensions''
** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10]
** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', [Math. Zeit. 188 (1985) 559-591]
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
* {{Cite journal | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1989 | title=Trisecting an Orthoscheme | journal=Computers Math. Applic. | volume=17 | issue=1-3 | pp=59-71 }}
* {{Cite journal|last=Stillwell|first=John|author-link=W:John Colin Stillwell|date=January 2001|title=The Story of the 120-Cell|url=https://www.ams.org/notices/200101/fea-stillwell.pdf|journal=Notices of the AMS|volume=48|issue=1|pages=17–25}}
* {{Cite book | last1=Conway | first1=John H. | author-link1=W:John Horton Conway | last2=Burgiel | first2=Heidi | last3=Goodman-Strauss | first3=Chaim | author-link3=W:Chaim Goodman-Strauss | year=2008 | title=The Symmetries of Things | publisher=A K Peters | place=Wellesley, MA | title-link=W:The Symmetries of Things }}
* {{Cite journal|last1=Perez-Gracia|first1=Alba|last2=Thomas|first2=Federico|date=2017|title=On Cayley's Factorization of 4D Rotations and Applications|url=https://upcommons.upc.edu/bitstream/handle/2117/113067/1749-ON-CAYLEYS-FACTORIZATION-OF-4D-ROTATIONS-AND-APPLICATIONS.pdf|journal=Adv. Appl. Clifford Algebras|volume=27|pages=523–538|doi=10.1007/s00006-016-0683-9|hdl=2117/113067|s2cid=12350382|hdl-access=free}}
* {{Cite arXiv | eprint=1903.06971 | last=Copher | first=Jessica | year=2019 | title=Sums and Products of Regular Polytopes' Squared Chord Lengths | class=math.MG }}
* {{Cite thesis|url= http://resolver.tudelft.nl/uuid:dcffce5a-0b47-404e-8a67-9a3845774d89 |title=Symmetry groups of regular polytopes in three and four dimensions|last=van Ittersum |first=Clara|year=2020|publisher=[[W:Delft University of Technology|Delft University of Technology]]}}
* {{cite arXiv|last1=Kim|first1=Heuna|last2=Rote|first2=G.|date=2016|title=Congruence Testing of Point Sets in 4 Dimensions|class=cs.CG|eprint=1603.07269}}
* {{cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|year=2013|publisher=DUTTON Penguin Group|isbn=978-0-525-95366-1}}
* {{Cite journal|last1=Waegell|first1=Mordecai|last2=Aravind|first2=P. K.|date=2009-11-12|title=Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem|journal=Journal of Physics A: Mathematical and Theoretical|volume=43|issue=10|page=105304|language=en|doi=10.1088/1751-8113/43/10/105304|arxiv=0911.2289|s2cid=118501180}}
* {{Cite book|title=Generalized Clifford parallelism|last1=Tyrrell|first1=J. A.|last2=Semple|first2=J.G.|year=1971|publisher=[[W:Cambridge University Press|Cambridge University Press]]|url=https://archive.org/details/generalizedcliff0000tyrr|isbn=0-521-08042-8}}
* {{Cite journal | last1=Mamone|first1=Salvatore | last2=Pileio|first2=Giuseppe | last3=Levitt|first3=Malcolm H. | year=2010 | title=Orientational Sampling Schemes Based on Four Dimensional Polytopes | journal=Symmetry | volume=2 | pages=1423-1449 | doi=10.3390/sym2031423 }}
* {{Cite journal|last=Dorst|first=Leo|title=Conformal Villarceau Rotors|year=2019|journal=Advances in Applied Clifford Algebras|volume=29|issue=44|url=https://doi.org/10.1007/s00006-019-0960-5}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}}
*{{Citation | last=Goucher | first=A.P. | title=Spin groups | date=19 November 2019 | journal=Complex Projective 4-Space | url=https://cp4space.hatsya.com/2012/11/19/spin-groups/ }}
* {{Citation|last=Christie|first=David Brooks|author-link=User:Dc.samizdat|year=2025|title=A symmetrical arrangement of eleven 11-cells|title-link=User:Dc.samizdat/A symmetrical arrangement of eleven 11-cells|journal=Wikiversity}}
{{Refend}}</text>
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      <text bytes="108761" sha1="bilj1i8ill5mafn8gslddxh2yiwczss" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|June 2023 - June 2025}}

&lt;blockquote&gt;'''Abstract:''' The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. A typical galaxy such as ours is a hollow [[w:3-sphere|4-dimensional 3-sphere]] with these objects distributed on its 3-dimensional surface. The black hole at the galaxy's center is nothing: the 4-ball of empty space they surround. Objects in our galaxy occupy this thin 3-dimensional surface, forming a filmy 4-dimensional soap-bubble of galactic size, thicker than an atom only in the interior of stars. Mass is confined to this 3-dimensional manifold by its inertia, also called gravity, the property of its ceaseless motion at a constant, universal velocity &lt;math&gt;c&lt;/math&gt;, the rate of causality at which the universe evolves. Atoms are always internally in inertial rotational motion, and externally in inertial translational motion through 4-space, at this universal rate of transformation. The observed universe appears to be a 3-sphere expanding radially from a central origin point at velocity &lt;math&gt;c&lt;/math&gt;, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light through 3-space as measured by all observers. All objects with mass move through 4-space at velocity &lt;math&gt;c&lt;/math&gt; as long as they exist, and acceleration only varies their direction. The propagation speed of light measured on a straight line through Euclidean 4-space is &lt;math&gt;c^\prime = 2c&lt;/math&gt;, so we can see in 4 dimensions, even though we are physically confined to a moving 3-dimensional manifold, where our direction of motion through 4-space is our proper time dimension. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at velocity &lt;math&gt;c&lt;/math&gt;. This model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries.&lt;/blockquote&gt;

== Symmetries ==
It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway|Burgiel|Goodman-Strauss|2008}}

As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. 

[[W:Coxeter group|Coxeter group]] theory did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups and obey the principle of relativity. As I understand Coxeter theory (which is not mathematically),{{Efn|Coxeter's formulation of the motions (congruent transformations) possible in an ''n''-dimensional Euclidean space:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}
&lt;blockquote&gt;Let Q denote a rotation, R a reflection, T a translation, and let Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T denote a product of several such transformations, all commutative with one another. Then RT is a glide-reflection (in two or three dimensions), QR is a rotary-reflection, QT is a screw-displacement, and Q&lt;sup&gt;2&lt;/sup&gt; is a double rotation (in four dimensions).&lt;br&gt;
Every orthogonal transformation is expressible as:&lt;br&gt;
{{spaces|10}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt;&lt;br&gt;
where 2''q'' + ''r'' ≤ ''n'', the number of dimensions.&lt;br&gt;
Transformations involving a translation are expressible as:&lt;br&gt;
{{spaces|10}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T&lt;br&gt;
where 2''q'' + ''r'' + 1 ≤ ''n''.&lt;br&gt;
For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q&lt;sup&gt;2&lt;/sup&gt;, or a screw-displacement QT (where the rotation component Q is a simple rotation). Every enantiomorphous transformation in 4-space (reversing chirality) is a QRT.&lt;/blockquote&gt;
If we assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a Q&lt;sup&gt;2&lt;/sup&gt; or a QT, because we can view any QT as a Q&lt;sup&gt;2&lt;/sup&gt; in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a Q&lt;sup&gt;2&lt;/sup&gt;. By the same principle, we can view any QT or Q&lt;sup&gt;2&lt;/sup&gt; as an isoclinic (equi-angled) Q&lt;sup&gt;2&lt;/sup&gt; by appropriate choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]]. The distinct symmetry groups of the regular polytopes each correspond to their characteristic isoclinic rotations. These isoclinic rotations are distinguished in geometry, relativity, and quantum mechanics.|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to relativity, in that we can only exchange the translation (T) for ''one'' of the two rotations (Q). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation up to uncertainty, and can always distinguish the direction of his own proper time arrow.|name=transformations}} the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic rather than algebraic methods), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional objects, and nature can be understood in terms of their [[W:group action|group actions]], including centrally [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]].

== Special relativity describes Euclidean 4-dimensional space ==
&lt;blockquote&gt;Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.{{Sfn|Goldberg|2013|loc=§10. Hidden Symmetries: Why some symmetries but not others?|p=264}}&lt;/blockquote&gt;

...cite Yamashita{{Sfn|Yamashita|2023}}

=== Minkowski spacetime and Euclidean 4-space in relativity ===
...

Is there a configuration in Euclidean space where every observer, and every observed object, is moving at velocity &lt;math&gt;c&lt;/math&gt;? Yes, there is one such configuration, in 4-dimensional Euclidean space. This configuration must be like the one described above, in our ''Abstract''.

== The rate of atomic symmetry operations ==
...

== General relativity describes a curved 3-dimensional manifold embedded in Euclidean 4-dimensional space ==
...

== The geometry of the atomic nucleus ==

In [[W:Euclidean 4-space|Euclidean four dimensional space]], an [[W:atomic nucleus|atomic nucleus]] is a one or more concentric 4-polytopes of increasing radius. Each concentric shell is a single or compound [[24-cell]], the regular 4-polytope with [[W:Coxeter group#Symmetry groups of regular polytopes|𝔽&lt;sub&gt;4&lt;/sub&gt; symmetry]]. Nuclear shells are concentric [[W:3-sphere|3-sphere]]s occupied (fully or partially) by the orbits of this 24-point [[#The 6 regular convex 4-polytopes|regular convex 4-polytope]]. An actual atomic nucleus is a rotating four dimensional object. It is not a ''rigid'' rotating object, it is a kinematic one, because the nucleus of an actual atom of a distinct [[W:nucleon number|nucleon number]] contains a distinct number of orbiting 24-cell vertices which may be in different isoclinic rotational orbits. These moving vertices never describe a compound of static 24-cells at any single instant in time, though their orbits do all the time. The physical configuration of a nucleus as concentric 24-cells can be reduced to the [[W:kinematics|kinematics]] of the orbits of its constituent protons and neutrons. The geometry of the atomic nucleus is therefore strictly [[W:Euclidean geometry#19th century|Euclidean]] in four dimensional space.

=== Rotations ===
The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out.

This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a precise [[24-cell|detailed description]] enabling the reader to properly visualize it runs to many pages and illustrations, with many accompanying pages of explanatory notes on basic phenomena that arise only in 4-dimensional space: [[24-cell#Squares|completely orthogonal planes]], [[24-cell#Hexagons|Clifford parallelism]] and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Helical hexagrams and their isoclines|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a surprise. [[#The 6 regular convex 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120, and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (generally), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It is much harder for us to visualize, because the only way we can experience it is in our imaginations; we have no body of sensory experience in 4-dimensional space to draw upon.

For that reason, descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than a single rigid 24-cell. 

To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with any other at any time.

That is still an example of a rigid object in a single distinct isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing the characteristic rotation of the 24-cell. But we can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same shell without collisions? In adjacent shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore questions of this kind of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[W:kinetics|kinetics]].

=== Isospin ===
A [[W:Nucleon|nucleon]] is a [[W:proton|proton]] or a [[W:neutron|neutron]]. The proton carries a positive net [[W:Electric charge|charge]], and the neutron carries a zero net charge. The proton's [[W:Mass|mass]] is only about 0.13% less than the neutron's, and since they are observed to be identical in other respects, they can be viewed as two states of the same nucleon, together forming an isospin doublet ({{nowrap|''I'' {{=}} {{sfrac|1|2}}}}). In isospin space, neutrons can be transformed into protons and conversely by actions of the [[W:SU(2)|SU(2)]] symmetry group. In nature, protons are very stable (the most stable particle known); a proton and a neutron are a stable nuclide; but free neutrons decay into protons in about 10 or 15 seconds.

According to the [[W:Noether theorem|Noether theorem]], [[W:Isospin|isospin]] is conserved with respect to the [[W:strong interaction|strong interaction]].&lt;ref name=Griffiths2008&gt;{{cite book |author=Griffiths, David J. |title=Introduction to Elementary Particles |edition=2nd revised |publisher=WILEY-VCH |year=2008 |isbn=978-3-527-40601-2}}&lt;/ref&gt;{{rp|129–130}} Nucleons are acted upon equally by the strong interaction, which is invariant under rotation in isospin space.

Isospin was introduced as a concept in 1932 by [[W:Werner Heisenberg|Werner Heisenberg]],&lt;ref&gt;
{{cite journal
 |last=Heisenberg |first=W. |author-link=W:Werner Heisenberg
 |year=1932
 |title=Über den Bau der Atomkerne
 |journal=[[W:Zeitschrift für Physik|Zeitschrift für Physik]]
 |volume=77 |issue=1–2 |pages=1–11
 |doi=10.1007/BF01342433
 |bibcode = 1932ZPhy...77....1H
 |s2cid=186218053
 |language=de}}&lt;/ref&gt; well before the 1960s development of the [[W:quark model|quark model]], to explain the symmetry of the proton and the then newly discovered neutron. Heisenberg introduced the concept of another conserved quantity that would cause the proton to turn into a neutron and vice versa. In 1937, [[W:Eugene Wigner|Eugene Wigner]] introduced the term &quot;isospin&quot; to indicate how the new quantity is similar to spin in behavior, but otherwise unrelated.&lt;ref&gt;
{{cite journal
 |last=Wigner |first=E. |author-link=W:Eugene Wigner
 |year=1937
 |title=On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei
 |journal=[[W:Physical Review|Physical Review]]
 |volume=51
 |pages=106–119
 |doi=10.1103/PhysRev.51.106
 |bibcode = 1937PhRv...51..106W
 |issue=2
}}&lt;/ref&gt; Similar to a spin-1/2 particle, which has two states, protons and neutrons were said to be of isospin 1/2. The proton and neutron were then associated with different isospin projections ''I''&lt;sub&gt;3&lt;/sub&gt;&amp;nbsp;=&amp;nbsp;+1/2 and −1/2 respectively.

Isospin is a different kind of rotation entirely than the ordinary spin which objects undergo when they rotate in three-dimensional space. Isospin does not correspond to a [[W:Rotations in 4-dimensional Euclidean space#Simple rotations|simple rotation]] in any space (of any number of dimensions). However, it does seem to correspond exactly to an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]] in a Euclidean space of four dimensions. Isospin space resembles the [[W:3-sphere|3-sphere]], the [[W:Elliptical space#Elliptic space (the 3D case)|curved 3-dimensional space]] that is the surface of a [[W:4-ball (mathematics)#In Euclidean space|4-dimensional ball]].

=== Spinors ===
[[File:Spinor on the circle.png|thumb|upright=1.5|A spinor visualized as a vector pointing along the [[W:Möbius band|Möbius band]], exhibiting a sign inversion when the circle (the &quot;physical system&quot;) is continuously rotated through a full turn of 360°.]][[W:Spinors|Spinors]] are [[W:representation of a Lie group|representations]] of a [[W:spin group|spin group]], which are [[W:Double covering group|double cover]]s of the [[W:special orthogonal group|special orthogonal groups]]. The spin group Spin(4) is the double cover of [[W:SO(4)|SO(4)]], the group of rotations in 4-dimensional Euclidean space. [[600-cell#Fibrations of isocline polygrams|Isoclines]], the helical geodesic paths followed by points under isoclinic rotation, correspond to spinors representing Spin(4).

Spinors can be viewed as the &quot;square roots&quot; of [[W:Section (fiber bundle)|cross sections]] of [[W:vector bundle|vector bundle]]s; in this correspondence, a fiber bundle of isoclines (of a distinct isoclinic rotation) is a cross section (inverse bundle) of a fibration of great circles (in the invariant planes of that rotation).

A spinor can be visualized as a moving vector on a Möbius strip which transforms to its negative when continuously rotated through 360°, just as [[24-cell#Helical hexagrams and their isoclines|an isocline can be visualized as a Möbius strip]] winding twice around the 3-sphere, during which [[24-cell#Isoclinic rotations|720° isoclinic rotation]] the rigid 4-polytope turns itself inside-out twice.{{Sfn|Goucher|2019|loc=Spin Groups}} Under isoclinic rotation, a rigid 4-polytope is an isospin-1/2 object with two states.

=== Isoclinic rotations in the nucleus ===
Isospin is regarded as a symmetry of the strong interaction under the [[W:Group action (mathematics)|action]] of the [[W:Lie group|Lie group]] [[W:SU(2)|SU(2)]], the two [[W:eigenstate|states]] being the [[W:Up quark|up flavour]] and [[W:Down quark|down flavour]]. A 360° isoclinic rotation of a rigid [[W:nuclide|nuclide]] would transform its protons into neutrons and vice versa, exchanging the up and down flavours of their constituent [[W:quarks|quarks]], by turning the nuclide and all its parts inside-out (or perhaps we should say upside-down). Because we never observe this, we know that the nucleus is not a ''rigid'' polytope undergoing isoclinic rotation.

If the nucleus ''were'' a rigid object, nuclides that were isospin-rotated 360° would be isoclinic mirror images of each other, isospin +1/2 and isospin −1/2 states of the whole nucleus. We don't see whole nuclides rotating as a rigid object, but considering what would happen if they ''were'' rigid tells us something about the geometry we must expect inside the nucleons. One way that an isospin-rotated neutron could become a proton would be if the up quark and down quark were a left and right mirror-image pair of the same object; exchanging them in place would turn each down-down-up neutron into an up-up-down proton. But the case cannot be quite that simple, because the up quark and the down quark are not mirror-images of the same object: they have very different mass and other incongruities.

Another way an isospin-rotated neutron could be a proton would be if the up and down quarks were asymmetrical kinematic polytopes (not indirectly congruent mirror-images, and not rigid polytopes), rotating within the nucleus in different ''hybrid'' orbits. By that we mean that they may have vertices orbiting in rotations characteristic of more than one 4-polytope, so they may change shape as they rotate. In that case their composites (protons and neutrons) could have a symmetry not manifest in their components, but emerging from their combination.

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=== Hybrid isoclinic rotations ===
The 24-cell has [[24-cell#Isoclinic rotations|its own characteristic isoclinic rotations]] in 4 Clifford parallel hexagonal planes (each intersecting 6 vertices), and also inherits the [[16-cell#Rotations|characteristic isoclinic rotations of its 3 Clifford parallel constituent 16-cells]] in 6 Clifford parallel square planes (each intersecting 4 vertices). The twisted circular paths followed by vertices in these two different kinds of rotation have entirely different geometries. Vertices rotating in hexagonal invariant planes follow [[24-cell#Helical hexagrams and their isoclines|helical geodesic curves whose chords form hexagrams]], and vertices rotating in square invariant planes follow [[24-cell#Helical octagrams and their isoclines|helical geodesic curves whose chords form octagrams]].

In a rigid isoclinic rotation, ''all'' the [[24-cell#Geodesics|great circle polygons]] move, in any kind of rotation. What distinguishes the hexagonal and square isoclinic rotations is the invariant planes of rotation the vertices stay in. The rotation described [[#Rotations|above]] (of 8 vertices rotating in 4 Clifford parallel hexagonal planes) is a single hexagonal isoclinic rotation, not a kinematic or hybrid rotation.

A ''kinematic'' isoclinic rotation in the 24-cell is any subset of the 24 vertices rotating through the same angle in the same time, but independently with respect to the choice of a Clifford parallel set of invariant planes of rotation and the chirality (left or right) of the rotation. A ''hybrid'' isoclinic rotation combines moving vertices from different kinds of isoclinic rotations, characteristic of different regular 4-polytopes. For example, if at least one vertex rotates in a square plane and at least one vertex rotates in a hexagonal plane, the kinematic rotation is a hybrid rotation, combining rotations characteristic of the 16-cell and characteristic of the 24-cell.

As an example of the simplest hybrid isoclinic rotation, consider a 24-cell vertex rotating in a square plane, and a second vertex, initially one 24-cell edge-length distant, rotating in a hexagonal plane. Rotating isoclinically at the same rate, the two moving vertices will never collide where their paths intersect, so this is a ''valid'' hybrid rotation.

To understand hybrid rotations in the 24-cell more generally, visualize the relationship between great squares and great hexagons. The [[24-cell#Squares|18 great squares]] occur as three sets of 6 orthogonal great squares,{{Efn|name=six orthogonal planes of the Cartesian basis}} each [[16-cell#Coordinates|forming a 16-cell]]. The three 16-cells are completely disjoint{{Efn|name=completely disjoint}} and [[24-cell#Clifford parallel polytopes|Clifford parallel]]: each has its own 8 vertices (on 4 orthogonal axes) and its own 24 edges (of length {{radic|2}}).{{Efn|name=three isoclinic 16-cells}} The 18 square great circles are crossed by 16 hexagonal great circles; each [[24-cell#Hexagons|hexagon]] has one axis (2 vertices) in each 16-cell.{{Efn|name=non-orthogonal hexagons}} The two [[24-cell#Triangles|great triangles]] inscribed in each great hexagon (occupying its alternate vertices, with edges that are its {{radic|3}} chords) have one vertex in each 16-cell. Thus ''each great triangle is a ring linking three completely disjoint great squares, one from each of the three completely disjoint 16-cells''.{{Efn|There are four different ways (four different ''fibrations'' of the 24-cell) in which the 8 vertices of the 16-cells correspond by being triangles of vertices {{radic|3}} apart: there are 32 distinct linking triangles. Each ''pair'' of 16-cells forms a tesseract (8-cell).{{Efn|name=three 16-cells form three tesseracts}} Each great triangle has one {{radic|3}} edge in each tesseract, so it is also a ring linking the three tesseracts.|name=great linking triangles}} Isoclinic rotations take the elements of the 4-polytope to congruent [[24-cell#Clifford parallel polytopes|Clifford parallel elements]] elsewhere in the 4-polytope. The square rotations do this ''locally'', confined within each 16-cell: for example, they take great squares to other great squares within the same 16-cell. The hexagonal rotations act ''globally'' within the entire 24-cell: for example, they take great squares to other great squares in ''different'' 16-cells. The [[16-cell#Helical construction|chords of the square rotations]] bind the 16-cells together internally, and the [[24-cell#Helical hexagrams and their isoclines|chords of the hexagonal rotations]] bind the three 16-cells together.

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=== Color ===
When the existence of quarks was suspected in 1964, [[W:Oscar W. Greenberg|Greenberg]] introduced the notion of color charge to explain how quarks could coexist inside some [[W:hadron|hadron]]s in [[W:quark model#The discovery of color|otherwise identical quantum states]] without violating the [[W:Pauli exclusion principle|Pauli exclusion principle]]. The modern concept of [[W:color charge|color charge]] completely commuting with all other charges and providing the strong force charge was articulated in 1973, by [[W:William A. Bardeen|William Bardeen]], [[W:de:Harald Fritzsch|Harald Fritzsch]], and [[W:Murray Gell-Mann|Murray Gell-Mann]].&lt;ref&gt;{{cite conference |author1=Bardeen, W. |author2=Fritzsch, H. |author3=Gell-Mann, M. |year=1973 |title=Light cone current algebra, ''π''&lt;sup&gt;0&lt;/sup&gt; decay, and ''e''&lt;sup&gt;+&lt;/sup&gt; ''e''&lt;sup&gt;&amp;minus;&lt;/sup&gt; annihilation |arxiv=hep-ph/0211388 |editor=Gatto, R. |book-title=Scale and conformal symmetry in hadron physics |page=[https://archive.org/details/scaleconformalsy0000unse/page/139 139] |publisher=[[W:John Wiley &amp; Sons|John Wiley &amp; Sons]] |isbn=0-471-29292-3 |bibcode=2002hep.ph...11388B |url-access=registration |url=https://archive.org/details/scaleconformalsy0000unse/page/139 }}&lt;/ref&gt;&lt;ref&gt;{{cite journal |title=Advantages of the color octet gluon picture |journal=[[W:Physics Letters B|Physics Letters B]] |volume=47 |issue=4 |page=365 |year=1973 |last1=Fritzsch |first1=H. |last2=Gell-Mann |first2=M. |last3=Leutwyler |first3=H. |doi=10.1016/0370-2693(73)90625-4 |bibcode=1973PhLB...47..365F |citeseerx=10.1.1.453.4712}}&lt;/ref&gt;

Color charge is not [[W:electric charge|electric charge]]; the whole point of it is that it is a quantum of something different. But it is related to electric charge, through the way in which the three different-colored quarks combine to contribute fractional quantities of electric charge to a nucleon. As we shall see, color is not really a separate kind of charge at all, but a partitioning of the electric charge into [[24-cell#Clifford parallel polytopes|Clifford parallel subspaces]].

The [[W:Color charge#Red, green, and blue|three different colors]] of quark charge might correspond to three different 16-cells, such as the three disjoint 16-cells inscribed in the 24-cell. Each color might be a disjoint domain in isospin space (the space of points on the 3-sphere).{{Efn|The 8 vertices of each disjoint 16-cell constitute an independent [[16-cell#Coordinates|orthonormal basis for a coordinate reference frame]].}} Alternatively, the three colors might correspond to three different fibrations of the same isospin space: three different ''sequences'' of the same total set of discrete points on the 3-sphere. These alternative possibilities constrain possible representations of the nuclides themselves, for example if we try to represent nuclides as particular rotating 4-polytopes. If the neutron is a (8-point) 16-cell, either of the two color possibilities might somehow make sense as far as the neutron is concerned. But if the proton is a (5-point) 5-cell, only the latter color possibility makes sense, because fibrations (which correspond to distinct isoclinic left-and-right rigid rotations) are the ''only'' thing the 5-cell has three of. Both the 5-cell and the 16-cell have three discrete rotational fibrations. Moreover, in the case of a rigid, isoclinically rotating 4-polytope, those three fibrations always come one-of-a-kind and two-of-a-kind, in at least two different ways. First, one fibration is the set of invariant planes currently being rotated through, and the other two are not. Second, when one considers the three fibrations of each of these 4-polytopes, in each fibration two isoclines carry the left and right rotations respectively, and the third isocline acts simply as a Petrie polygon, the difference between the fibrations being the role assigned to each isocline.

If we associate each quark with one or more isoclinic rotations in which the moving vertices belong to different 16-cells of the 24-cell, and the sign (plus or minus) of the electric charge with the chirality (right or left) of isoclinic rotations generally, we can configure nucleons of three quarks, two performing rotations of one chirality and one performing rotations of the other chirality. The configuration will be a valid kinematic rotation because the completely disjoint 16-cells can rotate independently; their vertices would never collide even if the 16-cells were performing different rigid square isoclinic rotations (all 8 vertices rotating in unison). But we need not associate a quark with a [[16-cell#Rotations|rigidly rotating 16-cell]], or with a single distinct square rotation.

Minimally, we must associate each quark with at least one moving vertex in each of three different 16-cells, following the twisted geodesic isocline of an isoclinic rotation. In the up quark, that could be the isocline of a right rotation; and in the down quark, the isocline of a left rotation. The chirality accounts for the sign of the electric charge (we have said conventionally as +right, −left), but we must also account for the quantity of charge: +{{sfrac|2|3}} in an up quark, and −{{sfrac|1|3}} in a down quark. One way to do that would be to give the three distinct quarks moving vertices of {{sfrac|1|3}} charge in different 16-cells, but provide up quarks with twice as many vertices moving on +right isoclines as down quarks have vertices moving on −left isoclines (assuming the correct chiral pairing is up+right, down−left).

Minimally, an up quark requires two moving vertices (of the up+right chirality).{{Efn|Two moving vertices in one quark could belong to the same 16-cell. A 16-cell may have two vertices moving in the same isoclinic square (octagram) orbit, such as an antipodal pair (a rotating dipole), or two vertices moving in different square orbits of the same up+right chirality.{{Efn|There is only one [[16-cell#Helical construction|octagram orbit]] of each chirality in each fibration of the 16-cell, so two octagram orbits of the same chirality cannot be Clifford parallel (part of the same distinct rotation). Two vertices right-moving on different octagram isoclines in the same 16-cell is a combination of two distinct rotations, whose isoclines will intersect: a kinematic rotation. It can be a valid kinematic rotation if the moving vertices will never pass through a point of intersection at the same time. Octagram isoclines pass through all 8 vertices of the 16-cell, and all eight isoclines (the left and right isoclines of four different fibrations) intersect at ''every'' vertex.}} However, the theory of [[W:Color confinement|color confinement]] may not require that two moving vertices in one quark belong to the same 16-cell; like the moving vertices of different quarks, they could be drawn from the disjoint vertex sets of two different 16-cells.}} Minimally, a down quark requires one moving vertex (of the down−left chirality). In these minimal quark configurations, a proton would have 5 moving vertices and a neutron would have 4.

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=== Nucleons ===
[[File:Symmetrical_5-set_Venn_diagram.svg|thumb|[[W:Branko Grünbaum|Grünbaum's]] rotationally symmetrical 5-set Venn diagram, 1975. It is the [[5-cell]]. Think of it as an [[W:Nuclear magnetic resonance|NMR image]] of the 4-dimensional proton in projection to the plane.]]
The proton is a very stable mass particle. Is there a stable orbit of 5 moving vertices in 4-dimensional Euclidean space? There are few known solutions to the 5-body problem, and fewer still to the [[W:n-body problem|{{mvar|n}}-body problem]], but one is known: the ''central configuration'' of {{mvar|n}} bodies in a space of dimension {{mvar|n}}-1. A [[W:Central configuration|central configuration]] is a system of [[W:Point particle|point masses]] with the property that each mass is pulled by the combined attractive force of the system directly towards the [[W:Center of mass|center of mass]], with acceleration proportional to its distance from the center. Placing three masses in an equilateral triangle, four at the vertices of a regular [[W:Tetrahedron|tetrahedron]], five at the vertices of a regular [[5-cell]], or more generally {{mvar|n}} masses at the vertices of a regular [[W:Simplex|simplex]] produces a central configuration [[W:Central configuration#Examples|even when the masses are not equal]]. In an isoclinic rotation, all the moving vertices orbit at the same radius and the same speed. Therefore if any 5 bodies are orbiting as an isoclinically rotating regular 5-cell (a rigid 4-simplex figure undergoing isoclinic rotation), they maintain a central configuration, describing 5 mutually stable orbits.

Unlike the proton, the neutron is not always a stable particle; a free neutron will decay into a proton. A deficiency of the minimal configurations is that there is no way for this [[W:beta minus decay|beta minus decay]] to occur. The minimal neutron of 4 moving vertices described [[#Color|above]] cannot possibly decay into a proton by losing moving vertices, because it does not possess the four up+right moving vertices required in a proton. This deficiency could be remedied by giving the neutron configuration 8 moving vertices instead of 4: four down−left and four up+right moving vertices. Then by losing 3 down−left moving vertices the neutron could decay into the 5 vertex up-down-up proton configuration.{{Efn|Although protons are very stable, during [[W:stellar nucleosynthesis|stellar nucleosynthesis]] two H&lt;sub&gt;1&lt;/sub&gt; protons are fused into an H&lt;sub&gt;2&lt;/sub&gt; nucleus consisting of a proton and a neutron. This [[W:beta plus decay|beta plus &quot;decay&quot;]] of a proton into a neutron is actually the result of a rare high-energy collision between the two protons, in which a neutron is constructed. With respect to our nucleon configurations of moving vertices, it has to be explained as the conversion of two 5-point 5-cells into a 5-point 5-cell and an 8-point 16-cell, emitting two decay products of at least 1-point each. Thus it must involve the creation of moving vertices, by the conversion of kinetic energy to point-masses.}} A neutron configuration of 8 moving vertices could occur as the 8-point 16-cell, the second-smallest regular 4-polytope after the 5-point 5-cell (the hypothesized proton configuration).

It is possible to double the neutron configuration in this way, without destroying the charge balance that defines the nucleons, by giving down quarks three moving vertices instead of just one: two −left vertices and one +right vertex. The net charge on the down quark remains −{{sfrac|1|3}}, but the down quark becomes heavier (at least in vertex count) than the up quark, as in fact its mass is measured to be.

A nucleon's quark configuration is only a partial specification of its properties. There is much more to a nucleon than what is contained within its three quarks, which contribute only about 1% of the nucleon's energy. The additional 99% of the nucleon mass is said to be associated with the force that binds the three quarks together, rather than being intrinsic to the individual quarks separately. In the case of the proton, 5 moving vertices in the stable orbits of a central configuration (in one of the [[5-cell#Geodesics and rotations|isoclinic rotations characteristic of the regular 5-cell]]) might be sufficient to account for the stability of the proton, but not to account for most of the proton's energy. It is not the point-masses of the moving vertices themselves which constitute most of the mass of the nucleon; if mass is a consequence of geometry, we must look to the larger geometric elements of these polytopes as their major mass contributors. The quark configurations are thus incomplete specifications of the geometry of the nucleons, predictive of only some of the nucleon's properties, such as charge.{{Efn|Notice that by giving the down quark three moving vertices, we seem to have changed the quark model's prediction of the proton's number of moving vertices from 5 to 7, which would be incompatible with our theory that the proton configuration is a rotating regular 5-cell in a central configuration of 5 stable orbits. Fortunately, the actual quark model has nothing at all to say about moving vertices, so we may choose to regard that number as one of the geometric properties the quark model does not specify.}} In particular, they do not account for the forces binding the nucleon together. Moreover, if the rotating regular 5-cell is the proton configuration and the rotating regular 16-cell is the neutron configuration, then a nucleus is a complex of rotating 5-cells and 16-cells, and we must look to the geometric relationship between those two very different regular 4-polytopes for an understanding of the nuclear force binding them together.

The most direct [[120-cell#Relationships among interior polytopes|geometric relationship among stationary regular 4-polytopes]] is the way they occupy a common 3-sphere together. Multiple 16-cells of equal radius can be compounded to form each of the larger regular 4-polytopes, the 8-cell, 24-cell, 600-cell, and 120-cell, but it is noteworthy that multiple regular 5-cells of equal radius cannot be compounded to form any of the other 4-polytopes except the largest, the 120-cell. The 120-cell is the unique intersection of the regular 5-cell and 16-cell: it is a compound of 120 regular 5-cells, and also a compound of 75 16-cells. All regular 4-polytopes except the 5-cell are compounds of 16-cells, but none of them except the largest, the 120-cell, contains any regular 5-cells. So in any compound of equal-radius 16-cells which also contains a regular 5-cell, whether that compound forms some single larger regular 4-polytope or does not, no two of the regular 5-cell's five vertices ever lie in the same 16-cell. So the geometric relationship between the regular 5-cell (our proton candidate) and the regular 16-cell (our neutron candidate) is quite a distant one: they are much more exclusive of each other's elements than they are distantly related, despite their complementary three-quark configurations and other similarities as nucleons. The relationship between a regular 5-cell and a regular 16-cell of equal radius is manifest only in the 120-cell, the most complex regular 4-polytope, which [[120-cell#Geometry|uniquely embodies all the containment relationships]] among all the regular 4-polytopes and their elements.

If the nucleus is a complex of 5-cells (protons) and 16-cells (neutrons) rotating isoclinically around a common center, then its overall motion is a hybrid isoclinic rotation, because the 5-cell and the 16-cell have different characteristic isoclinic rotations, and they have no isoclinic rotation in common.{{Efn|The regular 5-cell does not occur inscribed in any other regular 4-polytope except one, the 600-vertex 120-cell. No two of the 5 vertices of a regular 5-cell can be vertices of the same 16-cell, 8-cell, 24-cell, or 600-cell. The isoclinic rotations characteristic of the regular 5-cell maintain the separation of its 5 moving vertices in 5 disjoint Clifford-parallel subspaces at all times. The [[16-cell#Rotations|isoclinic rotation characteristic of the 16-cell]] maintains the separation of its 8 moving vertices in 2 disjoint Clifford-parallel subspaces (completely orthogonal great square planes) at all times. Therefore, in any hybrid rotation of a concentric 5-cell and 16-cell, at most one 5-cell subspace (containing 1 vertex) might be synchronized with one 16-cell subspace (containing 4 vertices), such that the 1 + 4 vertices they jointly contain occupy the same moving subspace continually, forming a rigid 5-vertex polytope undergoing some kind of rotation. If in fact it existed, this 5-vertex rotating rigid polytope would not be [[5-cell#Geometry|not a 5-cell, since 4 of its vertices are coplanar]]; it is not a 4-polytope but merely a polyhedron, a [[W:square pyramid|square pyramid]].}}

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=== Nuclides ===

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=== Quantum phenomena ===

The Bell-Kochen-Specker (BKS) theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a space of three or more dimensions can be given by exhibiting a finite set of lines through the origin that cannot each be colored black or white in such a way that (i) no two orthogonal lines are both black, and (ii) not all members of a set of ''d'' mutually orthogonal lines are white.{{Efn|&quot;The Bell-Kochen-Specker theorem rules out the existence of deterministic noncontextual hidden variables theories. A proof of the theorem in a Hilbert space of dimension d ≥ 3 can be given by exhibiting a finite set of rays [9] that cannot each be assigned the value 0 or 1 in such a way that (i) no two orthogonal rays are both assigned the value 1, and (ii) not all members of a set of d mutually orthogonal rays are assigned the value 0.&quot;{{Sfn|Waegell|Aravind|2009|loc=2. The Bell-Kochen-Specker (BKS) theorem}}|name=BKS theorem}}

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=== Motion ===
What does it mean to say that an object moves through space? Coxeter group theory provides precise answers to questions of this kind. A rigid object (polytope) moves by distinct transformations, changing itself in each discrete step into a congruent object in a different orientation and position.{{Efn|name=transformations}}

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== Galilean relativity in a space of four orthogonal dimensions ==

Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions.

General relativity is just Galilean relativity in a general space of four orthogonal dimensions, e.g. Euclidean 4-space &lt;math&gt;R^4&lt;/math&gt;, spherical 4-space &lt;math&gt;S^4&lt;/math&gt;, or any orthogonal 4-manifold.

Light is just reflection. Gravity (and all force) is just rotation. Both motions are just group actions, expressions of intrinsic symmetries. That is all of physics.

Every observer properly sees himself as stationary and the universe as a sphere with himself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and it can be measured by the observer as the speed of light.

=== Special relativity is just Galilean relativity in a Euclidean space of four orthogonal dimensions ===
Perspective effects occur because each observer's ordinary 3-dimensional space is only a curved manifold embedded in 4-dimensional Euclidean space, and its curvature complicates the calculations for him (e.g., he sometimes requires Lorentz transformations). But if  all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) except when you want to calculate a projection, or a shadow, that is, how things will appear from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} The universe really has four spatial dimensions, and space and time behave just as they do in classical 3-vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a spacetime to explain 4-dimensional perspective effects at high velocities, because 4-space is already spatially 4-dimensional, and those perspective effects fall out of the 4-dimensional Pythagorean theorem naturally, just as perspective does in three dimensions. The universe is only strange in the ways the Euclidean fourth dimension is strange; but that does hold many surprises for us. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way that 3-space is much more interesting than 2-space. But all Euclidean spaces are dimensionally analogous. Dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries.

=== General relativity is just Galilean relativity in a general space of four orthogonal dimensions ===
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=== Physics ===
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=== Thoreau's spherical relativity ===
Every observer may properly see himself as stationary and the universe as a 4-sphere with himself at the center observing it, perceptually equidistant from all points on its surface, including his own ''physical'' location which is one of those surface points, distinguished to him but not the center of anything. This statement of the principle of relativity is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's relativity of orthogonal group actions in Euclidean spaces of any number of dimensions.{{Efn|name=transformations}} It should be known as Thoreau's spherical relativity, since the first precise written statement of it appears in 1849: &quot;The universe is a sphere whose center is wherever there is intelligence.&quot;{{Sfn|Thoreau|1849|p=349|ps=; &quot;The universe is a sphere whose center is wherever there is intelligence.&quot; [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polytopes in any number of dimensions.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; &quot;Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassman and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions.&quot;}}]}}

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== Conclusions==

=== Spherical relativity ===

We began our inquiry by wondering why physical space should be limited to just three dimensions (why ''three''). By visualizing the universe as a Euclidian space of four dimensions, we recognize that relativistic and quantum phenomena are natural consequences of symmetry group operations (including reflections and rotations) in four orthogonal dimensions. We should not then be surprised to see that the universe does not have just four dimensions, either. Physical space must bear as many dimensions as we need to ascribe to it, though the distinct phenomena for which we find a need to do so, in order to explain them, seem to be fewer and fewer as we consider higher and higher dimensions. To laws of physics generally, such as the principle of relativity in particular, we should always append the phrase &quot;in Euclidean spaces of any number of dimensions&quot;. Laws of physics should operate in any flat Euclidean space &lt;math&gt;R^n&lt;/math&gt; and in its corresponding spherical space &lt;math&gt;S^n&lt;/math&gt;.

The first and simplest sense in which we are forced to contemplate a fifth dimension is to accommodate our normal idea of time. Just as Einstein was forced to admit time as a dimension, in his four-dimensional spacetime of three spatial dimensions plus time, for some purposes we require a fifth time dimension to accompany our four spatial dimensions, when our purpose is orthogonal to (in the sense of independent of) the four spatial dimensions. For example, if we theorize that we observe a finite homogeneous universe, and that it is a Euclidean 4-space overall, we may prefer not to have to identify any distinct place within that 4-space as the center where the universe began in a big bang. To avoid having to pick a distinct place as the center of the universe, our model of it must be expanded, at least to be a ''spherical'' 4-dimensional space with the fifth radial dimension as time. Essentially, we require the fifth dimension in order to make our homogeneous 4-space finite, by wrapping it around into a 4-sphere. But perhaps we can still resist admitting the fifth radial dimension as a full-fledged Euclidean spatial dimension, at least so long as we have not observed how any naturally occurring object configurations are best described as 5-polytopes.

One phenomenon which resists explanation in a space of just four dimensions is the propagation of light in a vacuum. The propagation of mass-carrying particles is explained as the consequence of their rotations in closed, curved spaces (3-spheres) of finite size, moving through four-dimensional Euclidean space at a universal constant speed, the speed of light. But an apparent paradox remains that light must seemingly propagate through four-dimensional Euclidean space at more than the speed of light. From an ''n''-dimensional viewpoint, this apparent paradox can be resolved, and in retrospect it is clear how massless particles can translate through four-dimensional space at twice the speed constant, since they are not simultaneously rotating.

Another phenomenon justifying a five-dimensional view of space is the relation between the the 5-cell proton and the 16-cell neutron (the 4-simplex and 4-orthoplex polytopes). Their indirect relationship can be observed in the 4-600-point polytope (the 120-cell), and in its 11-cells,{{Sfn|Christie|2025|loc=&quot;A symmetrical arrangement of eleven 11-cells&quot;}} but it is only directly observed (absent a 120-cell) in a five-dimensional reference frame.

=== Nuclear geometry ===
We have seen how isoclinic rotations (Clifford displacements) relate the orbits in the atomic nucleus to each other, just as they relate the regular convex 4-polytopes to each other, in a sequence of nested objects of increasing complexity. We have identified the proton as a  5-point, 5-cell 4-simplex 𝜶&lt;sub&gt;4&lt;/sub&gt;, the neutron as an 8-point, 16-cell 4-orthoplex 𝛽&lt;sub&gt;4&lt;/sub&gt;, and the shell of the atomic nucleus as a 24-point 24-cell. As Coxeter noted, that unique 24-point object stands quite alone in four dimensions, having no analogue above or below.

=== Atomic geometry ===
I'm on a plane flying to Eugene to visit Catalin, we'll talk after I arrive. I've been working on both my unpublished papers, the one going put for pre-publication review soon about 4D geometry, and the big one not going out soon about the 4D sun, 4D atoms, and 4D galaxies and n-D universe. I'vd just added the following paragraph to that big paper:

Atomic geometry

The force binding the protons and neutrons of the nucleus together into a distinct element is specifically an expression of the 11-cell 4-polytope, itself an expression of the pyritohedral symmetry, which binds the distinct 4-polytopes to each other, and relates the n-polytopes to their neighbors of different n by dimensional analogy.


flying over mt shasta out my right-side window at the moment, that last text showing &quot;not delivered&quot; yet because there's no wifi on this plane, gazing at that great peak of the world and feeling as if i've just made the first ascent of it

=== Molecular geometry ===
Molecules are 3-dimensional structures that live in the thin film of 3-membrane only one atom thick in most places that is our ordinary space, but since that is a significantly curved 3-dimensional space at the scale of a molecule, the way the molecule's covalent bonds form is influenced by the local curvature in 4-dimensions at that point.

In the water molecule, there is a reason why the hydrogen atoms are attached to the oxygen atom at an angle of 104.45° in 3-dimensional space, and at root it must be the same symmetry that locates any two of the hydrogen proton's five vertices 104.45° apart on a great circle arc of its tiny 3-sphere.

=== Cosmology ===

==== Solar systems ====

===== Stars =====
...

===== The Kepler problem =====
In the proper reference frame of some hypothetical observer in 4-dimensional Euclidean space, the Kepler problem has a solution in which all the planetary orbits are circles. This occurs because all bodies are always orbiting, each in some distinct isoclinic (equi-angled double) rotation. All atoms are rotating isoclinically at (double) the velocity &lt;math&gt;c&lt;/math&gt;. In the observer's proper reference frame, the isoclinic double rotation of each of his own atoms is most conveniently represented as an equivalent screw displacement: a linear translation at velocity &lt;math&gt;c&lt;/math&gt; (along the observer's proper time axis through 4-space), combined with a simple rotation at velocity &lt;math&gt;c&lt;/math&gt; (of the atom internally). 

This representation, though proper, is subject to the over-simplification of special relativity, because it ignores the fact that the observer is himself moving on some circular orbit; he is not linearly translating through 4-space. When the observer's own orbit is also represented, the screw displacement becomes an elliptical double rotation, with a very slow, very large-radius simple circular orbit (almost a linear translation), combined with a very fast, very small-radius simple circular orbit of each atom internally. This is the observer's proper reference frame according to general relativity.

An observer moving differently will perceive the motion of the observer and his atoms to be a different elliptical double rotation. We can find a proper reference frame, of some hypothetical observer moving hypothetically, in which the ratio of the radii of the two orthogonal rotations of the atom becomes any value we choose between 1 and &lt;math&gt;c&lt;/math&gt;. In particular there exists, conceptually accessible to all observers independent of their motion, a distinct reference frame in which an atom is stationary, rotating isoclinically at (double) the velocity &lt;math&gt;c&lt;/math&gt;. That is simply the stationary reference frame of the atom itself, such as the stationary reference frame of any observer and his own atoms. In 3-dimensional physics, it is known as the observer's proper inertial reference frame. But in 4-dimensional physics, that is ''not'' the most convenient or sensible reference frame in which to consider objects moving differently, in different proper reference frames. In 4-dimensional physics, a reference frame in which an observer and his atoms are translating linearly at velocity &lt;math&gt;c&lt;/math&gt; is known as the observer's proper inertial reference frame. Any such proper reference frame makes a great deal more sense for the purpose of considering the motion of objects moving differently in 4-space, just as a heliocentric solar system makes a great deal more sense than a geocentric solar system for the purpose of considering the motion of the planets.

...

==== Galaxies ====

The spacetime of general relativity is often illustrated as a projection to a curved 2D surface in which large gravitational objects make gravity wells or dimples in the surface. In the Euclidean 4D view of the universe the 3D surface of a large cosmic object such as a galaxy surrounds an empty 4D space, and large gravitational objects within the galaxy must make dimples in its surface. But should we see them as dimples exactly? Would they dimple inwards or outwards? In the spacetime illustrations they are naturally always shown as dimpling downwards, which is somewhat disingenuous, strongly suggesting to the viewer that the reason for gravity is that it flows downhill - the original tautology we are trying to surmount! In the Euclidean 4D galaxy the dimple, if it is one, must be either inward or outward, and which it is matters since the dimple is flying outward at velocity {{mvar|c}}. The galaxy is not collapsing inward. Is a large gravitational mass (such as a star) ''ahead'' of the smaller masses orbiting around it (such as its planets), or is it ''behind'' them, as they fly through 4-space on their Clifford parallel trajectories? The answer is ''both'' of course, because a star is not a dimple, it is a 4-ball, and it dimples the 3D surface both inwards and outwards. It is a thick place in the 3D surface. We should view it as having its gravitational center precisely at the surface of the expanding 3-sphere. 

What is a black hole? It is the hollow four-dimensional space that a galaxy is the three-dimensional surface of.

When we view another galaxy, such as Andromeda, we are seeing that whole galaxy from a distance, the way the moon astronauts looked back at the whole earth. We see our own milky way galaxy from where we are on its surface, the way we see the earth from its surface, except that the earth is solid, but the galaxy is hollow and transparent. We can look across its empty center and see all the other stars also on its surface, including those opposite ours on the far side of its 3-sphere. The thicker band of stars we see in our night sky and identify as the milky way is not our whole galaxy; the majority of the other visible stars also lie in our galaxy. That dense band is not thicker and brighter than other parts of our galaxy because it lies toward a dense galactic center (our galaxy has an empty center), but for exactly the opposite reason: those apparently more thickly clustered stars lie all around us on the galaxy's surface, in the nearest region of space surrounding us. They appear to be densely packed only because we are looking at them &quot;edge on&quot;. Actually, we are looking into this nearby apparently dense region ''face on'', not edge on, because we are looking at a round sphere of space surrounding us, not a disk. In contrast, stars in our galaxy outside that bright band lie farther off from us, across the empty center of the galaxy, and we see them spread out as they actually are, instead of &quot;edge on&quot; so they appear to be densely clustered. The &quot;dense band&quot; covers only an equatorial band of the night sky instead of all the sky, because when we look out into the four-dimensional space around us, we can see stars above and below our three-dimensional hyperplane in our four-dimensional space. Everything in our solar system lies in our hyperplane, and the nearby stars around us in our galaxy are near our hyperplane (just slightly below it). All the other, more distant stars in our galaxy are also below our hyperplane. We can see objects outside our galaxy, such as other galaxies, both above and below our hyperplane. We can see all around us above our hyperplane (looking up from the galactic surface into the fourth dimension), and all around us below our hyperplane (looking down through our transparent galaxy and out the other side).

== Revolutions ==
The original Copernican revolution displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the stars remaining on a fixed sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. 

In such fashion the Euclidean four-dimensional viewpoint initially lends itself to a big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the stars need not be equidistant from a single origin in time, any more than they all lie in the same galaxy, equidistant from its center in space. The expanding sphere of matter on the surface of which we find ourselves living might be one of many such spheres, with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe.

When we look up at the heavens, we have no obvious way of knowing whether the space we are looking into is a curved 3-spherical one or a flat 4-space. In this work we suggest a theory of how light travels that says we can see into all four dimensions, and so when we look up at night we see cosmological objects distributed in 4-dimensional space, and not all located on our own 3-spherical membrane. The view from our solar system suggests that our galaxy is its own hollow 3-sphere, and that galaxies generally are single roughly spherical 3-membranes, with the smaller objects within them all lying on that same 3-spherical surface, equidistant from the galaxy center in 4-space. 

The Euclidean four-dimensional viewpoint requires that all mass-carrying objects are in motion at constant velocity &lt;math&gt;c&lt;/math&gt;, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Since their paths away from their origin are not straight lines but various helical isoclines, their 3-sphere will be expanding radially at slightly less than the constant velocity &lt;math&gt;c&lt;/math&gt;. The view from our solar system does ''not'' suggest that each galaxy is its own distinct 3-sphere expanding at this great rate; rather, the standard theory has been that the entire observable universe is expanding from a single big bang origin in time. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also allows theories which require no single origin point in space and time.

These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and we have not slowed down since.

== Origins of the theory ==
Einstein himself was one of the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean sphere, in what was narrowly the first written articulation of the principle of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below). Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.&lt;ref&gt;{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}&lt;/ref&gt; He invited us to imagine &quot;A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions&quot;, but he was careful to disclaim parenthetically that &quot;The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice.&quot;

Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from his perspective; the forthshortenings, clock desynchronizations and other Lorentz transformations it predicts are exact calculations of actual perspective effects; but space is actually a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.''

The Euclidean 4-dimensional theory differs from the standard theory in being a description of the physical universe in terms of a geometry of four or more orthogonal spatial dimensions, rather than in the standard theory's terms of the [[w:Minkowski spacetime|Minkowski spacetime]] geometry (in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions). The invention of geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years. It was first worked out by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] around 1850. Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''polyscheme'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he discovered all the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the six convex regular polyschemes which can be constructed in a Euclidean space of four dimensions (a set analogous to the five [[w:Platonic solid|Platonic solids]] in three dimensional space). Thus he was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover all its astonishing regular objects. Because most of his work remained almost completely unknown until it was published posthumously in 1901, other researchers had more than fifty years to rediscover the regular polyschemes, and competing terms were coined; today [[W:Alicia Boole Stott|Alicia Boole Stott]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme''.{{Efn|Today Schläfli's original ''polyscheme'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}}

== Boundaries ==
&lt;blockquote&gt;Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.&lt;ref&gt;{{Cite book|author=Carlo Rovelli|title=Seven Brief Lessons on Physics}}&lt;/ref&gt;&lt;/blockquote&gt;

Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schlafli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it, is that there ''is'' a boundary between three and four dimensions. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our world apparently only three dimensional? Why would it have ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schlafli mapped? What is the nature of the boundary which confines us to just three? 

We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way by receiving light signals that traveled to us on straight lines through it. The reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creates, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not surprise us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell.

Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schlafli discovered something else: all the astonishing regular objects that exist in higher dimensions. So this conception now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and not a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for the rationale for a physical boundary in the geometry of space itself, which general relativity attributes to the gravitational or inertial force.

&lt;blockquote&gt;The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three ....

In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it.

We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed &quot;Dimensional Analogy.&quot;&lt;ref&gt;{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}&lt;/ref&gt;&lt;/blockquote&gt;

I believe, but I cannot prove, that our universe is properly a Euclidean space of four orthogonal spatial dimensions. Others will have to work out the physics and do the math, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages.

&lt;blockquote&gt;
::::::BEECH

:Where my imaginary line
:Bends square in woods, an iron spine
:And pile of real rocks have been founded.
:And off this corner in the wild,
:Where these are driven in and piled,
:One tree, by being deeply wounded,
:Has been impressed as Witness Tree
:And made commit to memory
:My proof of being not unbounded.
:Thus truth's established and borne out,
:Though circumstanced with dark and doubt—
:Though by a world of doubt surrounded.

:::::::—''The Moodie Forester''&lt;ref&gt;{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}&lt;/ref&gt;
&lt;/blockquote&gt;

== Sequence of regular 4-polytopes ==
{{Regular convex 4-polytopes|wiki=W:|columns=7}}

== Notes ==
{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}}

{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}}

{{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}}

{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}}

{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,–&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}}

{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}}

{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}}

{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are 4-dimensionally circular, but not all isoclines on 3-manifolds in 4-space are perfectly circular.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also
known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two
intersecting circles that are the cross-section of a torus by a well-chosen plane
cutting it. Picking one such circle and rotating it around the torus
axis, the resulting family of circles can be used to rule the torus. By nesting
tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the
(1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles].&quot;}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}}

{{Efn|[[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point.{{Sfn|Tyrrell|Semple|1971|loc=§3. Clifford's original definition of parallelism|pp=5-6}} A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the 2-sphere will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect; various sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. Perhaps the simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles.{{Efn|name=six orthogonal planes of the Cartesian basis}} Each completely orthogonal pair is Clifford parallel. The two circles cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 3-sphere.{{Efn|name=only some Clifford parallels are orthogonal}} Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]].|name=Clifford parallels}}

{{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}}

{{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}}

{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}}

{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}}

{{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}}

{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}}

{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}}

{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}}

{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}}

{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}}

{{Notelist|40em}}

== Citations ==
{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}}

{{Reflist|40em}}

== References ==
{{Refbegin}}
* {{Cite book | last=Kepler | first=Johannes | author-link=W:Johannes Kepler | title=Harmonices Mundi (The Harmony of the World) | title-link=W:Harmonices Mundi | publisher=Johann Planck | year=1619}}
* {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston}}
* {{Cite book | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1973 | orig-year=1948 | title=Regular Polytopes | publisher=Dover | place=New York | edition=3rd | title-link=W:Regular Polytopes (book) }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1991 | title=Regular Complex Polytopes | place=Cambridge | publisher=Cambridge University Press | edition=2nd }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1995 | title=Kaleidoscopes: Selected Writings of H.S.M. Coxeter | publisher=Wiley-Interscience Publication | edition=2nd | isbn=978-0-471-01003-6 | url=https://archive.org/details/kaleidoscopessel0000coxe | editor1-last=Sherk | editor1-first=F. Arthur | editor2-last=McMullen | editor2-first=Peter | editor3-last=Thompson | editor3-first=Anthony C. | editor4-last=Weiss | editor4-first=Asia Ivic | url-access=registration }}
** (Paper 3) H.S.M. Coxeter, ''Two aspects of the regular 24-cell in four dimensions''
** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10]
** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', [Math. Zeit. 188 (1985) 559-591]
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
* {{Cite journal | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1989 | title=Trisecting an Orthoscheme | journal=Computers Math. Applic. | volume=17 | issue=1-3 | pp=59-71 }}
* {{Cite journal|last=Stillwell|first=John|author-link=W:John Colin Stillwell|date=January 2001|title=The Story of the 120-Cell|url=https://www.ams.org/notices/200101/fea-stillwell.pdf|journal=Notices of the AMS|volume=48|issue=1|pages=17–25}}
* {{Cite book | last1=Conway | first1=John H. | author-link1=W:John Horton Conway | last2=Burgiel | first2=Heidi | last3=Goodman-Strauss | first3=Chaim | author-link3=W:Chaim Goodman-Strauss | year=2008 | title=The Symmetries of Things | publisher=A K Peters | place=Wellesley, MA | title-link=W:The Symmetries of Things }}
* {{Cite journal|last1=Perez-Gracia|first1=Alba|last2=Thomas|first2=Federico|date=2017|title=On Cayley's Factorization of 4D Rotations and Applications|url=https://upcommons.upc.edu/bitstream/handle/2117/113067/1749-ON-CAYLEYS-FACTORIZATION-OF-4D-ROTATIONS-AND-APPLICATIONS.pdf|journal=Adv. Appl. Clifford Algebras|volume=27|pages=523–538|doi=10.1007/s00006-016-0683-9|hdl=2117/113067|s2cid=12350382|hdl-access=free}}
* {{Cite arXiv | eprint=1903.06971 | last=Copher | first=Jessica | year=2019 | title=Sums and Products of Regular Polytopes' Squared Chord Lengths | class=math.MG }}
* {{Cite thesis|url= http://resolver.tudelft.nl/uuid:dcffce5a-0b47-404e-8a67-9a3845774d89 |title=Symmetry groups of regular polytopes in three and four dimensions|last=van Ittersum |first=Clara|year=2020|publisher=[[W:Delft University of Technology|Delft University of Technology]]}}
* {{cite arXiv|last1=Kim|first1=Heuna|last2=Rote|first2=G.|date=2016|title=Congruence Testing of Point Sets in 4 Dimensions|class=cs.CG|eprint=1603.07269}}
* {{cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|year=2013|publisher=DUTTON Penguin Group|isbn=978-0-525-95366-1}}
* {{Cite journal|last1=Waegell|first1=Mordecai|last2=Aravind|first2=P. K.|date=2009-11-12|title=Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem|journal=Journal of Physics A: Mathematical and Theoretical|volume=43|issue=10|page=105304|language=en|doi=10.1088/1751-8113/43/10/105304|arxiv=0911.2289|s2cid=118501180}}
* {{Cite book|title=Generalized Clifford parallelism|last1=Tyrrell|first1=J. A.|last2=Semple|first2=J.G.|year=1971|publisher=[[W:Cambridge University Press|Cambridge University Press]]|url=https://archive.org/details/generalizedcliff0000tyrr|isbn=0-521-08042-8}}
* {{Cite journal | last1=Mamone|first1=Salvatore | last2=Pileio|first2=Giuseppe | last3=Levitt|first3=Malcolm H. | year=2010 | title=Orientational Sampling Schemes Based on Four Dimensional Polytopes | journal=Symmetry | volume=2 | pages=1423-1449 | doi=10.3390/sym2031423 }}
* {{Cite journal|last=Dorst|first=Leo|title=Conformal Villarceau Rotors|year=2019|journal=Advances in Applied Clifford Algebras|volume=29|issue=44|url=https://doi.org/10.1007/s00006-019-0960-5}}
* {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}}
*{{Citation | last=Goucher | first=A.P. | title=Spin groups | date=19 November 2019 | journal=Complex Projective 4-Space | url=https://cp4space.hatsya.com/2012/11/19/spin-groups/ }}
* {{Citation|last=Christie|first=David Brooks|author-link=User:Dc.samizdat|year=2025|title=A symmetrical arrangement of eleven 11-cells|title-link=User:Dc.samizdat/A symmetrical arrangement of eleven 11-cells|journal=Wikiversity}}
{{Refend}}</text>
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    <title>Zhegalkin matrix</title>
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{{Zhegalkin stuff}}
The '''Zhegalkin matrix''' is an infinite binary matrix.

It is closely related to the infinite integer matrix of '''[[Gray code permutation powers]]''' ({{oeis|A195467}}) and to the '''[[algebraic normal form]]''' (ANF) of Boolean functions.&lt;br&gt;
&lt;small&gt;({{w|Ivan Zhegalkin}} was the inventor of the ANF. The naming choices made here are new.)&lt;/small&gt;

Its colums are the truth tables of all Boolean functions. The column index is the '''Zhegalkin index''' of the respective Boolean function. 

Its rows are a subset of the Walsh functions, namely the {{w|exclusive or|XOR}}&lt;nowiki&gt;s&lt;/nowiki&gt; of atoms forming a {{w|Sierpiński triangle}} ({{oeis|A001317}}).

[[File:Zhegalkin 256.svg|thumb|left|1300px|The columns of the 8×256 Zhegalkin matrix are the truth tables of the 256 3-ary Boolean functions.&lt;br&gt;&lt;small&gt;The 8×256 matrix above are the colum indices in &lt;nowiki&gt;little-&lt;/nowiki&gt;{{w|Endianness|endian}} binary. On the left are the Sierpiński triangle and the row indices.&lt;/small&gt;]]
{{clear}}
{{Collapsible START|as rows of a binary Walsh matrix|collapsed}}
This is a 256×256 binary {{w|Walsh matrix}}. Each row is the {{w|Variadic function|variadic}} XOR of the atoms shown in the 256×8 matrix on the left.
[[File:Walsh Zhegalkin 256.svg|1390px]]
{{Collapsible END}}


==Zhegalkin permutation==

{| class=&quot;wikitable&quot; style=&quot;text-align: center;&quot; style=&quot;float: right; text-align: center;&quot;
|+ sizes of finite Zhegalkin matrices
|-
! &lt;math&gt;n&lt;/math&gt;
| 0 || 1 || 2 || 3 || 4
|-
! &lt;math&gt;2^n \times 2^{2^n}&lt;/math&gt;
| 1×2 || 2×4 || 4×16 || 8×256 || 16×65536
|}

For arity &lt;math&gt;n&lt;/math&gt; the map from ANFs to truth tables gives a '''finite Zhegalkin matrix''' of size &lt;math&gt;2^n \times 2^{2^n}&lt;/math&gt;. &lt;small&gt;(It is the top left corner of the infinite matrix.)&lt;/small&gt;

It can be interpreted as a permutation of the integers &lt;math&gt;0~...~2^{2^n} - 1&lt;/math&gt;,
which shall be called '''Zhegalkin permutation''' &lt;math&gt;\Pi_n&lt;/math&gt;.&lt;br&gt;
&lt;small&gt;Keys and values in Π&lt;sub&gt;''n''&lt;/sub&gt; shall be called '''[[Zhegalkin twins]]''' &amp;mdash; e.g. 7 and 9 are Zhegalkin twins for arity 2.&lt;/small&gt;

It is a self-inverse [[Walsh permutation]] of degree 2&lt;sup&gt;''n''&lt;/sup&gt;. The corresponding element of {{w|general linear group|GL}}(2&lt;sup&gt;''n''&lt;/sup&gt;, 2) is the {{w|triangular matrix|lower}} Sierpiński triangle.&lt;br&gt;
&lt;small&gt;
Π&lt;sub&gt;2&lt;/sub&gt; is a Walsh permutation of degree 4, and permutes the integers 0 ... 15.
The corresponding element of GL(4, 2) is the 4×4 lower Sierpiński triangle.
&lt;/small&gt;

{{Zhegalkin matrix/Triangle Pi}}

In a finite Zhegalkin matrix, the columns with even/odd weight are in the left/right half. &amp;nbsp;
&lt;small&gt;(A truth table has a Zhegalkin twin with odd weight, iff its last digit is true.)&lt;/small&gt;&lt;br&gt;
&lt;small&gt;Boolean functions whose Zhegalkin index has even/odd weight shall be called {{w|evil number|evil}}/{{w|odious number|odious}}, which shall be called its '''''depravity'''''&lt;/small&gt;.

{{Zhegalkin matrix/triangle Pi compressed}}

===fixed points===

{| class=&quot;wikitable&quot; style=&quot;text-align: center;&quot; style=&quot;float: right; text-align: center;&quot;
|+ number of fixed points
|-
! &lt;math&gt;n&lt;/math&gt;
| 1 || 2 || 3 || 4 || 5
|-
! &lt;math&gt;2^{2^{n-1}}&lt;/math&gt;
| 2 || 4 || 16|| 256 || 65536
|}

The fixed points of Zhegalkin permutations correspond to [[noble Boolean functions]].

{{Zhegalkin matrix/Triangle Phi}}

==Python code==


{{Collapsible START|Python functions|collapsed gap-below}}
&lt;source lang=&quot;python&quot;&gt;
from sympy import binomial


def sierpinski(n):
    return int(sum([(binomial(n, i) % 2) * 2 ** i for i in range(n + 1)]))

def zhegalkin_perm(n, k):
    row_length = 1 &lt;&lt; (1 &lt;&lt; n)  # 2 ** 2 ** n
    assert k &lt; row_length
    string_length = 1 &lt;&lt; n  # 2 ** n
    k_binary = &quot;{0:b}&quot;.format(k).zfill(string_length)
    reflected_result = 0
    for i, binary_digit in enumerate(k_binary):
        if binary_digit == '1':
            s = sierpinski(i)
            reflected_result ^= s
    reflected_result_binary = &quot;{0:b}&quot;.format(reflected_result).zfill(string_length)
    result_binary = reflected_result_binary[::-1]
    return int(result_binary, 2)

def zhegalkin_fixed(n, k):
    if n == 0:
        assert k &lt; 2
        return k
    else:
        row_length = 1 &lt;&lt; (1 &lt;&lt; (n-1))  # 2 ** 2 ** (n-1)
        assert k &lt; row_length
    p = zhegalkin_perm(n-1, k)
    p_xor_k = p ^ k
    shifted_k = row_length * k
    return p_xor_k + shifted_k
&lt;/source&gt;
{{Collapsible END}}

{{Algebraic normal form/python}}


[[Category:Boolean functions; Zhegalkin stuff]]</text>
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      <text bytes="4470" sha1="5c1p3q97z0m1yl4oni5u32yzlna0klw" xml:space="preserve">{{Boolf header}}
{{Zhegalkin stuff}}
The '''Zhegalkin matrix''' is an infinite binary matrix.

It is closely related to the infinite integer matrix of '''[[Gray code permutation powers]]''' ({{oeis|A195467}}) and to the '''[[algebraic normal form]]''' (ANF) of Boolean functions.&lt;br&gt;
&lt;small&gt;({{w|Ivan Zhegalkin}} was the inventor of the ANF. The naming choices made here are new.)&lt;/small&gt;

Its colums are the truth tables of all Boolean functions. The column index is the '''Zhegalkin index''' of the respective Boolean function. 

Its rows are a subset of the Walsh functions, namely the {{w|exclusive or|XOR}}&lt;nowiki&gt;s&lt;/nowiki&gt; of atoms forming a {{w|Sierpiński triangle}} ({{oeis|A001317}}).

[[File:Zhegalkin 256.svg|thumb|left|1300px|The columns of the 8×256 Zhegalkin matrix are the truth tables of the 256 3-ary Boolean functions.&lt;br&gt;&lt;small&gt;The 8×256 matrix above are the colum indices in reversed binary. On the left are the Sierpiński triangle and the row indices.&lt;/small&gt;]]
{{clear}}
{{Collapsible START|as rows of a binary Walsh matrix|collapsed}}
This is a 256×256 binary {{w|Walsh matrix}}. Each row is the {{w|Variadic function|variadic}} XOR of the atoms shown in the 256×8 matrix on the left.
[[File:Walsh Zhegalkin 256.svg|1390px]]
{{Collapsible END}}


==Zhegalkin permutation==

{| class=&quot;wikitable&quot; style=&quot;text-align: center;&quot; style=&quot;float: right; text-align: center;&quot;
|+ sizes of finite Zhegalkin matrices
|-
! &lt;math&gt;n&lt;/math&gt;
| 0 || 1 || 2 || 3 || 4
|-
! &lt;math&gt;2^n \times 2^{2^n}&lt;/math&gt;
| 1×2 || 2×4 || 4×16 || 8×256 || 16×65536
|}

For arity &lt;math&gt;n&lt;/math&gt; the map from ANFs to truth tables gives a '''finite Zhegalkin matrix''' of size &lt;math&gt;2^n \times 2^{2^n}&lt;/math&gt;. &lt;small&gt;(It is the top left corner of the infinite matrix.)&lt;/small&gt;

It can be interpreted as a permutation of the integers &lt;math&gt;0~...~2^{2^n} - 1&lt;/math&gt;,
which shall be called '''Zhegalkin permutation''' &lt;math&gt;\Pi_n&lt;/math&gt;.&lt;br&gt;
&lt;small&gt;Keys and values in Π&lt;sub&gt;''n''&lt;/sub&gt; shall be called '''[[Zhegalkin twins]]''' &amp;mdash; e.g. 7 and 9 are Zhegalkin twins for arity 2.&lt;/small&gt;

It is a self-inverse [[Walsh permutation]] of degree 2&lt;sup&gt;''n''&lt;/sup&gt;. The corresponding element of {{w|general linear group|GL}}(2&lt;sup&gt;''n''&lt;/sup&gt;, 2) is the {{w|triangular matrix|lower}} Sierpiński triangle.&lt;br&gt;
&lt;small&gt;
Π&lt;sub&gt;2&lt;/sub&gt; is a Walsh permutation of degree 4, and permutes the integers 0 ... 15.
The corresponding element of GL(4, 2) is the 4×4 lower Sierpiński triangle.
&lt;/small&gt;

{{Zhegalkin matrix/Triangle Pi}}

In a finite Zhegalkin matrix, the columns with even/odd weight are in the left/right half. &amp;nbsp;
&lt;small&gt;(A truth table has a Zhegalkin twin with odd weight, iff its last digit is true.)&lt;/small&gt;&lt;br&gt;
&lt;small&gt;Boolean functions whose Zhegalkin index has even/odd weight shall be called {{w|evil number|evil}}/{{w|odious number|odious}}, which shall be called its '''''depravity'''''&lt;/small&gt;.

{{Zhegalkin matrix/triangle Pi compressed}}

===fixed points===

{| class=&quot;wikitable&quot; style=&quot;text-align: center;&quot; style=&quot;float: right; text-align: center;&quot;
|+ number of fixed points
|-
! &lt;math&gt;n&lt;/math&gt;
| 1 || 2 || 3 || 4 || 5
|-
! &lt;math&gt;2^{2^{n-1}}&lt;/math&gt;
| 2 || 4 || 16|| 256 || 65536
|}

The fixed points of Zhegalkin permutations correspond to [[noble Boolean functions]].

{{Zhegalkin matrix/Triangle Phi}}

==Python code==


{{Collapsible START|Python functions|collapsed gap-below}}
&lt;source lang=&quot;python&quot;&gt;
from sympy import binomial


def sierpinski(n):
    return int(sum([(binomial(n, i) % 2) * 2 ** i for i in range(n + 1)]))

def zhegalkin_perm(n, k):
    row_length = 1 &lt;&lt; (1 &lt;&lt; n)  # 2 ** 2 ** n
    assert k &lt; row_length
    string_length = 1 &lt;&lt; n  # 2 ** n
    k_binary = &quot;{0:b}&quot;.format(k).zfill(string_length)
    reflected_result = 0
    for i, binary_digit in enumerate(k_binary):
        if binary_digit == '1':
            s = sierpinski(i)
            reflected_result ^= s
    reflected_result_binary = &quot;{0:b}&quot;.format(reflected_result).zfill(string_length)
    result_binary = reflected_result_binary[::-1]
    return int(result_binary, 2)

def zhegalkin_fixed(n, k):
    if n == 0:
        assert k &lt; 2
        return k
    else:
        row_length = 1 &lt;&lt; (1 &lt;&lt; (n-1))  # 2 ** 2 ** (n-1)
        assert k &lt; row_length
    p = zhegalkin_perm(n-1, k)
    p_xor_k = p ^ k
    shifted_k = row_length * k
    return p_xor_k + shifted_k
&lt;/source&gt;
{{Collapsible END}}

{{Algebraic normal form/python}}


[[Category:Boolean functions; Zhegalkin stuff]]</text>
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    </revision>
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      <text bytes="4428" sha1="14g2i4tqebbxcezi4185zb8weyrk2o0" xml:space="preserve">{{Boolf header}}
{{Zhegalkin stuff}}
The '''Zhegalkin matrix''' is an infinite binary matrix.

It is closely related to the infinite integer matrix of '''[[Gray code permutation powers]]''' ({{oeis|A195467}}) and to the '''[[algebraic normal form]]''' (ANF) of Boolean functions.&lt;br&gt;
&lt;small&gt;({{w|Ivan Zhegalkin}} was the inventor of the ANF. The naming choices made here are new.)&lt;/small&gt;

Its colums are the truth tables of all Boolean functions. The column index is the '''Zhegalkin index''' of the respective Boolean function. 

Its rows are a subset of the Walsh functions, namely the {{w|exclusive or|XOR}}&lt;nowiki&gt;s&lt;/nowiki&gt; of atoms forming a {{w|Sierpiński triangle}} ({{oeis|A001317}}).

[[File:Zhegalkin 256.svg|thumb|left|1300px|The columns of the 8×256 Zhegalkin matrix are the truth tables of the 256 3-ary Boolean functions.&lt;br&gt;&lt;small&gt;The 8×256 matrix above are the colum indices. The blue columns are the fixed points.&lt;/small&gt;]]
{{clear}}
{{Collapsible START|as rows of a binary Walsh matrix|collapsed}}
This is a 256×256 binary {{w|Walsh matrix}}. Each row is the {{w|Variadic function|variadic}} XOR of the atoms shown in the 256×8 matrix on the left.
[[File:Walsh Zhegalkin 256.svg|1390px]]
{{Collapsible END}}


==Zhegalkin permutation==

{| class=&quot;wikitable&quot; style=&quot;text-align: center;&quot; style=&quot;float: right; text-align: center;&quot;
|+ sizes of finite Zhegalkin matrices
|-
! &lt;math&gt;n&lt;/math&gt;
| 0 || 1 || 2 || 3 || 4
|-
! &lt;math&gt;2^n \times 2^{2^n}&lt;/math&gt;
| 1×2 || 2×4 || 4×16 || 8×256 || 16×65536
|}

For arity &lt;math&gt;n&lt;/math&gt; the map from ANFs to truth tables gives a '''finite Zhegalkin matrix''' of size &lt;math&gt;2^n \times 2^{2^n}&lt;/math&gt;. &lt;small&gt;(It is the top left corner of the infinite matrix.)&lt;/small&gt;

It can be interpreted as a permutation of the integers &lt;math&gt;0~...~2^{2^n} - 1&lt;/math&gt;,
which shall be called '''Zhegalkin permutation''' &lt;math&gt;\Pi_n&lt;/math&gt;.&lt;br&gt;
&lt;small&gt;Keys and values in Π&lt;sub&gt;''n''&lt;/sub&gt; shall be called '''[[Zhegalkin twins]]''' &amp;mdash; e.g. 7 and 9 are Zhegalkin twins for arity 2.&lt;/small&gt;

It is a self-inverse [[Walsh permutation]] of degree 2&lt;sup&gt;''n''&lt;/sup&gt;. The corresponding element of {{w|general linear group|GL}}(2&lt;sup&gt;''n''&lt;/sup&gt;, 2) is the {{w|triangular matrix|lower}} Sierpiński triangle.&lt;br&gt;
&lt;small&gt;
Π&lt;sub&gt;2&lt;/sub&gt; is a Walsh permutation of degree 4, and permutes the integers 0 ... 15.
The corresponding element of GL(4, 2) is the 4×4 lower Sierpiński triangle.
&lt;/small&gt;

{{Zhegalkin matrix/Triangle Pi}}

In a finite Zhegalkin matrix, the columns with even/odd weight are in the left/right half. &amp;nbsp;
&lt;small&gt;(A truth table has a Zhegalkin twin with odd weight, iff its last digit is true.)&lt;/small&gt;&lt;br&gt;
&lt;small&gt;Boolean functions whose Zhegalkin index has even/odd weight shall be called {{w|evil number|evil}}/{{w|odious number|odious}}, which shall be called its '''''depravity'''''&lt;/small&gt;.

{{Zhegalkin matrix/triangle Pi compressed}}

===fixed points===

{| class=&quot;wikitable&quot; style=&quot;text-align: center;&quot; style=&quot;float: right; text-align: center;&quot;
|+ number of fixed points
|-
! &lt;math&gt;n&lt;/math&gt;
| 1 || 2 || 3 || 4 || 5
|-
! &lt;math&gt;2^{2^{n-1}}&lt;/math&gt;
| 2 || 4 || 16|| 256 || 65536
|}

The fixed points of Zhegalkin permutations correspond to [[noble Boolean functions]].

{{Zhegalkin matrix/Triangle Phi}}

==Python code==


{{Collapsible START|Python functions|collapsed gap-below}}
&lt;source lang=&quot;python&quot;&gt;
from sympy import binomial


def sierpinski(n):
    return int(sum([(binomial(n, i) % 2) * 2 ** i for i in range(n + 1)]))

def zhegalkin_perm(n, k):
    row_length = 1 &lt;&lt; (1 &lt;&lt; n)  # 2 ** 2 ** n
    assert k &lt; row_length
    string_length = 1 &lt;&lt; n  # 2 ** n
    k_binary = &quot;{0:b}&quot;.format(k).zfill(string_length)
    reflected_result = 0
    for i, binary_digit in enumerate(k_binary):
        if binary_digit == '1':
            s = sierpinski(i)
            reflected_result ^= s
    reflected_result_binary = &quot;{0:b}&quot;.format(reflected_result).zfill(string_length)
    result_binary = reflected_result_binary[::-1]
    return int(result_binary, 2)

def zhegalkin_fixed(n, k):
    if n == 0:
        assert k &lt; 2
        return k
    else:
        row_length = 1 &lt;&lt; (1 &lt;&lt; (n-1))  # 2 ** 2 ** (n-1)
        assert k &lt; row_length
    p = zhegalkin_perm(n-1, k)
    p_xor_k = p ^ k
    shifted_k = row_length * k
    return p_xor_k + shifted_k
&lt;/source&gt;
{{Collapsible END}}

{{Algebraic normal form/python}}


[[Category:Boolean functions; Zhegalkin stuff]]</text>
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  <page>
    <title>Wikiversity:Colloquium/archives/November 2022</title>
    <ns>4</ns>
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      <text bytes="23340" sha1="d0h7nmbfj4qwrzpsga39qctjxeks87k" xml:space="preserve">== Invitation to attend “Ask Me Anything about Movement Charter” Sessions ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[[m:Special:MyLanguage/Movement Charter/Community Consultation/Announcement/Ask Me Anything Sessions|You can find this message translated into additional languages on Meta-wiki.]]''
:&lt;div class=&quot;plainlinks&quot;&gt;''[[m:Special:MyLanguage/Movement Charter/Community Consultation/Announcement/Ask Me Anything Sessions|{{int:interlanguage-link-mul}}]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Movement Charter/Community Consultation/Announcement/Ask Me Anything Sessions}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''&lt;/div&gt;
Hello all, 

During the 2022 Wikimedia Summit, the [[m:Special:MyLanguage/Movement Charter/Drafting Committee|Movement Charter Drafting Committee]] (MCDC) presented the first outline of the Movement Charter, giving a glimpse on the direction of its future work, and the Charter itself. The MCDC then integrated the initial feedback collected during the Summit. Before proceeding with writing the Charter for the whole Movement, the MCDC wants to interact with community members and gather feedback on the drafts of the three sections: Preamble, Values &amp; Principles, and Roles &amp; Responsibilities (intentions statement). The Movement Charter drafts will be available on the Meta page [[m:Special:MyLanguage/Movement Charter/Content|here]] on November 14, 2022. Community wide consultation period on MC will take place from November 20 to December 18, 2022. Learn more about it [[m:Special:MyLanguage/Movement Charter/Community Consultation|here]]. 

With the goal of ensuring that people are well informed to fully participate in the conversations and are empowered to contribute their perspective on the Movement Charter, three '''“Ask Me Anything about Movement Charter&quot;''' sessions have been scheduled in different time zones. Everyone in the Wikimedia Movement is invited to attend these conversations. The aim is to learn about Movement Charter - its goal, purpose, why it matters, and how it impacts your community. MCDC members will attend these sessions to answer your questions and hear community feedback.     

The “Ask Me Anything” sessions accommodate communities from different time zones. Only the presentation of the session is recorded and shared afterwards, no recording of conversations. Below is the list of planned events: 

* '''Asia/Pacific''': November 4, 2022 at 09:00 UTC ([https://zonestamp.toolforge.org/1667552400 your local time]). Interpretation is available in Chinese and Japanese.   
* '''Europe/MENA/Sub Saharan Africa''': November 12, 2022 at 15:00 UTC ([https://zonestamp.toolforge.org/1668265257 your local time]). Interpretation is available in  Arabic, French and Russian.  
* '''North and South America/ Western Europe''': November 12, 2022 at 15:00 UTC ([https://zonestamp.toolforge.org/1668265257 your local time]). Interpretation is available in Spanish and Portuguese. 

On the [[m:Special:MyLanguage/Movement Charter/Community Consultation|Meta page]] you will find more details; Zoom links will be shared 48 hours ahead of the call.

'''Call for Movement Charter Ambassadors'''

Individuals or groups from all communities who wish to help include and start conversations in their communities on the Movement Charter are encouraged to become [[m:Special:MyLanguage/Movement Strategy and Governance/Movement Charter Ambassadors Program/About|Movement Charter Ambassadors]] (MC Ambassadors). MC Ambassadors will carry out their own activities and get financial support for enabling conversations in their own languages. [[m:Special:MyLanguage/Movement Strategy and Governance/Team|Regional facilitators]] from the Movement Strategy and Governance team are available to support applicants with MC Ambassadors grantmaking. If you are interested please sign up [[m:Special:MyLanguage/Movement Strategy and Governance/Movement Charter Ambassadors Program/About|here]]. Should you have specific questions, please reach out to the MSG team via email: strategy2030@wikimedia.org or on the MS forum. 

We thank you for your time and participation. 

On behalf of the Movement Charter Drafting Committee,&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MNadzikiewicz (WMF)|MNadzikiewicz (WMF)]] ([[User talk:MNadzikiewicz (WMF)|discuss]] • [[Special:Contributions/MNadzikiewicz (WMF)|contribs]]) 15:38, 7 November 2022 (UTC)

== Philosophical essay on life versus technology ==

I have written a philosophical essay: [[User:Dan Polansky/Technology as a challenger and a threat to living things and their forms and patterns]].

I wonder whether its content can be used in any form in the mainspace or whether the subject and treatment are so hopelessly subjective that they are beyond saving. Given this is philosophy, the objective validity and acceptability can be questioned as usual. If there is a chance for mainspace in some form, I would try to find sources that make some of the arguments and trace to them, although the arguments should largely stand on their own; the attempt is at philosophical analysis that depends mostly on generally known empirical facts easily verifiable by anyone. I may be able to address issues raised in a possible peer review. Thank you for any effort.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:07, 10 November 2022 (UTC)

:@[[User:Dan Polansky|Dan Polansky]]: Wikiversity's [[Wikiversity:Mission|mission]] includes hosting a range of free-content, multilingual learning materials/resources. The essay is certainly a learning resource. Wikiversity doesn't require [[Wikipedia:NPOV]].
:I would just ask what you want others to learn from this essay. Are you only sharing your point of view, or do want readers to think through the issues and develop their own point of view? If you're just sharing your view, it's probably fine as is.
:If you want others to develop their own point of view, I would consider breaking it up so that there is a main overview page, probably with a much shorter title, and then subpages for each of the different issues raised. That way, each of them can be addressed individually with their own resources, and perhaps expanded in the future by yourself or others.
:[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 15:07, 10 November 2022 (UTC)
:: Thank you. I am not sure what my goal is. I want to share my ideas with the world (they are not so original so in a way not really my own), but do so in a possibly as objective, neutral and factual matter as possible. I hope reader to be able to use these distinctions, subtopics and arguments as a starting point for learning more and finding more sources online, and to eliminate some of the initial misconceptions. The subobjective is to draw relevant contrasts of analysis and raise key points, and provide some good relevant links for a start, e.g. to Stanford Encyclopedia of Philosophy but also to journalistic sources. The title is indeed rather long, but its point is to make it unabiguous. I could make it shorter, though:
::* Technology as a challenger and a threat to living things and their forms
::* Technology as a harm and a threat to living things and their forms
::* Technology as a harm and a threat to life and its forms
::* Technology as a harm and a threat to life (but I wanted to emphasize forms as well)
::* Technology as a threat to life and its forms
:: I would probably be quite happy with &quot;Technology as a harm and a threat to living things and their forms&quot;. I prefer &quot;living things&quot; to &quot;life&quot; as less ambiguous, and I want the word &quot;form&quot; or &quot;diversity&quot; to be there to emphasize that it is not only about continued existence of the whole but also richness of form. Maybe reducing &quot;harm and a threat&quot; to &quot;threat&quot; is okay, although &quot;threat&quot; suggests potentiality whereas the harm has already been done.

:: If you are okay with it, I would copy the content to the mainspace under the same title or one of the proposed ones, and then continue working on it there. Editors can then decide what they want to do with it and how to reshape it, but hopefully not delete it. If you have an idea for another shorter title, let's consider it. I considered &quot;life versus technology&quot;, &quot;man versus technology&quot;, and &quot;man versus nature&quot;, but all those are ambiguous or much broader. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:55, 10 November 2022 (UTC)
::: I went ahead and put it to &quot;[[Technology as a threat or promise for life and its forms]]&quot;. It can be renamed if wished, and in the worst case deleted, but your comments suggest this won't be necessary. There is some inline sourcing as well, although the linked Wikipedia articles provide many more sources beyond that. Someone could wish to create a wikidebate based on the content or in that direction. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 19:27, 10 November 2022 (UTC)

== Opportunities open for the Ombuds commission and the Case Review Committee ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
&lt;div style=&quot;margin:.2em 0 .5em;margin-{{#switch:{{PAGELANGUAGE}}|ar|arc|ary|arz|azb|bcc|bgn|ckb|bqi|dv|fa|fa-af|glk|ha-arab|he|kk-arab|kk-cn|ks|ku-arab|ms-arab|mzn|pnb|prd|ps|sd|ug|ur|ydd|yi=right|left}}:3ex;&quot;&gt;
[[m:Special:MyLanguage/Wikimedia Foundation Legal department/Announcement/2023 OC and CRC appointments process|''You can find this message translated into additional languages on Meta-wiki.'']]

''&lt;span class=&quot;plainlinks&quot;&gt;[[m:Special:MyLanguage/Wikimedia Foundation Legal department/Announcement/2023 OC and CRC appointments process|{{int:interlanguage-link-mul}}]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Wikimedia Foundation Legal department/Announcement/2023 OC and CRC appointments process}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]&lt;/span&gt;''
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Hi everyone! The Ombuds commission (OC) and the Case Review Committee (CRC) are looking for members. People are encouraged to nominate themselves or encourage others they feel would contribute to these groups to do so. There is more information below about the opportunity and the skills that are needed.

'''About the Ombuds commission'''

The Ombuds commission (OC) works on all Wikimedia projects to investigate complaints about violations of the privacy policy, especially in use of [[m:Special:MyLanguage/CheckUser policy|CheckUser]] and [[m:Special:MyLanguage/Oversight policy|Oversight]] (also known as Suppression) tools. The Commission mediates between the parties of the investigation and, when violations of the policies are identified, advises the Wikimedia Foundation on best handling. They may also assist the General Counsel, the Chief Executive Officer, or the Board of Trustees of the Foundation in these investigations when legally necessary. For more on the OC's duties and roles, '''[[m:Special:MyLanguage/Ombuds commission|see Ombuds commission on Meta-Wiki]]'''.

Volunteers serving in this role should be experienced Wikimedians, active on any project, who have previously used the CheckUser/Oversight tools OR who have the technical ability to understand these tools and the willingness to learn them. They must be able to communicate in English, the common language of the commission. They are expected to be able to engage neutrally in investigating these concerns and to know when to recuse when other roles and relationships may cause conflict. Commissioners will serve '''two-year terms''' (note that this is different from past years, when the terms have been for one year).

'''About the Case Review Committee'''

The Case Review Committee (CRC) reviews appeals of eligible Trust &amp; Safety office actions. The CRC is a critical layer of oversight to ensure that Wikimedia Foundation office actions are fair and unbiased. They also make sure the Wikimedia Foundation doesn’t overstep established practices or boundaries. For more about the role, '''[[m:Special:MyLanguage/Case Review Committee|see Case Review Committee on Meta-Wiki]]'''.

We are looking for current or former functionaries and experienced volunteers with an interest in joining this group. Applicants must be fluent in English (additional languages are a strong plus) and willing to abide by the [[m:Special:MyLanguage/Trust_and_Safety/Case_Review_Committee/Charter|terms of the Committee charter]]. If the work resonates and you qualify, please apply. Committee members will serve '''two-year terms''' (note that this is different from past years, when the terms have been for one year).

'''Applying to join either of these groups'''

Members are required to sign the [[m:Special:MyLanguage/Confidentiality agreement for nonpublic information|Confidentiality agreement for nonpublic information]] and must be willing to comply with the appropriate Wikimedia Foundation board policies (such as the [[m:Special:MyLanguage/Access to nonpublic information policy|access to non-public information policy]] and the [[foundation:Special:MyLanguage/Privacy policy|Foundation privacy policy]]). These positions requires a high degree of discretion and trust. Members must also be over 18 years of age.

'''If you are interested in serving in either capacity listed above,''' please write in English to the Trust and Safety team at ca[[File:At sign.svg|16x16px|link=|(_AT_)]]wikimedia.org (to apply to the OC) or to the Legal Team at legal[[File:At sign.svg|16x16px|link=|(_AT_)]]wikimedia.org (to apply to the CRC) with information about:

* Your primary projects
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* Your thoughts on what you could bring to the OC or CRC if appointed
* Any experience you have with the Checkuser or Oversight tools (OC only)
* Any other information you think is relevant

There will be two conversation hours to answer any questions that potential applicants may have:

* 17 October 2022, 03:00 UTC ([[toolforge:zonestamp/1665975648|other timezones]]) ([https://wikimedia.zoom.us/j/89111812234?pwd=KzVuNG85T0JXUUhuV3Z4RzFZM2JxQT09 Zoom meeting link]) ([https://calendar.google.com/event?action=TEMPLATE&amp;tmeid=MXQ3ZWZvNmFhNmYzZHM3cjFtcW5jZ3BqZ3MgeGVub0B3aWtpbWVkaWEub3Jn&amp;tmsrc=xeno%40wikimedia.org add to calendar])
* 16 November 2022, 18:00 UTC ([[toolforge:zonestamp/1668621642|other timezones]]) ([https://wikimedia.zoom.us/j/86718566846?pwd=bGhaN0N0emhPK0F1UmozNWxKOHZUdz09 Zoom meeting link]) ([https://calendar.google.com/event?action=TEMPLATE&amp;tmeid=bDhqNG1tNWNiZDc4amYydjA0a2tjb2hjaDAgeGVub0B3aWtpbWVkaWEub3Jn&amp;tmsrc=xeno%40wikimedia.org add to calendar])

'''The deadline for applications is 31 December 2022 in any timezone.'''

Please feel free to pass this invitation along to any users who you think may be qualified and interested. Thank you!

On behalf of the Committee Support team,&lt;br /&gt;&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MNadzikiewicz (WMF)|MNadzikiewicz (WMF)]] ([[User talk:MNadzikiewicz (WMF)|discuss]] • [[Special:Contributions/MNadzikiewicz (WMF)|contribs]]) 11:08, 14 November 2022 (UTC)

== You're all invited to a Zoom workshop tonight! ==

Hi all!

I'm [[User:Greg_at_Higher_Math_Help|Greg Stanton]], and I'm running a Zoom workshop tonight with my collaborator [[User:Professorbrendan|Brendan Sullivan]]. With [https://meta.wikimedia.org/wiki/Grants:Project/Eventmath grant support from the Wikimedia Foundation], we're building an exciting new Wikiversity project to promote mathematical literacy. By attending tonight's workshop, you'll be making a huge difference, since we're expecting an education reporter from a major news outlet! Your comments could be featured in the story.

Our goal is to help students wield math as a tool for understanding their world. Since our project combines current events and math, we call it [[Eventmath]]. Basically, it's a Wikiversity learning project where math educators can share math lesson plans based on current events. Each lesson plan is based on a news article or social media post.

During the introductory talk, we'll explain that this approach to building mathematical literacy has special advantages. There will be an interactive portion afterward, where you'll have a chance to ask questions or make a small contribution to the project. The workshop runs over Zoom from 7:00 PM to 8:30 PM [https://www.google.com/search?q=eastern+time&amp;oq=Eastern+Time&amp;aqs=chrome.0.0i131i433i512j0i433i512j0i131i433i512l2j0i512l4j0i131i433i512j0i512.1652j0j7&amp;sourceid=chrome&amp;ie=UTF-8 Eastern Time]. You can register for the event through [https://docs.google.com/forms/d/e/1FAIpQLSdA9AY02ARarbrfYhLfvjfDWeLpPg98ltFj6_DHCw6q7FHB8A/viewform a short online form]. No preparation is required to attend. You just need to show up! And of course, like everything on Wikiversity, the workshop is free.

P.S.

If you cannot attend but are interested to know about future events, you're welcome to join the [https://docs.google.com/forms/d/1gyy2ywlQs3fzvpiEbue6fhgEjY8OcYiz7ENI__-5sh4/edit Eventmath mailing list]. If you fill out the workshop form, we'll add you to the mailing list automatically.

Thank you so much!
--[[User:Greg at Higher Math Help|Greg at Higher Math Help]] ([[User talk:Greg at Higher Math Help|discuss]] • [[Special:Contributions/Greg at Higher Math Help|contribs]]) 18:32, 16 November 2022 (UTC)

== Intent to deprecate RoundBox templates ==

* [[Template:RoundBoxTop]]
* [[Template:RoundBoxNext]]
* [[Template:RoundBoxBottom]]

A number of pages on this wiki use these templates to apply background colors to sections of the page. While this adds a pleasant splash of color, it comes with a nasty drawback: it makes those pages incompatible with the visual editor. Any text or other content present between these two templates is treated as a single block of &quot;template content&quot; by the visual editor and cannot be edited normally. Users must either open the page in the source editor and edit the wikitext directly (which inexperienced users may be uncomfortable doing), or open the block in the template editor and edit the wikitext content there (which is even more cumbersome). Since the visual editor is used by default for most pages on Wikiversity, this has the effect of making it much more difficult for users to edit resources which use these templates, which may discourage them from contributing.

For an example of this behavior, view the article [[Ruby]], then open the visual editor and try to modify any of the text on the page.

Unless there is any objection, I'd like to modify these templates to make them no longer transclude any content onto the page. This will remove the formatting they applied to pages and make it possible to use the visual editor on those pages. Once this is done, the templates can safely be removed at a later date. I realize this will make these pages less visually appealing, but usability for editors ('''especially''' ones who are new to the site!) feels like it should be a higher priority than appearance. [[User:Omphalographer|Omphalographer]] ([[User talk:Omphalographer|discuss]] • [[Special:Contributions/Omphalographer|contribs]]) 00:49, 18 November 2022 (UTC)

:I think I'd rather just remove the templates from pages in main space and leave the templates themselves as is. If a user wants to have round boxes in user pages, for example, it's up to them. Once the templates are removed from main space pages, we can look at any templates that include them to see if they need to be cleaned up as well. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 04:44, 18 November 2022 (UTC)
:Having just looked at the templates involved, I want to redouble this recommendation. Altering the base templates is not the way to go. Too many pages will be negatively impacted unnecessarily. The correct solution is to not include these templates in pages typical users would edit. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 04:49, 18 November 2022 (UTC)
::My initial concern was the sheer number of pages involved. There are 1000+ transclusions of RoundBoxTop in the main namespace alone. That's why my initial recommendation would be to disable the template at the source. That way, not only are all the pages fixed at once, but the styling can be restored if we come up with a way to make it compatible with the visual editor - doing a batch edit is slower and more intrusive, and would be harder to revert.
::If you're concerned about allowing these templates to be used in userspace, it should be possible to implement that in template logic using [[mediawikiwiki:Help:Magic words#Namespaces|the &lt;nowiki&gt;{{NAMESPACE}}&lt;/nowiki&gt; macro]]. I have a bit of experience doing crazy things with templates. :) [[User:Omphalographer|Omphalographer]] ([[User talk:Omphalographer|discuss]] • [[Special:Contributions/Omphalographer|contribs]]) 05:19, 18 November 2022 (UTC)
:::I suspect the right way to do this is with [[mw:Help:TemplateStyles]]. I don't have time to work on it right now, though. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 02:36, 21 November 2022 (UTC)
::::Unfortunately, I don't think that's going to be sufficient here. TemplateStyles would allow the CSS in the RoundBox templates to be extracted to a separate page, but the visual editor problems are caused by the HTML elements those templates create to apply their styles to, not by the styles themselves. In this case, those element are a table, but '''EDIT: I've now confirmed that''' any other HTML element would have the same problem. [[User:Omphalographer|Omphalographer]] ([[User talk:Omphalographer|discuss]] • [[Special:Contributions/Omphalographer|contribs]]) 03:43, 21 November 2022 (UTC)
:::::I think it should be up to the project or the primary editor whether or not to use this. For example, this is a primary design choice in all of the [[Motivation and emotion]] chapters. That's 10+ years of work by real-world students with a professor who is still active and using this resource. Likewise, any use in user space should be preserved as a choice by the user, which it was.
:::::On the other hand, I am happy to see it removed from resources like [[Introduction to Computer Science]]. So far, I'm not sure this can or should be automated, though. Many of the resources using this are 15 years old and need more attention than just hiding the boxes. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:52, 21 November 2022 (UTC)
::::::{{support}} for your comment, Dave [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 10:30, 29 November 2022 (UTC)</text>
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  <page>
    <title>Noble Boolean functions</title>
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      <text bytes="8681" sha1="4tkxv5s7tv8ka2f74eaupxmr02orhfp" xml:space="preserve">{{Boolf header}}
{{Zhegalkin stuff}}
Noble Boolean functions are those who are their own [[Zhegalkin twins]], i.e. the binary expression of their [[Algebraic normal form|ANF]] is equal to their truth table.&lt;br&gt;
They correspond to {{w|Fixed point (mathematics)|fixed points}} in the [[Zhegalkin matrix#Zhegalkin permutation|Zhegalkin permutation]].&lt;br&gt;
They are all even, i.e. the first digit of their truth table is false.&lt;br&gt;
When a Boolean function is noble, its whole [[Boolf-EC#P|faction]] is noble.&lt;br&gt;
&lt;small style=&quot;opacity: .5;&quot;&gt;Within the [[Studies of Boolean functions|this project]] it is slightly misleading to apply the term ''noble'' to [[Boolf-term#BF|Boolean functions]]. It is a property of a [[Boolf-term#TT|truth table]] with a specific length.&lt;/small&gt;

{{Zhegalkin matrix/Triangle Pi|collapsed}}

{{Zhegalkin matrix/Triangle Phi|collapsed}}

{{Collapsible START|3-ary nobles &lt;small&gt;(Venn diagrams)&lt;/small&gt; assigned to juniors &lt;small&gt;(tesseract vertices)&lt;/small&gt;|open gap-below}}
[[File:3-ary nobles in tesseract.svg|500px]]
{{Collapsible END}}

{{Collapsible START|3-ary and 4-ary nobles assigned to juniors &lt;small&gt;(in square matrices)&lt;/small&gt;|collapsed gap-below}}
These matrices show the 2-ary and 3-ary Boolean functions, represented by the big gray integers &lt;small&gt;(corresponding to the truth tables)&lt;/small&gt;.&lt;/small&gt;&lt;br&gt;
The small black integers above them are the senior nobles &lt;small&gt;(i.e. one arity above)&lt;/small&gt;.&lt;br&gt;
&lt;small style=&quot;opacity: .5;&quot;&gt;(The highlighted big numbers are the king indices.)&lt;/small&gt;
{|
| [[File:2T principality; overview.svg|thumb|center|250px|3-ary nobles]]
| [[File:3T principality; overview.svg|thumb|center|600px|4-ary nobles]]
|}
{{Collapsible END}}

{{Collapsible START|&lt;math&gt;\Phi_3&lt;/math&gt; as 8×16 matrix {{spaces|8}} &lt;math&gt;\Phi_4&lt;/math&gt; as 16×256 matrix|collapsed  gap-below}}
[[File:Fixed points in Zhegalkin permutation 3.svg|thumb|left|195px|row 3]]
{{clear}}
[[File:Fixed points in Zhegalkin permutation 4.svg|thumb|left|1440px|row 4]]
{{clear}}
The images show how &lt;math&gt;\Phi_n&lt;/math&gt; is derived from &lt;math&gt;\Pi_{n-1}&lt;/math&gt;, the permutation of the same length.&lt;br&gt;
The long matrices have two halves:&lt;br&gt;
In the upper half the bit pattern in column &lt;math&gt;k&lt;/math&gt; is that of &lt;math&gt;\Xi_{n-1,~k} ~ = ~ \Pi_{n-1,~k} \oplus k&lt;/math&gt;.
&amp;nbsp;&amp;nbsp;&amp;nbsp;&lt;small&gt;(Compare triangle Ξ in the next section.)&lt;/small&gt;&lt;br&gt;
The bit pattern in the lower half is identical to that of the gray column indices.

&lt;math&gt;\Phi_{n,~k} ~~ = ~~ \Xi_{n-1,~k} + \bigl(2^{2^{n-1}} \cdot k \bigr) ~~ = ~~ \bigl(\Pi_{n-1,~k} \oplus k \bigr) + \bigl(2^{2^{n-1}} \cdot k \bigr)&lt;/math&gt;

The small matrices on the left are divided in the same way:&lt;br&gt;
The upper half is a Sierpiński triangle without the main diagonal, and the lower half is the main diagonal.

These properties of noble Boolean functions can be derived from this:&lt;br&gt;
* They are even, i.e. place 0 is always false.
* The 1-bit places (e.g. 1, 2, 4, 8) have the same truth value. &lt;small&gt;(Those where it is false/true shall be called weak/strong.)&lt;/small&gt;
* Half of them are evil/odious, which is indicated by the last place being false/true. &lt;small&gt;(The odious ones are on the right, just like in triangle &amp;Pi;.)&lt;/small&gt;
{{Collapsible END}}

{{Noble Boolean functions/row sums}}

===quadrants===

It is easily seen, that the left and right half of each row differ only in the last digit.&lt;br&gt;
Those on the left/right have even/odd weight. They shall be called evil/odious.

{{Noble Boolean functions/Python half rows}}

There is a second way to partition the nobles in two halves:&lt;br&gt;
Those in even/odd places of the triangle row have false/true entries in all 1-bit places of their truth table. They shall be called weak/strong.

So the nobles can be partitioned into four quadrants by depravity and strength.

{{Collapsible START|illustration of quadrants for ''n'' &amp;equals; 3|open}}
Vertically adjacent quadrants contain relative complements. Horizontally adjacent quadrants differ only in the central vertex.&lt;br&gt;
&lt;small&gt;(40 and 214 are relative complements. 40 and 168 differ only in the central vertex.)&lt;/small&gt;&lt;br&gt;

The 16 noble 3-ary Boolean functions form 8 factions. So there are 2 royal factions.
[[File:Noble 3-ary Boolean functions.svg|650px|center]]
{{Collapsible END}}

Nobles that are evil and weak shall be called '''''royal'''''.&lt;br&gt;
Each noble corresponds to a royal, and can easily be derived from it. &lt;small style=&quot;opacity: .5;&quot;&gt;(A royal corresponds to itself.)&lt;/small&gt;&lt;br&gt;
When a Boolean function is royal, its whole [[Boolf-EC#P|faction]] is royal.&lt;br&gt;
The function with the smallest Zhegalkin index in a faction shall be called '''''king''''', and be used to represent it.&lt;br&gt;
So all nobles of a given arity can effectively be represented by a rather short list of kings.

{{Noble Boolean functions/royal triangle|collapsed}}

{{Collapsible START|4-ary royals in 16×64 matrix|collapsed light gap-below}}
The columns of this matrix are the 4-ary royal Boolean functions.&lt;br&gt;
[[File:4-ary royal Boolean functions in matrix.svg|x180px]]&lt;br&gt;
Compare &lt;math&gt;\Phi_4&lt;/math&gt; as 16×256 matrix, shown above.&lt;br&gt;
&lt;small&gt;The 16×6 matrix on the left is shown as the 16×8 matrix from that file, with the left and right column blacked out.&lt;/small&gt;
{{Collapsible END}}

{{Noble Boolean functions/triangle of kings|collapsed}}

{{Collapsible START|representatives of 4-ary noble factions|collapsed}}
[[File:Representatives of 4-ary noble factions.svg|1200px]]

The top left corner in each 2×2 matrix is a king. The other corners are its equivalents in the other quadrants.&lt;br&gt;
&lt;small style=&quot;opacity: .5;&quot;&gt;(Vertically adjacent quadrants contain relative complements. Horizontally adjacent quadrants differ only in the central vertex.)&lt;/small&gt;

The two tables below correspond to the image above. The one on the left shows the same numbers as the image.&lt;br&gt;
The one on the right shows the [[smallest Zhegalkin index]] for each of the 44 factions. &lt;small style=&quot;opacity: .5;&quot;&gt;(They differ only for the odd factions, i.e. those with green and blue background.)&lt;/small&gt;

{| style=&quot;width: 100%;&quot;
| {{Noble reps/outer/match}}
| {{Noble reps/outer/minimal}}
|}

The black integers are Zhegalkin indices. The gray numbers below are their noble indices, i.e. the positions in the sequence of nobles.&lt;br&gt;
The beige numbers in the image are faction sizes, i.e. the number of different permutations of the example shown.
{{Collapsible END}}

{{Collapsible START|4-ary kings|collapsed light gap-above}}
[[File:Representatives of 4-ary royal factions.svg|800px]]
{{Collapsible END}}

===group under exclusive or===

With XOR as a group operation the ''n''-ary noble and royal Boolean functions form a power of the {{w|cyclic group}} C&lt;sub&gt;2&lt;/sub&gt;.

{{Collapsible START|Python example|collapsed light gap-below}}
The 3-ary nobles form the group C&lt;sub&gt;2&lt;/sub&gt;&lt;sup&gt;4&lt;/sup&gt;.

The Python operator &lt;code&gt;^&lt;/code&gt; represents the {{w|bitwise operation#XOR|bitwise XOR}}.

&lt;source lang=&quot;python&quot;&gt;
nobles = [0,  30,  40, 54,  72, 86, 96, 126, 128, 158, 168, 182, 200, 214, 224, 254]

for i, a in enumerate(nobles):
    for j, b in enumerate(nobles):
        assert nobles.index(a ^ b) == i ^ j
&lt;/source&gt;

This works for any row of the noble triangle &lt;math&gt;\Phi&lt;/math&gt;, or from the royal triangle. &lt;small&gt;(But not from the triangle of kings.)&lt;/small&gt;
{{Collapsible END}}


==patrons==

The XOR of twins is noble, i.e. the XOR of a key and a value in &lt;math&gt;\Pi_n&lt;/math&gt; is an entry of &lt;math&gt;\Phi_n&lt;/math&gt;.&lt;br&gt;
For a Boolean function this means, that the XOR of its ANF and its truth table is a noble Boolean function, which shall be called its '''''patron'''''.&lt;br&gt;
The patron of a noble is the contradiction.

{{Zhegalkin matrix/triangle Xi|collapsed}}

For &lt;math&gt;n \ge 1&lt;/math&gt; the entries in &lt;math&gt;\Xi_n&lt;/math&gt; are repetitions of those in &lt;math&gt;\Phi_n&lt;/math&gt;. &lt;span style=&quot;opacity: .6;&quot;&gt;E.g. &lt;math&gt;\Xi_2&lt;/math&gt; contains the entries &lt;math&gt;\{0, 6, 8, 14\}&lt;/math&gt;, each repeated four times.&lt;/span&gt;

The set of places where &lt;math&gt;\Xi_n&lt;/math&gt; has entries &lt;math&gt;\Phi_{n,~k}&lt;/math&gt; can be calculated by XORing &lt;math&gt;\Pi_{n-1,~k}&lt;/math&gt; with the entries of &lt;math&gt;\Phi_n&lt;/math&gt;.

===3-ary Boolean functions with patron 168===

{{Zhegalkin matrix/matrix pi xor phi}}

{{Zhegalkin matrix/clusters with patron 168}}

{{Collapsible START|positions in matrix|collapsed gap-above}}
[[File:3-ary Boolean functions; patrons 10.svg|thumb|center|500px|Boolean functions with patron 168 in octeract matrix&lt;br&gt;&lt;small&gt;(This is the transpose of [[c:File:3-ary Boolean functions; quaestor 03 (indices).svg|Zhegalkin indices with quaestor 3]].)&lt;/small&gt;]]
{{Collapsible END}}


[[Category:Boolean functions; Zhegalkin stuff]]</text>
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{{CountryHeader|File:Philippines (orthographic projection).svg|https://en.wikipedia.org/wiki/Philippines}}{{HTitle|Brief Country Information }}The Philippines is a stunning archipelagic country located in Southeast Asia, consisting of a vast expanse of more than 7,600 islands, which are divided into three primary geographical areas, namely Luzon, Visayas, and Mindanao. As of the 2020 census, the country's population has grown to 109,035,343, positioning the Philippines as the 13th most populous country globally (Philippine Statistics Authority, 2022). 

Filipino and English are the most spoken languages in the country, serving as the official languages, followed by Cebuano, Ilocano, Hiligaynon, Waray, and several other regional languages and dialects (Ethnologue, 2022). 

The Philippines is widely recognized for its natural beauty, featuring picturesque landscapes, coral reefs, and idyllic beaches. It's a country with a rich and diverse cultural heritage, shaped by its past as a Spanish, American, and Asian colony, with historical landmarks and heritage sites representing the influence of various cultures over the centuries.{{HTitle|Incidence and Prevalence of Hearing Loss}}Hearing loss is a common problem across all age groups in the Philippines, and the prevalence rates are higher than global estimates (Newall et al., 2020). The national prevalence of moderate or worse hearing loss is 7.5% in children, 14.7% in working-age adults, and 49.1% in the elderly (Newall et al., 2020).

The prevalence rates are also high regionally, with a study conducted in Southern Tagalog Region IV-A: CALABARZON (Cavite, Laguna, Batangas, Rizal, and Quezon) showing that around 71% of people have at least mild hearing loss, and 26.33% have disabling hearing impairment (Pardo et al., 2022). Among children aged between 4 and 18 years, 11.87% have disabling hearing loss, while among working adults aged between 19 and 64 years, the prevalence rate is 8.97%. In older adults aged 65+, the rate is 3.17% (Pardo et al., 2022).

Local studies reveal that hereditary factors play a significant role. Research on cochlear implant patients found a frequent genetic mutation SLC26A4 c.706C&gt;G underlying hearing impairment (Chiong et al., 2018). Another study of an indigenous Filipino community identified genetic factors like SLC26A4 variants as major contributors to otitis media and conductive hearing loss (Santos-Cortez et al., 2016).

Outer and middle ear conditions, often caused by chronic infections, can also increase the risk of hearing impairment (Newall et al., 2020). Socioeconomic status is also a factor, with higher income associated with lower odds of moderate hearing loss. Wax occlusion affects 12.2% of people, while middle ear disease is present in 14.2% (Newall et al., 2020).

The number of Filipinos with severe to profound hearing loss is higher than in developed countries. Given the higher prevalence and severity rates, hearing loss is a significant public health concern that requires urgent attention to curb the rising disability.{{HTitle|Education and Professional Practice}}
Clinical audiology education is primarily offered at two institutions: the University of Santo Tomas (UST) and the University of the Philippines (UP). Both universities provide a Master's program in Clinical Audiology, which integrates theoretical knowledge with clinical applications. 

1. [https://www.ust.edu.ph/academics/programs/health/# UST Clinical Audiology Program]

The Master in Clinical Audiology at the University of Santo Tomas stands as a pioneering program in the Philippines, establishing itself as the nation's first two-year graduate degree in this specialized field. Since its inception over twenty years ago, the program has cultivated a network of nearly 300 clinical audiologists who now serve diverse healthcare settings both within the Philippines and internationally. 
Through strategic collaborations with leading universities, hospitals, and industry partners worldwide, the curriculum seamlessly integrates rigorous theoretical coursework with intensive hands-on clinical training. The program's commitment to excellence in audiology education, evidence-based practice, research innovation, and community outreach enables it to produce an average of 20 highly qualified clinical audiologists annually, contributing significantly to the advancement of hearing healthcare services.

2.[https://cm.upm.edu.ph/p/ms-clinical-audiology/ UP Clinical Audiology Program]

Jointly offered by the College of Medicine and the College of Allied Medical Professions, it exemplifies the university's commitment to academic excellence and community service. This collaborative initiative, supported by the Department of Otorhinolaryngology and the Department of Speech Pathology, aims to develop highly skilled audiologists who can address critical healthcare needs in hearing prevention, diagnosis, and treatment.

This two-year graduate program integrates comprehensive theoretical foundations with hands-on clinical experience. The curriculum encompasses four core areas: audiologic evaluation, audiologic habilitation, hearing conservation, and audiology service delivery program development. Through this rigorous training, graduates emerge prepared to deliver exceptional patient care while contributing to the advancement of audiological services and research.

The program's structure reflects the university's dual mission of providing outstanding advanced education and fostering meaningful community impact through professional healthcare services. By combining academic rigor with practical application, the program prepares the next generation of audiologists to meet evolving healthcare challenges and serve diverse community needs.{{HTitle|Challenges and Opportunities}}
=== Challenges ===
* '''Limited access to services'''
The prevalence of hearing loss in the Philippines is increasing, yet access to audiological services remains limited, particularly in rural and underserved areas. This lack of access highlights the need for expanded healthcare infrastructure and improved distribution of audiologists and trained hearing care healthcare workers across regions. Unfortunately, the disparities in the existing healthcare infrastructure significantly impact the quality of life of people living in these areas. 
* '''Shortage of qualified professionals''' 
The Philippines currently needs more skilled audiologists and other healthcare professionals specializing in hearing care. This shortage is impeding the nation's ability to meet the increasing demand for hearing healthcare services, highlighting the need for investment in education and training programs to develop a competent workforce.
* '''Brain drain'''
A significant challenge confronting audiology in the Philippines is the phenomenon of brain drain, wherein most locally-trained audiologists seek better opportunities overseas. This trend of emigration of skilled professionals exacerbates the shortfall of audiologists in the country and undermines initiatives to enhance the local healthcare system. The resulting shortage of qualified audiologists in the Philippines poses a severe concern for the delivery of ear and hearing care services and the population's overall well-being. Therefore, measures must be taken to address this issue and retain local talent in audiology.
* '''Lack of health insurance coverage for hearing devices'''
One significant problem in the Philippines is the need for health insurance coverage for hearing devices. This applies to both national insurance and private health insurance. As a result, individuals requiring hearing devices often have to pay for them out of their pockets or seek assistance from various sources. This includes seeking sponsorship from local politicians, NGOs, and social welfare services or receiving donations of refurbished hearing aids from other countries.
* '''Unregulated hearing centers and dispensing of hearing aids'''
The establishment of hearing centers and the distribution of hearing aids without appropriate licensing or training pose significant challenges to audiology practice in the Philippines. The lack of regulations and oversight results in substandard care, inaccurate diagnosis, and inappropriate management of hearing disorders, ultimately jeopardizing patient safety and outcomes. Implementing stringent guidelines and qualifications for hearing center establishments and hearing aid dispensers is imperative to ensure that qualified and trained professionals provide quality audiological care. Failure to do so may lead to detrimental consequences for patients with hearing impairments and the audiological profession.
*'''Awareness and stigma'''
In the Philippines, most of the general population lacks awareness and knowledge about hearing health issues. As a result of the stigma attached to hearing loss, people often delay seeking services, which can lead to insufficient management of auditory disorders. It is crucial to address this stigma through public education and awareness campaigns to promote early intervention, management, and (re)habilitation.

{{HTitle|References}}

# [https://psa.gov.ph/population-and-housing/node/186896Philippine Statistics Authority. (2022). 2020 Census of Population and Housing.]
# [https://www.ethnologue.com/country/PH Ethnologue. (2022). Languages of the World - Philippines.]
# Newall, J. P., Martinez, N., Swanepoel, W., &amp; McMahon, C. M. (2020). A National Survey of Hearing Loss in the Philippines. Asia-Pacific journal of public health, 32(5), 235–241. https://doi.org/10.1177/1010539520937086
# Pardo, P. M., Niñal-Vilog,  . , Acuin, J. M., Calaquian, C. E.,  &amp; Onofre-Telan, R. D.(2022).Hearing and clinical otologic profile of Filipinos living in Southern Tagalog Region IV-A (CALABARZON), Philippines: The Southern Tagalog ENT Hearing Specialists (STENTS) Survey 2012-2017. Philippine Journal of Otolaryngology Head and Neck Surgery, 37(2), 8-15
# Chiong, C. M., Reyes-Quintos, M. R. T., Yarza, T. K. L., Tobias-Grasso, C. A. M., Acharya, A., Leal, S. M., Mohlke, K. L., Mayol, N. L., Cutiongco-de la Paz, E. M., &amp; Santos-Cortez, R. L. P. (2018). The SLC26A4 c.706C&gt;G (p.Leu236Val) Variant is a Frequent Cause of Hearing Impairment in Filipino Cochlear Implantees. Otology &amp; neurotology : official publication of the American Otological Society, American Neurotology Society [and] European Academy of Otology and Neurotology, 39(8), e726–e730. https://doi.org/10.1097/MAO.0000000000001893
# Santos-Cortez, R. L., Reyes-Quintos, M. R., Tantoco, M. L., Abbe, I., Llanes, E. G., Ajami, N. J., Hutchinson, D. S., Petrosino, J. F., Padilla, C. D., Villarta, R. L., Jr, Gloria-Cruz, T. L., Chan, A. L., Cutiongco-de la Paz, E. M., Chiong, C. M., Leal, S. M., &amp; Abes, G. T. (2016). Genetic and Environmental Determinants of Otitis Media in an Indigenous Filipino Population. Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery, 155(5), 856–862. https://doi.org/10.1177/0194599816661703
# University of the Philippines Manila. (n.d.). Master in Clinical Audiology. College of Medicine. https://cm.upm.edu.ph/p/ms-clinical-audiology/
# University of Santo Tomas. (n.d.). Programs in health. https://www.ust.edu.ph/academics/programs/health/
# 
{{:Global Audiology/Authors-1|Joyce Rodvie Sagun|https://www.linkedin.com/in/joyce-rodvie-sagun-4691bb182}}
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      <text bytes="54968" sha1="tr4040qp9w8i3sew7zkbzwmszvegm6t" xml:space="preserve">== Dressmakers, Modistes, Costumiers, Perruquiers and Jewelers ==

=== Not to Mention Seamstresses, Tailors, Lace-makers, Milliners, and Lady's Maids ===
Dominated as the social world was by women, fashion was an important part of the reportage on social events, with some reporters demonstrating knowledge of fabrics, cuts, laces, and so on. The Victorians had specialized terms for people who designed and made clothing, especially very fashionable clothes or haut couture, and specialized careers for those people who assisted women to acquire, manage and wear that clothing. Because of the popularity of fancy-dress or costume parties, some of the people assisting them were costumiers from the world of theatre and opera. The terminology and examples that follow are generally focused on the end of the 19th century in London.

== Fashion Houses, Couturiers and Modistes ==
The ''Gentlewoman'' says, &quot;A great number of well-known modistes in London were also called upon to supply dresses.&quot;&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} Among those who helped construct the costumes and wigs include the following:

=== Doucet ===
A gossipy article in ''Derbyshire Times and Chesterfield Herald'' (citing the ''Daily Mail'') says, &quot;Lady de Grey is going as Zenobia, and is getting her dress from Doucet, I hear,&quot;&lt;ref name=&quot;:11&quot;&gt;“Derbyshire Sayings and Doings.” ''Derbyshire Times and Chesterfield Herald'' 12 June 1897, Saturday: 5 [of 8], Col. 2A. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000228/18970612/018/0005.&lt;/ref&gt; although she went as Cleopatra and not Zenobia (only the Duchess of Devonshire went as Zenobia).

=== Mme Durrant ===

Mme Durrant's concern, at the end of the 19th century, at least, was at 116 &amp; 117 New Bond-street, London W. An ad in ''The Queen'' says,&lt;blockquote&gt;Court Dressmaker and Milliner. The Latest Paris Models in Morning, Afternoon, Tailor, and Evening Gowns, Millinery, and Mantles.&quot;&lt;ref&gt;&quot;Madame Durrant, Court Dressmaker and Milliner.&quot; ''The Queen'' 15 April 1899, Saturday: 11 [of 88], Cols. 2–3c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18990415/082/0011.&lt;/ref&gt;&lt;/blockquote&gt;Mme Durrant made the costumes for the following guests at the ball:

# [[Social Victorians/People/Londonderry#Theresa, Marchioness of Londonderry|Theresa, Marchioness of Londonderry]]&lt;ref&gt;&quot;Lines for the Ladies.&quot; ''Daily Gazette for Middlesbrough'' Thursday 16 June 1898: 4 [of 4], Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000159/18980616/060/0004.&lt;/ref&gt; The dress and fabrics for the Marchioness of Londonderry as well as her quadrille, were made in Britain or Ireland.&lt;ref name=&quot;:02&quot;&gt;&quot;This Morning’s News.&quot; London ''Daily News'' 6 July 1897, Tuesday: 7 [of 12], Col. 3b. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970706/038/0007.&lt;/ref&gt;

Mme Durrant made at least a couple of dresses for Queen Mary (early 20th century).&lt;ref&gt;{{Cite web|url=https://tr.pinterest.com/pin/278730664423122186/|title=1900 - 1919 Clothing panosundaki Pin|website=Pinterest|language=en|access-date=2023-03-08}} https://pin.it/2GUiBm7 and https://pin.it/2GUiBm7.&lt;/ref&gt; Also, perhaps early 20th-c, Durrant had an address on Dover Street.&lt;ref&gt;{{Cite web|url=http://www.elisarolle.com/queerplaces/ch-d-e/Edwin%20Hardy%20Amies.html|title=queerplaces - Sir Edwin Hardy Amies|website=www.elisarolle.com|access-date=2023-03-08}} http://www.elisarolle.com/queerplaces/ch-d-e/Edwin%20Hardy%20Amies.html.&lt;/ref&gt; ''The Queen'' also has ads for a &quot;Mr. Durrrant's Ladies' Taylor and Habit Maker&quot; in Edinburgh and Glasgow in 1892.&lt;ref&gt;&quot;Durrant Ladies' Taylor and Habit Maker.&quot; [advertisement] ''The Queen'' 06 February 1892, Saturday: 5 [of 81], Cols. 2–3c [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18920206/043/0005.&lt;/ref&gt;

=== Mrs. Mason ===
M. or Mrs. Mason, of 4, New Burlington Street, W.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* &quot;Dress and Fashion&quot; answer by Adern Holt in the ''Queen'' to queries posed by &quot;Correspondents&quot;: &quot;F&lt;small&gt;ANCY&lt;/small&gt; D&lt;small&gt;RESS&lt;/small&gt;. — For the beautiful ball such as you describe you cannot do better than go to Mrs Mason, New Burlington-street, for the costume about which you inquire. It needs very careful making and the most artistic designs, and these you would be sure to obtain there, for the dresses she made for the Duchess of Devonshire's ball were quite artistic masterpieces.&quot;&lt;ref&gt;Holt, Ardern. &quot;Dress and Fashion. To Correspondents.&quot; The ''Queen'' 17 July 1897, Saturday: 48 [of 97], Col. 1a [of 3]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18970717/231/0049.&lt;/ref&gt;
Mrs. Mason made costumes for the following guests at the ball:

# [[Social Victorians/People/Pless|Daisy, Princess of Pless]]
# [[Social Victorians/People/Ashburton#Mabel, Lady Ashburton|Mabel, Lady Ashburton]]
# [[Social Victorians/People/de Trafford#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Violet, Lady de Trafford]]
# [[Social Victorians/People/Cadogan#Lady Sophie Scott|Lady Sophie Scott]]
# Lady Lurgan&lt;ref name=&quot;:6&quot; /&gt;
# [[Social Victorians/People/Leeds#Katherine, Duchess of Leeds|Katherine, Duchess of Leeds]]
# [[Social Victorians/People/Sutherland#Millicent, Duchess of Sutherland|Millicent, Duchess of Sutherland]]
# [[Social Victorians/People/Meysey-Thompson#Lady Ethel Meysey Thompson|Lady Ethel Meysey Thompson]]
# [[Social Victorians/People/Muriel Wilson|Muriel Wilson]]
# [[Social Victorians/People/Edmonstone#Lady Ida Edmonstone|Lady Ida Edmonstone]]
# [[Social Victorians/People/Goelet#Costumes at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Mary Goelet]]
#[[Social Victorians/People/Cavendish#Lady Edward Cavendish|Lady Edward Cavendish]]
#[[Social Victorians/People/Sarah Spencer-Churchill Wilson#Lady Sarah Wilson|Lady Sarah Wilson]]
#[[Social Victorians/People/Derby#Constance Villiers Stanley, Countess of Derby|Countess of Derby]]
#Mrs [[Social Victorians/People/Bourke|Gwendolen Bourke]]&lt;ref name=&quot;:6&quot; /&gt;
#Duchess of Roxburghe&lt;ref name=&quot;:6&quot; /&gt;

=== Morin-Blossier ===
The French &quot;tailoring workshop&quot;&lt;ref&gt;{{Cite web|url=https://fashion.mam-e.it/morin-blossier/|title=Morin-Blossier -|date=2016-02-05|language=it-IT|access-date=2022-04-07}}&lt;/ref&gt; of Morin-Blossier &quot;possibly&quot;&lt;ref name=&quot;:6&quot; /&gt; made the dress worn to  the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball]] by

* Alexandra, Princess of Wales&lt;ref name=&quot;:6&quot; /&gt;
* [[Social Victorians/People/Prince Charles of Denmark|Princess Maud of Wales]] (Princess Charles of Denmark)&lt;ref name=&quot;:43&quot;&gt;Harris, Russell. &quot;Prince and Princess Carl of Denmark, later King Haakon VII (1872-1957) and Queen Maud of Norway (1869-1938),  and Princess Victoria of Wales (1868-1935), as a 16th century Danish courtier, and Ladies-in-Waiting at to Marguerite de Valois.&quot; &quot;List of Sitters.&quot; ''In Calm Prose''. 2011 http://www.rvondeh.dircon.co.uk/incalmprose/denmark.html.&lt;/ref&gt;
* Duchess of York&lt;ref name=&quot;:6&quot; /&gt;
* Princess Victoria&lt;ref name=&quot;:6&quot; /&gt;

=== Messrs Russell and Allen ===
Old Bond-street., W.

Made presentation dresses for 8 of the following in 1913&lt;ref&gt;&quot;Their Majesties' Court.&quot; ''Lady's Pictorial'' 17 May 1913, Saturday: 35 [of 64], Col. 2c [of 3]. ''British Newspaper Archive''https://www.britishnewspaperarchive.co.uk/viewer/bl/0005980/19130517/296/0035. Same print title, p. 787.&lt;/ref&gt;:

* Mrs. A. C. Hardy, of Montreal
* Mrs. Thorburn
* Mrs. Ralph Berners
* Miss Spencer Warwick
* [[Social Victorians/People/Bourke|Miss [Daphne] Bourke]]
* Mrs. Henry Barran
* Miss D. Hickman
* Hon. Irene Molesworth
* The Hon. Edith Winn
* The Hon. Hilaria St. Aubyn
* The Hon. Mary Charteris
* Miss Grace Holley

=== Mrs Sims' Court Dress Establishment, Dublin ===
Mrs Mary Sims, Dawson Street, Dublin

Mrs Sims made a dress decorated with beetle wings in c. 1880; this dress still exists and, according to Elaine Hewitt, is in the NMI collections.&lt;ref name=&quot;:13&quot;&gt;Objects in Focus: New Research Seminar, Naional Museum of Ireland, Decoraive Arts and History, Collins Barracks. Saturday 16th February 2013. https://www.academia.edu/2455567/The_material_culture_of_infancy_and_early_childhood_in_Ireland_c_1680_1830?auto=download.&lt;/ref&gt; Hewitt's precis for an exhibit called ''Objects in Focus: New Research Seminar, National Museum of Ireland, Decoraive Arts and History, Collins Barracks'' says, &quot;Mary Sims was a court dressmaker by Royal appointment, who established herself from 1863 as the most prominent dressmaker in Dublin.&quot;

Mrs Sims made costumes for the following guests at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:

* [[Social Victorians/People/Cadogan#Lady Beatrix, Countess Cadogan|Lady Beatrix, Countess Cadogan]]

Other people Mrs Sims made clothes for:

* Alexandra, Princess of Wales, 1885: Kate Strasdin offers an example of Alexandra's strategic use of clothing: a gown Alexandra wore to a Drawing Room at Buckingham Palace was, according to the ''Times'', &quot;a dress of rich yellow satin and silver brocade, draped with silver lace, corsage to correspond, made by Mrs Sims of Dublin.&quot;{{rp|1885, p. 11}} What is strategic is the release of Mrs Sims's name, according to Strasdin, since &quot;[t]he communication of this detail can only have come from the royal household itself, demonstrating the control that Alexandra exerted over details released to the press relating to her appearance.&quot;&lt;ref&gt;Strasdin, Kate, &quot;Reporting Royal Dress: Queen Alexandra and Royal Image Making.&quot; Falmouth University Research Repository. http://repository.falmouth.ac.uk.&lt;/ref&gt;
* Ishbel, Marchioness Aberdeen, 1886: &quot;Ishbel, Lady Aberdeen (1857–1939), [wore a &quot;costume of an Irish lady in the thirteenth century&quot;] in 1886 while presiding over a garden party at the Vice Regal Lodge in the Phoenix Park in Dublin, an event to which the 2,000 invited guests were expected to wear clothes of Irish manufacture.&quot;&lt;ref&gt;Alex Ward, &quot;Dress and National Identity: Women’s Clothing and the Celtic Revival,&quot; ''Costume'', 48:2, 2014, 193-212, DOI: https://doi.org/10.1179/0590887614Z.00000000050.&lt;/ref&gt;{{rp|199}}

=== Smaller Concerns ===
* Madame Fréderic: made the costume for Princess Mary of Teck&lt;ref name=&quot;:6&quot; /&gt;
* Jays, Ltd., Regent-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* M. Machinka, Conduit-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* Maison Lucille: made Mrs. James's costume&lt;ref name=&quot;:6&quot; /&gt;
* Mrs. Nettleship: made the Countess of Yarborough's costume&lt;ref name=&quot;:6&quot; /&gt;
* Paquin, of Dover-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}: made the dress of Madame von André&lt;ref name=&quot;:6&quot; /&gt;

=== Worth, of Paris ===
Located in Paris, Maison Worth or the House of Worth — named for owner and designer Englishman Charles Frederick Worth — was a very influential couturier in the 2nd half of the 19th and the first quarter of the 20th centuries.&lt;blockquote&gt;Worth’s designs are notable for his use of lavish fabrics and trimmings, his incorporation of elements of historic dress, and his attention to fit. While the designer still created one-of-a-kind pieces for his most important clients, he is especially known for preparing a variety of designs that were shown on live models at the House of Worth. Clients made their selections and had garments tailor-made in Worth’s workshop.&lt;ref name=&quot;:7&quot;&gt;{{Cite web|url=https://www.metmuseum.org/toah/hd/wrth/hd_wrth.htm|title=Charles Frederick Worth (1825–1895) and the House of Worth {{!}} Essay {{!}} The Metropolitan Museum of Art {{!}} Heilbrunn Timeline of Art History|last=Krick|first=Authors: Jessa|website=The Met’s Heilbrunn Timeline of Art History|language=en|access-date=2024-07-12}} https://www.metmuseum.org/toah/hd/wrth/hd_wrth.htm.&lt;/ref&gt;&lt;/blockquote&gt;After having won design prizes at the 1851 Great Exhibition in London, which was housed at the Crystal Palace, and the 1854 Exposition Universelle in Paris, Worth opened his own design house in Paris in 1858.&lt;ref name=&quot;:7&quot; /&gt; The Empress Eugénie appointed him designer to the court of France&lt;ref&gt;{{Cite journal|date=2024-07-03|title=House of Worth|url=https://en.wikipedia.org/w/index.php?title=House_of_Worth&amp;oldid=1232307431|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/House_of_Worth.&lt;/ref&gt;:&lt;blockquote&gt;Worth’s rise as a designer coincided with the establishment of the Second Empire in France. The restoration of a royal house in 1852, with Napoleon III (1808–1873) as the new emperor, once again made Paris an imperial capital and the setting for numerous state occasions. Napoleon III implemented a grand vision for both Paris and France, initiating changes and modernization that revitalized the French economy and made Paris into a showpiece of Europe. The demand for luxury goods, including textiles and fashionable dress, reached levels that had not been seen since before the French Revolution (1789–99). When Napoleon III married Empress Eugénie (1826–1920), her tastes set the style at court .... The empress’ patronage ensured Worth’s success as a popular dressmaker from the 1860s onward.&lt;ref name=&quot;:7&quot; /&gt;&lt;/blockquote&gt;Other patrons included women from Empress Eugénie's court, &quot;Elizabeth of Austria, Margherita of Italy, Mme. de Castiglione, Mme. de Pourtales, and every reigning star in the theatrical and operatic world.&quot;&lt;ref&gt;[Worth, House of.] {{Cite book|url=http://archive.org/details/AHistoryOfFeminineFashion|title=A History Of Feminine Fashion (1800s to 1920s)}} Before 1927. [Likely commissioned by Worth. Link is to Archive.org; info from Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Worth_Biarritz_salon.jpg.]&lt;/ref&gt; (6) By the end of the 19th century, wealthy women from the US, the UK and around Europe were making their way to Maison Worth in Paris.

Besides his contributions to in developments in models of promotion and business for the couture fashion house, Worth's real influence took the form of a particular look, which for the end of the century we call the [[Social Victorians/Terminology#Traditional Style|traditional Victorian style]]. After Charles Worth's death in 1895, his sons Gaston-Lucien and Jean-Philippe &quot;succeeded in maintaining his high standards,&quot; and Jean-Philippe especially &quot;follow[ed] his father’s aesthetic, with his use of dramatic fabrics and lavish trimmings.&quot;&lt;ref name=&quot;:7&quot; /&gt; While we associate a particular look with it, the House of Worth designed its clothing for its customers, whose relationship with the traditional style could be nuanced and fluctuating. For example, Lillie Langtry sometimes purchased her gowns at Maison Worth, even at the time she was known not to be corseted, so the style of the House of Worth is also less static and extreme than the gowns of some of its customers might suggest.

==== Costumes for the Fancy-dress Ball ====
The House of Worth made costumes for the following guests at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:

# [[Social Victorians/People/Louisa Montagu Cavendish|Louise, Duchess of Devonshire]], although the costume was designed by [[Social Victorians/People/Dressmakers and Costumiers#M. Comelli|Attilio Comelli]].
# Lady Randolph Churchill&lt;ref name=&quot;:6&quot; /&gt;
# Mrs. Arthur Paget&lt;ref name=&quot;:6&quot; /&gt;
# Daisy, Countess of Warwick&lt;ref name=&quot;:6&quot; /&gt;

== Costumiers for Theatres and Operas ==
At the end of the 19th century, the profession of costumier depended on a knowledge of the history of clothing, although the costumiers themselves  generally did not feel constrained by notions of [[Social Victorians/Terminology#Historical Accuracy|historical accuracy]] for the productions they designed for. ['''until the industrial revolution women made fabrics and clothing, plus ppl wore clothing every day, so clothing was not considered important. Planché; actual history of clothing vs just looking at portraits. History of clothing: foundation garments, items specific to a particular time like a codpiece, fabrics changed and evolved over time, plus a greater variety of fabrics; fabric and empires. The idea of a coherent production design with costumes designed for the particular actor in that production may have been changing about this time; before this actors provided their own costumes; Ellen Terry was probably part of this, Gilbert and Sullivan.''']

Not present at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] but certainly very involved in it were the people who made or provided the clothing, hats, wigs, jewelry, and other accessories. Besides people who made the costumes (costumiers, dressmakers, and modistes) and wigs (perruquiers), embroiderers, jewelers and shoemakers are occasionally mentioned although almost never named in the newspaper accounts.

Not all of these may have been costumiers, at least professional ones; some of the less well known might have been [[Social Victorians/People/Dressmakers and Costumiers#Fashion Houses, Couturiers and Modistes|clothiers]] instead.

=== Mr. Charles Alias ===
Mr. Charles Alias, 36 Soho Square

==== Personal Details ====

* Charles Georges Alias (1852 – 11 May 1921&lt;ref name=&quot;:5&quot;&gt;Principal Probate Registry. ''Calendar of the Grants of Probate and Letters of Administration made in the Probate Registries of the High Court of Justice in England''. London, England © Crown copyright. Ancestry.com. ''England &amp; Wales, National Probate Calendar (Index of Wills and Administrations), 1858-1995'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt;)
* Sarah Alias ()

Notes

# Will probated on 6 October 1921, effects of £6376 18s. 5d. to Marie Alias, widow.&lt;ref name=&quot;:5&quot; /&gt;
# 1881 Census: Charles Alias was born in France; they lived at 114 St Martins Lane in St Martin in the Fields; his occupation is listed as Costumier (Milliner); 2 boarders and a servant were living with them: Robert Soutar (age 51, comedian/actor), Harriet Morgan (age 28, comedian/actor) and the general domestic servant Lucy Ann Hewitt (age 23). Other servants' names follow, but apparently they were not living in 114 St Martins Lane.&lt;ref&gt;''Census Returns of England and Wales, 1881''. Kew, Surrey, England: The National Archives of the UK (TNA): Public Record Office (PRO), 1881. Class: ''RG11''; Piece: ''328''; Folio: ''42''; Page: ''27''; GSU roll: ''1341071''. Ancestry.com and The Church of Jesus Christ of Latter-day Saints. ''1881 England Census'' [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2004.&lt;/ref&gt;
# 1891 Census: Charles Alias was born in France; they lived at 36 Soho Square; his occupation is listed as Theatrical Costumier;

==== Costumier ====
[[Social Victorians/People/Dressmakers and Costumiers#Comelli|M. Comelli]], designer and costumier at Covent Garden, designed the costumes that were constructed by Mr. Alias of Soho Square.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* Several newspapers specifically name Mr. Alias as one of their sources of information about the costumes for the Duchess of Devonshire's ball: The London ''Echo''&lt;ref&gt;“A Jubilee Ball. Brilliant Scene at Devonshire House. Some of the Costumes Worn.” The London ''Echo'' 3 July 1897, Saturday: 2 [of 4], Cols. 6a – 7a [of 7]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0004596/18970703/027/0002.&lt;/ref&gt;{{rp|p. 2, Col. 6a}}; the London ''Evening Standard'' &lt;ref name=&quot;:8&quot;&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 5b}}
* The column &quot;Girls' Gossip&quot; names M. Alias in its discussion of the costumes:&lt;blockquote&gt;Herr von André was a splendid Benvenuto Cellini in brown and crimson, a perfect triumph of M. Alias's art. In fact, it was owing to the studious research and historical accuracy displayed by this clever costumier that so many of the dresses were so realistically pictorial. Alias dressed the Prince of Wales, the Duke and Duchess of Connaught, Duke of York, Prince Christian, Lord Lathom, and about a hundred other great ones of our island for the occasion.&lt;ref name=&quot;:12&quot;&gt;“Girls’ Gossip.” ''Truth'' 8 July 1897, Thursday: 41 [of 70], Col. 1b – 42, Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0002961/18970708/089/0041.&lt;/ref&gt;{{rp|42, Col. 2c}}&lt;/blockquote&gt;
*&quot;Charles Alias was French and very small. He had started as a traveller in artificial flowers and married a little dressmaker in Long Acre. They started making theatrical costumes and later moved to 36 Soho Square.&quot;&lt;ref&gt;{{Cite book|url=https://books.google.com/books?id=ZJ8fAQAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgMEAI|title=As You Were: Reminiscences|last=Byng|first=Douglas|date=1970|publisher=Duckworth|isbn=978-0-7156-0543-1|language=en}} https://books.google.com/books?id=ZJ8fAQAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgMEAI.&lt;/ref&gt;
* In its Appendix of Royal Warrant Holders, the 1902 ''Debrett's'' also says &quot;Charles Alias, Costumier, 36, Soho Square. W.&quot;&lt;ref&gt;{{Cite book|url=https://books.google.com/books?id=cLc7AQAAMAAJ&amp;pg=RA2-PP7&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgGEAI#v=onepage&amp;q=Alias%20Soho%20dressmaker%20costumier&amp;f=false|title=Debrett's Peerage, Baronetage, Knightage, and Companionage: Comprising Information Concerning All Persons Bearing Hereditary Or Courtesy Titles, Knights, and Companions of All the Various Orders, and the Collateral Branches of All Peers and Baronets|date=1902|publisher=Dean &amp; Son, Limited|language=en}} https://books.google.com/books?id=cLc7AQAAMAAJ&amp;pg=RA2-PP7&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgGEAI#v=onepage&amp;q=Alias%20Soho%20dressmaker%20costumier&amp;f=false.&lt;/ref&gt; (n.p.; end of book)
* The ''Encyclopedia of the Musical Theatre'', Vol. 1, says, &quot;Alias &amp; Co prospered in the 1880s, having a major success with their new costumes for the transferred version of the amazing ''Dorothy'' [a comic opera by Alfred Cellier, libretto by B. C. Stephenson, &quot;transferred&quot; from the Gaiety to the Prince of Wales's Theatre in 1886 and then to the Lyric Theatre in 1888, the most successful of the productions&lt;ref&gt;{{Cite journal|date=2023-03-25|title=Dorothy (opera)|url=https://en.wikipedia.org/w/index.php?title=Dorothy_(opera)&amp;oldid=1146605626|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Dorothy_(opera).&lt;/ref&gt;], and on into the 1890s by which ...&quot;; &quot;The Aliases made their mark in the West End when they provided the costumes for the original London production of La Fille de ...&quot;&lt;ref&gt;{{Cite book|url=https://books.google.com/books?id=2myfAAAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgEEAI|title=The Encyclopedia of the Musical Theatre|last=G?nzl|first=Kurt|date=1994|publisher=Schirmer Books|isbn=978-0-02-871445-5|language=en}} https://books.google.com/books?id=2myfAAAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgEEAI.&lt;/ref&gt; (taking from snippets)
* BNA search: Alias, Costumier, 36, Soho Square, London: 1898 shows a lot of advertisements.
* In 1892 Mr. C. Alias, 36, Soho Square, W., was a director of the 13th Annual Dramatic Ball, at the Freemasons' Tavern.&lt;ref&gt;{{Cite web|url=https://www.britishnewspaperarchive.co.uk/account/register?countrykey=0&amp;showgiftvoucherclaimingoptions=false&amp;gift=false&amp;nextpage=%2faccount%2flogin%3freturnurl%3d%252fviewer%252fbl%252f0001682%252f18920213%252f011%252f0004&amp;rememberme=false&amp;cookietracking=false&amp;partnershipkey=0&amp;newsletter=false&amp;offers=false&amp;registerreason=none&amp;showsubscriptionoptions=false&amp;showcouponmessaging=false&amp;showfreetrialmessaging=false&amp;showregisteroptions=false&amp;showloginoptions=false&amp;showcaptchaerrormessage=false&amp;isonlyupgradeable=false|title=Register {{!}} British Newspaper Archive|website=www.britishnewspaperarchive.co.uk|access-date=2023-04-28}} https://www.britishnewspaperarchive.co.uk/viewer/bl/0001682/18920213/011/0004.&lt;/ref&gt;
* In a gushing piece written for the 15 December 1899 ''Music Hall and Theatre Review'', &quot;The Bohemian Girl&quot; says that Alias executed Comelli designs for a Christmas pantomime ''Triumph of Music''. She goes on to talk about Willie Clarkson's work for another pantomime and a visit by Mrs. Langtry.&lt;ref&gt;&quot;Bohemian Girl, The.&quot; &quot;Preparing for the Pantomime.&quot; ''Music Hall and Theatre Review'' 15 December 1899, Friday: 24 [of 60], Cols. 1b–c and 2b–c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002237/18991215/160/0024.&lt;/ref&gt;
Russell Harris quotes ''The Encyclopedia of the Musical Theatre'' (Blackwell, 1994. Vol. 1, p. 19.):&lt;blockquote&gt;ALIAS, Charles (b France, 184-?; d London, 11 May 1921). The most famous name in British theatrical costumery in the second half of the 19th century.

The son of a French doctor, the young Alias fought alongside his father in the Franco-Prussian war where he is said to have lost the sight in one eye. He visited Britain and the Philharmonic Theatre, Islington, shortly afterwards as a dresser with the French dance troupe, Les Clodoches, and there he met and married Miss Price, the theatre's costumer. Although Alias had no experience in the theatre, he joined his wife in setting up the freelance firm of M et Mme Alias &amp; Co, '''someties''' designing and manufacturing, or more often just making up from the designs of such artists as [Comelli or] Wilhelm or [[Social Victorians/People/Faustin Betbeder|Faustin]], the costumes for an ever-extending series of musical shows.

The Aliases made their mark in the West End when theyprovided the costumes for the original London production of ''La Fille de Madame Angot'' (1873), and thereafter they costumes, either wholly or partly, many of London's most important musical productions including the burlesques at the Gaiety Theatre (''The Bohemian G'yurl, Little Dr Faust, Gulliver, Il Sonnambulo, Pretty Esmeralda'' etc), the Royalty (''Madcap, '''Pluto''''' '''etc'''), and the Strand (''The '''Lying''' Dutchman, L'Africaine, Nemesis, Loo, Antarctic, Champagne, The Baby, Intimidad''), Gilbert's early ''Tospyturveydom'' and ''Princess Toto'', Gilbert and Sullivan premières at the '''OPera''' Comique (''The Pirates of Penzance'') and the Savoy (''Iolanthe''), the vast spectaculars at the Alhambra (''La Poule aux oeufs d'or'' etc) and, most noticeably, the long string of French opéras-bouffes and opéras-comiques which were produced in Britain in the 1870s and 1880s. These included the record-breaking ''Trouillat (La Belle Normande), Le Jour et la nuit (Manola), La Timbale d'argent (The Duke's Daughter), La Marjolaine, Les Prés St Gervais'' and most of the long string of adaptations from the French made by Alias's close friend Henry Farnie, and produced by Alexander Henderson.

Alias maintained a close connection with his homeland. His home at 48 Soho Square became well known as a first stopping place for Frenchmen new to London and a congenial gathering place for theatricals, and he as a useful and friendly intermediary in various theatrical dealings between London and Paris. Hervé, Planquette, Chassaigne, Audran and Lecocq were all guests at Soho Square and the little costumier was said to have been instrumental in the brothers Mansell bringing Hervé and his ''Chilpéric'' (1870) to London, and thus helping set off the craze for opéra-bouffe which dominated the 1870s musical theatre in England. He also encouraged Planquette to work with H B Farnie on an original musical for Britain - the result of which was the enduring ''Rip van Winkle''.

Alias &amp; Co prospered in the 1880s, having a major succss with their new costumes for the transferred version of the amazing ''Dorothy'', and on into the 1890s by which stage they had become largely costume-makers rather than designers. Alias himself had by this time become one of the 'characters' of the London theatre, always anxiously asking 'What time de répétition générale?' as an opening approached, but always punctually ready with the show's costumes on dress-rehearsal night.

When Mme Alias died, Charles remarried and continued the business with his new wife, Mme Marie Wallet Floret from the Paris Opéra wardrobe, up to his death.&lt;ref&gt;Harris, Russell. {{Cite web|url=http://lafayette.org.uk/edw1335.html|title=King Edward VII at the Devonshire House Ball 1897, by Lafayette|website=lafayette.org.uk|access-date=2024-07-23}} Lafayette Negative Archive http://lafayette.org.uk/edw1335.html.  Quoting ''The Encyclopedia of the Musical Theatre'' (Vol. 1, Blackwell, 1994, p. 19).&lt;/ref&gt;&lt;/blockquote&gt;'''Costumes for the Fancy-dress Ball'''

Mr. Alias made costumes for the following guests at the Duchess of Devonshire’s 1897 fancy-dress ball:

# [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]]
# The [[Social Victorians/People/Connaught|Duke of Connaught]]
# The [[Social Victorians/People/George and Mary|Duke of York]]
# Duke of Fife&lt;ref name=&quot;:6&quot;&gt;Harris, Russell. &quot;Costumes by Named Dressmakers.&quot; {{Cite web|url=http://www.rvondeh.dircon.co.uk/incalmprose/|title=The Devonshire House Ball 1897 photographed by Lafayette|website=www.rvondeh.dircon.co.uk|access-date=2024-05-21}} 2011. http://www.rvondeh.dircon.co.uk/incalmprose/.&lt;/ref&gt;
# The Duke of Devonshire&lt;ref name=&quot;:6&quot; /&gt;
# [[Social Victorians/People/Stonor#Julia Caroline Stonor, Marquise of Hautpoul|Julia Stonor, Marquise of Hartpoul]]
# [[Social Victorians/People/Bourke|Hon. Mrs. Gwendolen Bourke]]
# [[Social Victorians/People/Mar and Kellie#Violet, Countess of Mar and Kellie|Violet, Countess of Mar and Kellie]]
# [[Social Victorians/People/Tweedmouth#Fanny, Baroness Tweedmouth|Fanny, Baroness Tweedmouth]]
# [[Social Victorians/People/Victoria of Schleswig-Holstein#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Princess Victoria of Schleswig-Holstein]]
# [[Social Victorians/People/Connaught#Princess Louise, Duchess of Connaught|Princess Louise, Duchess of Connaught]]
# [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton|Mary, Dowager Duchess of Hamilton]]
# [[Social Victorians/People/Portland|The Duchess of Portland]]
# [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]]
# Adolf von André&lt;ref name=&quot;:6&quot; /&gt;
# Lady St. Oswald&lt;ref name=&quot;:6&quot; /&gt;
# Earl of Rosebery&lt;ref name=&quot;:6&quot; /&gt;

=== Faustin Bedbeter ===
[[Social Victorians/People/Faustin Betbeder|Faustin Bedbeter]] was a caricaturist and painter who left France after Bismarck's seige of Paris and settled in London, working for the ''London Figaro'' and ''Punch''. He was a costumier beginning at least in 1875. He designed the costumes for a 1909 revival of [[Social Victorians/People/Gilbert|Gilbert]] and [[Social Victorians/People/Arthur Sullivan|Sullivan]]'s ''The Pirates of Penzance''.

=== Willie Clarkson ===
Mr. W. Clarkson, of Wellington-street

Clarkson is also listed among the [[Social Victorians/People/Dressmakers and Costumiers#Perruquiers|perruquiers]]. Clarkson made the costumes for the following guests at the ball:

* Grand Duke Michael of Russia&lt;ref name=&quot;:0&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4A–8 Col. 2B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;{{rp|p. 8, Col. 2a}}
* The Duke of Manchester&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
* [[Social Victorians/People/Gleichen#Laura, Princess Victor of Hohenlohe Langenburg|Laura, Princess Victor of Hohenlohe]]&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
* Princess Louise&lt;ref name=&quot;:1&quot; /&gt;

=== M. Comelli ===
Attilio Giuseppe de Comelli von Stuckenfeld (1858-1925).

Comelli &quot;was appointed house designer to the Royal Opera House in the 1890s&quot;&lt;ref name=&quot;:2&quot;&gt;&quot;Attilio Comelli Design Collection.&quot; ''Royal Opera House''  https://www.rohcollections.org.uk/collectionComelli.aspx (retrieved February 2024).&lt;/ref&gt; continuing &quot;to the early 1920s.&quot;&lt;ref&gt;{{Citation|title=Drury Lane Design Collection|url=https://collections.vam.ac.uk/item/O1172507/drury-lane-design-collection-costume-design-comelli-attilio/|date=1915|accessdate=2024-02-13|first=Attilio|last=Comelli}}. https://collections.vam.ac.uk/item/O1172507/drury-lane-design-collection-costume-design-comelli-attilio/.&lt;/ref&gt; At the same time, &quot;He was credited as Artist in Chief at the Alhambra, Theatre Royal, Drury Lane and the Royal Opera House in London, and also found time to provide costumes for some of the Savoy operas and for Christmas pantomimes in London and Australia.&quot;&lt;ref name=&quot;:2&quot; /&gt; After coming &quot;to London in the late 19th century [he] quickly established himself as one of the most prolific designers for the London stage.&quot;&lt;ref name=&quot;:2&quot; /&gt;

He described his research process for costume design for the July 1902 ''Cassell's Magazine'':&lt;blockquote&gt;When I get the order to prepare designs for a new play … [sic ellipsis] I first spend some weeks in studying, at the British and South Kensington [now the Victoria &amp; Albert] Museum, every available authority on the period, and I frequently send my brother to Paris and Berlin, if there is a chance of getting information there that is not available in London’. (‘The Art of Theatrical Disguise’ by Sidney Dark, ''Cassell’s Magazine'', July 1902, pp.162–7).&lt;ref name=&quot;:2&quot; /&gt;&lt;/blockquote&gt;According to the Royal Opera House, he &quot;appears to have had several siblings, including possibly Emilio Andrea Comelli (1862–1929).&quot;&lt;ref name=&quot;:2&quot; /&gt;  Also, perhaps another relative, Italian painter Dante Comelli (1880–1958) designed for the Royal Opera House in Covent Garden later.

Comelli's designs for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:
* Comelli designed the costumes that were constructed by [[Social Victorians/People/Dressmakers and Costumiers#Mr. Charles Alias|Mr. Alias of Soho Square]].&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}

* Comelli designed the costumes of the attendants of [[Social Victorians/People/Louisa Montagu Cavendish|Louise, Duchess of Devonshire]] as well as her own costume. Alias did not construct her costume, [[Social Victorians/People/Dressmakers and Costumiers#The House of Worth|the House of Worth]] did.
* Comelli may have designed the costumes of the entourage of [[Social Victorians/People/Pless#Daisy, Princess Henry of Pless|Daisy, Princess of Pless]], although Mrs. Mason made Daisy's dress.&lt;ref&gt;&quot;Dresses Worn at the Duchess of Devonshire's Ball on July 2. Made by Mrs. Mason, 4 New Burlington Street, W.&quot; The ''Queen'' 10 July 1897, Saturday: 48 [of 98 BNA; p. 74 print page), Col. 1a–3c [of 3]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/BL/0002627/18970710/168/0048?browse=true.&lt;/ref&gt; George Cornwallis-West says his costume was &quot;designed by a famous theatrical designer of the day.&quot;&lt;ref&gt;Qtd. in Martin Spies, &quot;&quot;Late Victorian Aristocrats and the Racial Other: The Devonshire House Ball of 1897.&quot; ''Race &amp; Class'' April–June 2016 (57.4): 95–103.&lt;/ref&gt;{{rp|97}}
[[File:Ellen Terry as Lady Macbeth.jpg|thumb|''Ellen Terry as Lady Macbeth'', Sargent 1889]]

=== Alice Comyns Carr and Ada Nettleship ===
According to Smallhythe Place, the &quot;beetle wing dress&quot; for Ellen Terry's 1888 performance as Lady Macbeth was designed by Alice Comyns Carr and constructed by Ada Nettleship, the &quot;team&quot; that made Ellen Terry's costumes for perhaps 2 decades.&lt;ref name=&quot;:14&quot;&gt;&quot;'Beetle Wing Dress' for Lady Macbeth.&quot; Smallhythe Place, Kent. The National Trusts Collections. Object NT 1118839.1 (1888) https://www.nationaltrustcollections.org.uk/object/1118839.1.&lt;/ref&gt; John Singer Sargent's 1889 portrait of Terry in this dress is at right. (Smallhythe Place, Kent, part of the National Trust, was Terry's home from 1899 to her death. This dress is part of that collection.)

Nettleship crocheted the sleeves and skirt of Terry's costume to resemble &quot;soft chain armour,&quot;&lt;ref name=&quot;:14&quot; /&gt; which she overlaid with wing cases from 1,000 beetles.&lt;ref name=&quot;:15&quot;&gt;{{Cite web|url=https://womenwhomeantbusiness.com/2021/01/21/ada-nettleship-1856-1932/|title=Ada Nettleship (1856-1932)|last=B|first=Lizzie|date=2021-01-21|website=Women Who Meant Business|language=en|access-date=2025-06-06}}&lt;/ref&gt;&lt;p&gt;
Comyn Carr and Nettleship's beetle-wing costume was not the only or even the first dress decorated with the iridescent wings. Ada Nettleship had used beetle wings in &quot;an 1886 dress and an 1887 hat for Constance Lloyd that were oversewn with iridescent green beetle wings&quot;&lt;ref name=&quot;:16&quot;&gt;{{Cite journal|date=2025-04-21|title=Ada Nettleship|url=https://en.wikipedia.org/w/index.php?title=Ada_Nettleship&amp;oldid=1286707541|journal=Wikipedia|language=en}}&lt;/ref&gt; — and [[Social Victorians/People/Dressmakers and Costumiers#Mrs Sims' Court Dress Establishment, Dublin|Mrs Sims]] had used some for a dress in c. 1880.&lt;ref name=&quot;:13&quot; /&gt;

==== Personal Details ====
Alice Laura Vansittart Comyns Carr designed costumes, and dressmaker Adaline Cort Nettleship constructed Comyns Carr's designs. They were a &quot;costume team&quot; separate from those who did the costumes for &quot;the rest of the Lyceum company.&quot;&lt;ref name=&quot;:14&quot; /&gt; They appear to have maintained individual establishments, with Nettelship often constructing costumes for Terry that were designed by Comyns Carr.

Alice Comyns Carr (1850–1927) was married to J. Comyns Carr, &quot;drama and art critic, author, playwright and director of the Grosvenor Gallery.&quot;&lt;ref&gt;{{Cite journal|date=2025-04-21|title=Alice Comyns Carr|url=https://en.wikipedia.org/w/index.php?title=Alice_Comyns_Carr&amp;oldid=1286707345|journal=Wikipedia|language=en}}&lt;/ref&gt; She was associated with the [[Social Victorians/Terminology#Progressive Style|aesthetic dress movement]] and was friends with Edward Burne-Jones and John Singer Sargent as well as Lawrence Alma-Tadema, &quot;the writers Robert Browning and Henry James and composers Hubert Parry and [[Social Victorians/People/Arthur Sullivan|Arthur Sullivan]].&quot;&lt;ref name=&quot;:15&quot; /&gt;

Ada (Adaline) Cort Nettleship (1856 – 19 December 1932&lt;ref name=&quot;:16&quot; /&gt;) was married to painter John Trivett Nettleship. Some of her &quot;[n]otable clients included the soprano Marie Tempest, and the actors Ellen Terry, Winifred Emery, Sarah Bernhardt, and Mrs Patrick Campbell.&quot;&lt;ref name=&quot;:16&quot; /&gt; Like Comyns Carr, Nettleship was an advocate of [[Social Victorians/Terminology#Progressive Style|aesthetic dress design]], making dresses for Constance Lloyd in that progressive style, including her dress for her wedding to [[Social Victorians/People/Oscar Wilde|Oscar Wilde]]. Nettleship &quot;in her youth had been a noted ‘art-embroiderer’ in the style of May Morris.&quot;&lt;ref name=&quot;:15&quot; /&gt;

Alice Comyns Carr published her ''Reminiscences'' in 1926, the year before her death. Ada Nettleship was covered by the newspapers from time to time (&quot;''St James Gazette'' 30/5/1883; ''Dundee Evening Telegraph'' 7/7/1884; ''Morning Post'' 16/10/1886; ''The Queen'' 13/8/1887; ‘Ellen Terry’s gowns and the woman who makes them’ by Bessie O’Connor in ''Harpers Bazaar'' 9th Jan 1897; ‘What Actresses Pay For Their Dresses’ in ''New Zealand Herald'' 25/08/1900; ''South Wales Daily News'' 25/1/1902; ''Leeds Mercury'' 13/2/1914.&quot;&lt;ref name=&quot;:15&quot; /&gt;)

=== Miss Mary E. Fisher ===
Mme. or Miss Mary E. Fisher, 26, Bedford-street, Covent-garden&lt;ref name=&quot;:9&quot;&gt;{{Cite book|url=https://books.google.co.in/books?id=cVQZAAAAYAAJ&amp;pg=RA3-PR2&amp;dq=Mr.+May,+Garrick-street,+Covent-garden&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;redir_esc=y|title=The Play-pictorial|date=1908|publisher=Greening &amp; Company, Limited|language=en}} P. ADVT ii. ''Google Books'' https://books.google.com/books?id=cVQZAAAAYAAJ.&lt;/ref&gt; &lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
*Miss Mary E. Fisher is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}

=== Charles H. Fox ===
Fox: &quot;perruquier and costumier Charles H. Fox. Since 1878, Fox had been a major supplier of wigs and costumes for private theatricals and fancy dress balls.&quot;&lt;ref name=&quot;:3&quot;&gt;&quot;B. J. Simmons &amp; Co.: An Inventory of Its Costume Design Records at the Harry Ransom Center.&quot; ''B. J. Simmons &amp; Co. Costume Design Records''. Harry Ransom Center. The University of Texas. 2023. Retrieved February 2024. https://norman.hrc.utexas.edu/fasearch/findingAid.cfm?eadID=01440.&lt;/ref&gt;

=== Harrison ===
Harrison's, Ltd., 31, Bow-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* In a chatty column written as a letter to &quot;Dearest Amy,&quot; the article in ''Truth'' on the ball says, &quot;Princess Henry of Pless was another [Queen of Sheba], and her dress was absolutely magnificent. The conception of it was both poetic and artistic, and is due, I believe, to the genius of Mrs. Harrison.&quot;&lt;ref name=&quot;:12&quot; /&gt;{{rp|42, Col. 1b}}
* There are ads for Harrison's.

=== May ===
Mr. May, Garrick-street, Covent-garden&lt;ref name=&quot;:9&quot; /&gt;

* Mr. May is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}

=== Nathan ===
Messrs. L. and H. Nathan, Coventry-street, Haymarket; 17, Convent-street, Picadilly

*Messrs. L. and H. Nathan is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}
*Mr. Karl, artist, designed the costumes made by Messrs. L. and H. Nathan of Coventry-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} &lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}
*Messrs Nathan made the costumes for the following people:
**[[Social Victorians/People/Harcourt#Elizabeth Harcourt|Elizabeth, Lady Harcourt]]
**[[Social Victorians/People/Rothschild Family#Emma, Lady Rothschildand Nathan Mayer, Lord Rothschild|Emma, Lady Rothschild]]

=== Simmons and Sons ===
Messrs. John Simmons and Sons, Coventry House, Haymarket.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} Simmons, 7 and 8, King Street, Covent Garden.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} Possibly there are 2 Simmonses?

The Harry Ransom Center has a collection on this firm:&lt;blockquote&gt;The London costumier B. J. Simmons &amp; Co. was founded in 1857 by a Mr. B. J. Simmons and operated by his direct descendants well into the 1930s. Simmons' costumes were known for their correctness of period, sophisticated design, and high quality. ... In their busy Covent Garden workshop, dressmakers turned out immaculately constructed stage apparel, often from renderings by leading costume designers. Successful theater managers repeatedly turned to Simmons for historical costumes, especially Herbert Beerbohm Tree whose magnificent stagings of Shakespeare were often outfitted by Simmons.

While best known as a historical costumier for the London stage, Simmons' output was diverse. The company created costumes for a variety of shows in the West End, the provinces, and overseas, ranging from Victorian pantomime to the &quot;kitchen sink&quot; dramas of the 1960s. ... In addition to making new costumes for professional productions, Simmons operated a thriving rental business which allowed operatic and dramatic societies across England to hire beautifully made garments for amateur productions. Like many theatrical costumiers, Simmons maintained a substantial nontheatrical trade.

Simmons began as a family-run outfit known variously as B. J. Simmons, J. B. Simmons, John Simmons &amp; Son/Sons, Simmons/Symmons/Simmonds Brothers, G. B. Simmons, and B. &amp; G. Simmons. The force majeure seems to have been John Simmons, whose name appears in ''The London Stage'' and in London newspapers until 1922. According to J. P. Wearing, between 1890 and 1899 Simmons provided costumes for at least forty-two theatre productions in London.&lt;ref name=&quot;:3&quot; /&gt;&lt;/blockquote&gt;Simmons' contributions to costumes for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:
* Messrs. John Simmons and Son is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}
* Simmons and Sons made costumes for the following guests at the ball:
** [[Social Victorians/People/Ellesmere#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Francis Egerton, 3rd Earl of Ellesmere]]&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** The Duke of Somerset&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** The Marquis of Winchester&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Earl Beauchamp&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Earl Carrington&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Earl Essex&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Viscount Esher&lt;ref name=&quot;:6&quot; /&gt;
** Lord Ampthill&lt;ref name=&quot;:6&quot; /&gt;
** Lady Ampthill&lt;ref name=&quot;:6&quot; /&gt;
Simmons and Sons is also sometimes listed as having made clothing for other social events:

* For the [[Social Victorians/1892-02-10 Alington Leigh Wedding|very fashionable February 1892 wedding between Henry Sturt, Lord Alington and Evelyn Leigh]] — the &quot;most important social event of last week in the social world&quot;&lt;ref name=&quot;:03&quot;&gt;&quot;Lord Alington to Miss Leigh.&quot; ''Gentlewoman'' 20 February 1892, Saturday: 21 [of 46], Cols. 1a–3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18920220/092/0021. Same print title, p. 237.&lt;/ref&gt;{{rp|Col. 1a}} — &quot;Messrs. Simmons &amp; Sons, of Coventry House, Haymarket, made the charming little suits for the pages, which were so much admired.&quot;&lt;ref name=&quot;:03&quot; /&gt;{{rp|Col. 3a}}

=== Smaller Concerns ===
* Mme. Auguste, of Wellington-street&lt;ref name=&quot;:42&quot;&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 42, Col. 3b}}
* Mr. W. Clarkson, 44, Wellington Street (costumes and wigs)&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}

=== Unknown Whether Costumier or Dressmaker ===
*Mme. Ellis: &quot;The pretty costumes of Merlin and Vivian worn by [[Social Victorians/People/Walker|Mr and Mrs Willie Walker]] at the Devonshire House Ball, were made by Mme. Ellis, 16, Upper George-street, Bryanston-square.&quot;&lt;ref&gt;Holt, Ardern. &quot;Dress and Fashion. To Correspondents.&quot; The ''Queen'' 24 July 1897, Saturday: 54 [of 88], Col. 1a [of 3]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18970724/271/0054.&lt;/ref&gt;
* Madame Frederic, of Lower Grosvenor Place
* &quot;and many others&quot;&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}

== Perruquiers ==
Mr. W. Clarkson &quot;supplied the wigs and headdresses for the Royal Family&quot;&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}} for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:&lt;blockquote&gt;At the Duchess of Devonshire's ball, on the 2d inst., the Prince of Wales looked as if he had stepped out of a masterpiece by one of the old painters. His wig, which completed a correct make-up as Knight of Malta, was specially made and fitted by that favoured &quot;Royal Perruquier&quot; Mr Willie Clarkson, who also had the honour of making and fitting the wigs worn by Prince Charles of Denmark, the Duke of York, and the Duke and Duchess of Connaught, and of dressing the hair of the Duchess of York and the Princess Victoria of Schleswig-Holstein. Mr Clarkson also supplied a number of the costumes, including those worn by the Grand Duke Michael of Russia, Princess Louise, and the Duke of Manchester. It would not be safe to say how many crowned heads have literally &quot;passed through the hands&quot; of Mr Clarkson. The art of the perruquier is a very difficult one, requiring historical knowledge, patient research, and great taste. It is most essential to the success of any theatrical performance or of an historical ball.&lt;ref name=&quot;:1&quot;&gt;“Foreign Plays and Players.” ''The Era'' 10 July 1897, Saturday: 15 [of 28], Col. 3c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000053/18970710/032/0015.&lt;/ref&gt;&lt;/blockquote&gt;Clarkson also provided costumes and wigs for the [[Social Victorians/Royals Amateur Theatricals|amateur theatricals]] that the royals took part in to entertain themselves.

== Jewelers ==
After naming costumiers for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]], the ''Gentlewoman'' specifically mentions the Parisian Company for its jewelry and Mr. Norman of Bond Street for the shoes he made:&lt;blockquote&gt;Among other firms [than the costumiers] who lent their aid to make the great ball a huge success was the Parisian Company, whose sparkling gems and jewels, and whose ropes of pearls and precious stones, enhanced the charms of many a fair dame in her dainty old-world costume, and the firm of Mr. Norman, 69, New Bond-street, who designed and made the shoes for the Princess of Wales, the Duchess of Buccleuch, &amp;c., &amp;c.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3c}}&lt;/blockquote&gt;According to the ''Westminster Gazette'', &quot;One very great lady indeed had been lent, by a jeweller, diamonds worth about £13,000.&quot;&lt;ref name=&quot;:4&quot;&gt;“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.&lt;/ref&gt;{{rp|p. 5, Col. 2c}}

== People Who Made Costumes for the Ball ==
The ''Queen'' often mentions the dressmaker or costumier in its reports on the costumes at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball at Devonshire House]] as well as in general.

The ''Gentlewoman'' covered this topic explicitly in its report on the ball:&lt;blockquote&gt;Very great credit is due to the taste and artistic powers of the designers of these dresses, and particular mention must be made of M. Comelli, of Covent Garden Theatre, whose facile pen designed most of the superb toilettes so ably carried out by Messrs. Alias, of Soho-square. Other theatrical costumiers who brought all their special talents to bear on the historical and fancy costumes required for this function were Messrs. Nathan (artist, Mr. Karl), of Coventry-street; Messrs. John Simmons &amp; Sons, Haymarket; Mme. Auguste, of Wellington-street; Harrison's, Ltd., 31, Bow-street; Simmons, 7 and 8, King-street; Mr. Clarkson, 44, Wellington-street; Mme. Fisher, 26, Bedford-street; and many others. A great number of well-known modistes in London were also called upon to supply dresses. Amongst these we chronicle M. Mason, New Burlington-street; M. Machinka, Conduit-street; Paquin, of Dover-street; Jays, Ltd., Regent-street; Messrs. Durrant, 116, Bond-street (who made Lady Londonderry's magnificent gown), and numerous others.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}&lt;/blockquote&gt;The London ''Evening Standard'' cites the sources of its information about the costumes:&lt;blockquote&gt;We are indebted for some of the particulars of the dresses to Mr. Charles Alias, Soho-square; Messrs. L. and H. Nathan, Coventry-street, Haymarket; Messrs. John Simmons and Son, Coventry House, Haymarket; Mr. May, Garrick-street, Covent-garden; Miss Mary E. Fisher, 26 Bedford-street, Covent-garden; and the ''Lady'' newspaper.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}&lt;/blockquote&gt;The ''Morning Post'' also addressed the costumiers. It named Mr. Alias in association with the royals, as well as mentioning several other costumiers by name:&lt;blockquote&gt;The costumes worn by the Prince of Wales, the Duke of York, and the Duchess of Connaught, as well as many others were supplied by Mr. Alias, of Soho-square. Those worn by the Grand Duke Michael of Russia, the Duke of Manchester, Princess Victor of Hohenlohe, and others were made by Mr. W. Clarkson, of Wellington-street, who also supplied the wigs and headdresses for the Royal Family. Messrs. Simmons and Sons, of the Haymarket, made a large number of costumes, including those of the Duke of Somerset, the Marquis of Winchester, Earls Beauchamp, Carrington, Ellesmere, and Essex. Nathan, of Coventry-street, and Simmons, of King-street, Covent-garden; Madame Frederic, of Lower Grosvenor-place, and Mrs. Mason, of New Burlington-street, also made some of the principal costumes.&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}&lt;/blockquote&gt;On 3 July 1897, the day after the ball, the ''Belfast News-letter'' says,&lt;blockquote&gt;For weeks past all the leading London dressmakers and costumiers had been hard at work executing the orders for this great ball. At Alias Nathan's, Clarkson's, Auguste's, and Simmons' all hands set to with a will, and it is gratifying to know that the dresses entrusted to them more than held their own with those sent over from Paris.&lt;ref name=&quot;:10&quot;&gt;&quot;The Duchess of Devonshire's Fancy Dress Ball. Special Telegram.&quot; ''Belfast News-Letter'' Saturday 03 July 1897: 5 [of 8], Col. 9c [of 9]–6, Col. 1a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0000038/18970703/015/0005.&lt;/ref&gt;{{rp|p. 5, Col. 9a}}&lt;/blockquote&gt;

According to the ''Derbyshire Times and Chesterfield Herald'', citing the ''Daily Mail'',&lt;blockquote&gt;Lady de Grey is going as Zenobia, and is getting her dress from Doucet, I hear, while Worth also is making a great many costumes; but the greatest number are being made in England. The Duchess of Portland, the Duchess of Hamilton, Lady Mar and Kellie, and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]] are all going to the costumier in Soho-square, and Alias has also been summoned to Marlborough House for a consultation.
&lt;p&gt;
Mr. Caryl Craven, who is so clever in such matters, is helping the Duchess of Leeds with her dress; in fact, everyone seems pressed into the service, and the result will be one of the most brilliant sights that ever was seen.&lt;ref name=&quot;:11&quot; /&gt;&lt;/blockquote&gt;
== Notes and Questions ==

# Which costumier was this? &quot;A well-known West End dressmaker booked for the Duchess of Devonshire's fancy dress ball orders representing £27000.&quot;&lt;ref&gt;&quot;London Letter.&quot; ''Western Daily Press'' 15 July 1897, Thursday: 8 [of 8], Col. 7c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000264/18970715/146/0008.&lt;/ref&gt;

== References ==
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      <text bytes="54976" sha1="bz0tymn3vxgaoeuuiw1a9p5noq01p6r" xml:space="preserve">== Dressmakers, Modistes, Costumiers, Perruquiers and Jewelers ==

=== Not to Mention Seamstresses, Tailors, Lace-makers, Milliners, and Lady's Maids ===
Dominated as the social world was by women, fashion was an important part of the reportage on social events, with some reporters demonstrating knowledge of fabrics, cuts, laces, and so on. The Victorians had specialized terms for people who designed and made clothing, especially very fashionable clothes or haut couture, and specialized careers for those people who assisted women to acquire, manage and wear that clothing. Because of the popularity of fancy-dress or costume parties, some of the people assisting them were costumiers from the world of theatre and opera. The terminology and examples that follow are generally focused on the end of the 19th century in London.

== Fashion Houses, Couturiers and Modistes ==
The ''Gentlewoman'' says, &quot;A great number of well-known modistes in London were also called upon to supply dresses.&quot;&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} Among those who helped construct the costumes and wigs include the following:

=== Doucet ===
A gossipy article in ''Derbyshire Times and Chesterfield Herald'' (citing the ''Daily Mail'') says, &quot;Lady de Grey is going as Zenobia, and is getting her dress from Doucet, I hear,&quot;&lt;ref name=&quot;:11&quot;&gt;“Derbyshire Sayings and Doings.” ''Derbyshire Times and Chesterfield Herald'' 12 June 1897, Saturday: 5 [of 8], Col. 2A. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000228/18970612/018/0005.&lt;/ref&gt; although she went as Cleopatra and not Zenobia (only the Duchess of Devonshire went as Zenobia).

=== Mme Durrant ===

Mme Durrant's concern, at the end of the 19th century, at least, was at 116 &amp; 117 New Bond-street, London W. An ad in ''The Queen'' says,&lt;blockquote&gt;Court Dressmaker and Milliner. The Latest Paris Models in Morning, Afternoon, Tailor, and Evening Gowns, Millinery, and Mantles.&quot;&lt;ref&gt;&quot;Madame Durrant, Court Dressmaker and Milliner.&quot; ''The Queen'' 15 April 1899, Saturday: 11 [of 88], Cols. 2–3c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18990415/082/0011.&lt;/ref&gt;&lt;/blockquote&gt;Mme Durrant made the costumes for the following guests at the ball:

# [[Social Victorians/People/Londonderry#Theresa, Marchioness of Londonderry|Theresa, Marchioness of Londonderry]]&lt;ref&gt;&quot;Lines for the Ladies.&quot; ''Daily Gazette for Middlesbrough'' Thursday 16 June 1898: 4 [of 4], Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000159/18980616/060/0004.&lt;/ref&gt; The dress and fabrics for the Marchioness of Londonderry as well as her quadrille, were made in Britain or Ireland.&lt;ref name=&quot;:02&quot;&gt;&quot;This Morning’s News.&quot; London ''Daily News'' 6 July 1897, Tuesday: 7 [of 12], Col. 3b. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970706/038/0007.&lt;/ref&gt;

Mme Durrant made at least a couple of dresses for Queen Mary (early 20th century).&lt;ref&gt;{{Cite web|url=https://tr.pinterest.com/pin/278730664423122186/|title=1900 - 1919 Clothing panosundaki Pin|website=Pinterest|language=en|access-date=2023-03-08}} https://pin.it/2GUiBm7 and https://pin.it/2GUiBm7.&lt;/ref&gt; Also, perhaps early 20th-c, Durrant had an address on Dover Street.&lt;ref&gt;{{Cite web|url=http://www.elisarolle.com/queerplaces/ch-d-e/Edwin%20Hardy%20Amies.html|title=queerplaces - Sir Edwin Hardy Amies|website=www.elisarolle.com|access-date=2023-03-08}} http://www.elisarolle.com/queerplaces/ch-d-e/Edwin%20Hardy%20Amies.html.&lt;/ref&gt; ''The Queen'' also has ads for a &quot;Mr. Durrrant's Ladies' Taylor and Habit Maker&quot; in Edinburgh and Glasgow in 1892.&lt;ref&gt;&quot;Durrant Ladies' Taylor and Habit Maker.&quot; [advertisement] ''The Queen'' 06 February 1892, Saturday: 5 [of 81], Cols. 2–3c [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18920206/043/0005.&lt;/ref&gt;

=== Mrs. Mason ===
M. or Mrs. Mason, of 4, New Burlington Street, W.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* &quot;Dress and Fashion&quot; answer by Adern Holt in the ''Queen'' to queries posed by &quot;Correspondents&quot;: &quot;F&lt;small&gt;ANCY&lt;/small&gt; D&lt;small&gt;RESS&lt;/small&gt;. — For the beautiful ball such as you describe you cannot do better than go to Mrs Mason, New Burlington-street, for the costume about which you inquire. It needs very careful making and the most artistic designs, and these you would be sure to obtain there, for the dresses she made for the Duchess of Devonshire's ball were quite artistic masterpieces.&quot;&lt;ref&gt;Holt, Ardern. &quot;Dress and Fashion. To Correspondents.&quot; The ''Queen'' 17 July 1897, Saturday: 48 [of 97], Col. 1a [of 3]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18970717/231/0049.&lt;/ref&gt;
Mrs. Mason made costumes for the following guests at the ball:

# [[Social Victorians/People/Pless|Daisy, Princess of Pless]]
# [[Social Victorians/People/Ashburton#Mabel, Lady Ashburton|Mabel, Lady Ashburton]]
# [[Social Victorians/People/de Trafford#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Violet, Lady de Trafford]]
# [[Social Victorians/People/Cadogan#Lady Sophie Scott|Lady Sophie Scott]]
# Lady Lurgan&lt;ref name=&quot;:6&quot; /&gt;
# [[Social Victorians/People/Leeds#Katherine, Duchess of Leeds|Katherine, Duchess of Leeds]]
# [[Social Victorians/People/Sutherland#Millicent, Duchess of Sutherland|Millicent, Duchess of Sutherland]]
# [[Social Victorians/People/Meysey-Thompson#Lady Ethel Meysey Thompson|Lady Ethel Meysey Thompson]]
# [[Social Victorians/People/Muriel Wilson|Muriel Wilson]]
# [[Social Victorians/People/Edmonstone#Lady Ida Edmonstone|Lady Ida Edmonstone]]
# [[Social Victorians/People/Goelet#Costumes at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Mary Goelet]]
#[[Social Victorians/People/Cavendish#Lady Edward Cavendish|Lady Edward Cavendish]]
#[[Social Victorians/People/Sarah Spencer-Churchill Wilson#Lady Sarah Wilson|Lady Sarah Wilson]]
#[[Social Victorians/People/Derby#Constance Villiers Stanley, Countess of Derby|Countess of Derby]]
#Mrs [[Social Victorians/People/Bourke|Gwendolen Bourke]]&lt;ref name=&quot;:6&quot; /&gt;
#Duchess of Roxburghe&lt;ref name=&quot;:6&quot; /&gt;

=== Morin-Blossier ===
The French &quot;tailoring workshop&quot;&lt;ref&gt;{{Cite web|url=https://fashion.mam-e.it/morin-blossier/|title=Morin-Blossier -|date=2016-02-05|language=it-IT|access-date=2022-04-07}}&lt;/ref&gt; of Morin-Blossier &quot;possibly&quot;&lt;ref name=&quot;:6&quot; /&gt; made the dress worn to  the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball]] by

* Alexandra, Princess of Wales&lt;ref name=&quot;:6&quot; /&gt;
* [[Social Victorians/People/Prince Charles of Denmark|Princess Maud of Wales]] (Princess Charles of Denmark)&lt;ref name=&quot;:43&quot;&gt;Harris, Russell. &quot;Prince and Princess Carl of Denmark, later King Haakon VII (1872-1957) and Queen Maud of Norway (1869-1938),  and Princess Victoria of Wales (1868-1935), as a 16th century Danish courtier, and Ladies-in-Waiting at to Marguerite de Valois.&quot; &quot;List of Sitters.&quot; ''In Calm Prose''. 2011 http://www.rvondeh.dircon.co.uk/incalmprose/denmark.html.&lt;/ref&gt;
* Duchess of York&lt;ref name=&quot;:6&quot; /&gt;
* Princess Victoria&lt;ref name=&quot;:6&quot; /&gt;

=== Messrs Russell and Allen ===
Old Bond-street., W.

Made presentation dresses for 8 of the following in 1913&lt;ref&gt;&quot;Their Majesties' Court.&quot; ''Lady's Pictorial'' 17 May 1913, Saturday: 35 [of 64], Col. 2c [of 3]. ''British Newspaper Archive''https://www.britishnewspaperarchive.co.uk/viewer/bl/0005980/19130517/296/0035. Same print title, p. 787.&lt;/ref&gt;:

* Mrs. A. C. Hardy, of Montreal
* Mrs. Thorburn
* Mrs. Ralph Berners
* Miss Spencer Warwick
* [[Social Victorians/People/Bourke|Miss [Daphne] Bourke]]
* Mrs. Henry Barran
* Miss D. Hickman
* Hon. Irene Molesworth
* The Hon. Edith Winn
* The Hon. Hilaria St. Aubyn
* The Hon. Mary Charteris
* Miss Grace Holley

=== Mrs Sims' Court Dress Establishment, Dublin ===
Mrs Mary Sims, Dawson Street, Dublin

Mrs Sims made a dress decorated with beetle wings in c. 1880; this dress still exists and, according to Elaine Hewitt, is in the NMI collections.&lt;ref name=&quot;:13&quot;&gt;Objects in Focus: New Research Seminar, Naional Museum of Ireland, Decoraive Arts and History, Collins Barracks. Saturday 16th February 2013. https://www.academia.edu/2455567/The_material_culture_of_infancy_and_early_childhood_in_Ireland_c_1680_1830?auto=download.&lt;/ref&gt; Hewitt's precis for an exhibit called ''Objects in Focus: New Research Seminar, National Museum of Ireland, Decoraive Arts and History, Collins Barracks'' says, &quot;Mary Sims was a court dressmaker by Royal appointment, who established herself from 1863 as the most prominent dressmaker in Dublin.&quot;

Mrs Sims made costumes for the following guests at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:

* [[Social Victorians/People/Cadogan#Lady Beatrix, Countess Cadogan|Lady Beatrix, Countess Cadogan]]

Other people Mrs Sims made clothes for:

* Alexandra, Princess of Wales, 1885: Kate Strasdin offers an example of Alexandra's strategic use of clothing: a gown Alexandra wore to a Drawing Room at Buckingham Palace was, according to the ''Times'', &quot;a dress of rich yellow satin and silver brocade, draped with silver lace, corsage to correspond, made by Mrs Sims of Dublin.&quot;{{rp|1885, p. 11}} What is strategic is the release of Mrs Sims's name, according to Strasdin, since &quot;[t]he communication of this detail can only have come from the royal household itself, demonstrating the control that Alexandra exerted over details released to the press relating to her appearance.&quot;&lt;ref&gt;Strasdin, Kate, &quot;Reporting Royal Dress: Queen Alexandra and Royal Image Making.&quot; Falmouth University Research Repository. http://repository.falmouth.ac.uk.&lt;/ref&gt;
* Ishbel, Marchioness Aberdeen, 1886: &quot;Ishbel, Lady Aberdeen (1857–1939), [wore a &quot;costume of an Irish lady in the thirteenth century&quot;] in 1886 while presiding over a garden party at the Vice Regal Lodge in the Phoenix Park in Dublin, an event to which the 2,000 invited guests were expected to wear clothes of Irish manufacture.&quot;&lt;ref&gt;Alex Ward, &quot;Dress and National Identity: Women’s Clothing and the Celtic Revival,&quot; ''Costume'', 48:2, 2014, 193-212, DOI: https://doi.org/10.1179/0590887614Z.00000000050.&lt;/ref&gt;{{rp|199}}

=== Smaller Concerns ===
* Madame Fréderic: made the costume for Princess Mary of Teck&lt;ref name=&quot;:6&quot; /&gt;
* Jays, Ltd., Regent-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* M. Machinka, Conduit-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* Maison Lucille: made Mrs. James's costume&lt;ref name=&quot;:6&quot; /&gt;
* Mrs. Nettleship: made the Countess of Yarborough's costume&lt;ref name=&quot;:6&quot; /&gt;
* Paquin, of Dover-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}: made the dress of Madame von André&lt;ref name=&quot;:6&quot; /&gt;

=== Worth, of Paris ===
Located in Paris, Maison Worth or the House of Worth — named for owner and designer Englishman Charles Frederick Worth — was a very influential couturier in the 2nd half of the 19th and the first quarter of the 20th centuries.&lt;blockquote&gt;Worth’s designs are notable for his use of lavish fabrics and trimmings, his incorporation of elements of historic dress, and his attention to fit. While the designer still created one-of-a-kind pieces for his most important clients, he is especially known for preparing a variety of designs that were shown on live models at the House of Worth. Clients made their selections and had garments tailor-made in Worth’s workshop.&lt;ref name=&quot;:7&quot;&gt;{{Cite web|url=https://www.metmuseum.org/toah/hd/wrth/hd_wrth.htm|title=Charles Frederick Worth (1825–1895) and the House of Worth {{!}} Essay {{!}} The Metropolitan Museum of Art {{!}} Heilbrunn Timeline of Art History|last=Krick|first=Authors: Jessa|website=The Met’s Heilbrunn Timeline of Art History|language=en|access-date=2024-07-12}} https://www.metmuseum.org/toah/hd/wrth/hd_wrth.htm.&lt;/ref&gt;&lt;/blockquote&gt;After having won design prizes at the 1851 Great Exhibition in London, which was housed at the Crystal Palace, and the 1854 Exposition Universelle in Paris, Worth opened his own design house in Paris in 1858.&lt;ref name=&quot;:7&quot; /&gt; The Empress Eugénie appointed him designer to the court of France&lt;ref&gt;{{Cite journal|date=2024-07-03|title=House of Worth|url=https://en.wikipedia.org/w/index.php?title=House_of_Worth&amp;oldid=1232307431|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/House_of_Worth.&lt;/ref&gt;:&lt;blockquote&gt;Worth’s rise as a designer coincided with the establishment of the Second Empire in France. The restoration of a royal house in 1852, with Napoleon III (1808–1873) as the new emperor, once again made Paris an imperial capital and the setting for numerous state occasions. Napoleon III implemented a grand vision for both Paris and France, initiating changes and modernization that revitalized the French economy and made Paris into a showpiece of Europe. The demand for luxury goods, including textiles and fashionable dress, reached levels that had not been seen since before the French Revolution (1789–99). When Napoleon III married Empress Eugénie (1826–1920), her tastes set the style at court .... The empress’ patronage ensured Worth’s success as a popular dressmaker from the 1860s onward.&lt;ref name=&quot;:7&quot; /&gt;&lt;/blockquote&gt;Other patrons included women from Empress Eugénie's court, &quot;Elizabeth of Austria, Margherita of Italy, Mme. de Castiglione, Mme. de Pourtales, and every reigning star in the theatrical and operatic world.&quot;&lt;ref&gt;[Worth, House of.] {{Cite book|url=http://archive.org/details/AHistoryOfFeminineFashion|title=A History Of Feminine Fashion (1800s to 1920s)}} Before 1927. [Likely commissioned by Worth. Link is to Archive.org; info from Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Worth_Biarritz_salon.jpg.]&lt;/ref&gt; (6) By the end of the 19th century, wealthy women from the US, the UK and around Europe were making their way to Maison Worth in Paris.

Besides his contributions to in developments in models of promotion and business for the couture fashion house, Worth's real influence took the form of a particular look, which for the end of the century we call the [[Social Victorians/Terminology#Traditional Style|traditional Victorian style]]. After Charles Worth's death in 1895, his sons Gaston-Lucien and Jean-Philippe &quot;succeeded in maintaining his high standards,&quot; and Jean-Philippe especially &quot;follow[ed] his father’s aesthetic, with his use of dramatic fabrics and lavish trimmings.&quot;&lt;ref name=&quot;:7&quot; /&gt; While we associate a particular look with it, the House of Worth designed its clothing for its customers, whose relationship with the traditional style could be nuanced and fluctuating. For example, Lillie Langtry sometimes purchased her gowns at Maison Worth, even at the time she was known not to be corseted, so the style of the House of Worth is also less static and extreme than the gowns of some of its customers might suggest.

==== Costumes for the Fancy-dress Ball ====
The House of Worth made costumes for the following guests at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:

# [[Social Victorians/People/Louisa Montagu Cavendish|Louise, Duchess of Devonshire]], although the costume was designed by [[Social Victorians/People/Dressmakers and Costumiers#M. Comelli|Attilio Comelli]].
# Lady Randolph Churchill&lt;ref name=&quot;:6&quot; /&gt;
# Mrs. Arthur Paget&lt;ref name=&quot;:6&quot; /&gt;
# Daisy, Countess of Warwick&lt;ref name=&quot;:6&quot; /&gt;

== Costumiers for Theatres and Operas ==
At the end of the 19th century, the profession of costumier depended on a knowledge of the history of clothing, although the costumiers themselves  generally did not feel constrained by notions of [[Social Victorians/Terminology#Historical Accuracy|historical accuracy]] for the productions they designed for. ['''until the industrial revolution women made fabrics and clothing, plus ppl wore clothing every day, so clothing was not considered important. Planché; actual history of clothing vs just looking at portraits. History of clothing: foundation garments, items specific to a particular time like a codpiece, fabrics changed and evolved over time, plus a greater variety of fabrics; fabric and empires. The idea of a coherent production design with costumes designed for the particular actor in that production may have been changing about this time; before this actors provided their own costumes; Ellen Terry was probably part of this, Gilbert and Sullivan.''']

Not present at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] but certainly very involved in it were the people who made or provided the clothing, hats, wigs, jewelry, and other accessories. Besides people who made the costumes (costumiers, dressmakers, and modistes) and wigs (perruquiers), embroiderers, jewelers and shoemakers are occasionally mentioned although almost never named in the newspaper accounts.

Not all of these may have been costumiers, at least professional ones; some of the less well known might have been [[Social Victorians/People/Dressmakers and Costumiers#Fashion Houses, Couturiers and Modistes|clothiers]] instead.

=== Mr. Charles Alias ===
Mr. Charles Alias, 36 Soho Square

==== Personal Details ====

* Charles Georges Alias (1852 – 11 May 1921&lt;ref name=&quot;:5&quot;&gt;Principal Probate Registry. ''Calendar of the Grants of Probate and Letters of Administration made in the Probate Registries of the High Court of Justice in England''. London, England © Crown copyright. Ancestry.com. ''England &amp; Wales, National Probate Calendar (Index of Wills and Administrations), 1858-1995'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt;)
* Sarah Alias ()

Notes

# Will probated on 6 October 1921, effects of £6376 18s. 5d. to Marie Alias, widow.&lt;ref name=&quot;:5&quot; /&gt;
# 1881 Census: Charles Alias was born in France; they lived at 114 St Martins Lane in St Martin in the Fields; his occupation is listed as Costumier (Milliner); 2 boarders and a servant were living with them: Robert Soutar (age 51, comedian/actor), Harriet Morgan (age 28, comedian/actor) and the general domestic servant Lucy Ann Hewitt (age 23). Other servants' names follow, but apparently they were not living in 114 St Martins Lane.&lt;ref&gt;''Census Returns of England and Wales, 1881''. Kew, Surrey, England: The National Archives of the UK (TNA): Public Record Office (PRO), 1881. Class: ''RG11''; Piece: ''328''; Folio: ''42''; Page: ''27''; GSU roll: ''1341071''. Ancestry.com and The Church of Jesus Christ of Latter-day Saints. ''1881 England Census'' [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2004.&lt;/ref&gt;
# 1891 Census: Charles Alias was born in France; they lived at 36 Soho Square; his occupation is listed as Theatrical Costumier;

==== Costumier ====
[[Social Victorians/People/Dressmakers and Costumiers#Comelli|M. Comelli]], designer and costumier at Covent Garden, designed the costumes that were constructed by Mr. Alias of Soho Square.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* Several newspapers specifically name Mr. Alias as one of their sources of information about the costumes for the Duchess of Devonshire's ball: The London ''Echo''&lt;ref&gt;“A Jubilee Ball. Brilliant Scene at Devonshire House. Some of the Costumes Worn.” The London ''Echo'' 3 July 1897, Saturday: 2 [of 4], Cols. 6a – 7a [of 7]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0004596/18970703/027/0002.&lt;/ref&gt;{{rp|p. 2, Col. 6a}}; the London ''Evening Standard'' &lt;ref name=&quot;:8&quot;&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 5b}}
* The column &quot;Girls' Gossip&quot; names M. Alias in its discussion of the costumes:&lt;blockquote&gt;Herr von André was a splendid Benvenuto Cellini in brown and crimson, a perfect triumph of M. Alias's art. In fact, it was owing to the studious research and historical accuracy displayed by this clever costumier that so many of the dresses were so realistically pictorial. Alias dressed the Prince of Wales, the Duke and Duchess of Connaught, Duke of York, Prince Christian, Lord Lathom, and about a hundred other great ones of our island for the occasion.&lt;ref name=&quot;:12&quot;&gt;“Girls’ Gossip.” ''Truth'' 8 July 1897, Thursday: 41 [of 70], Col. 1b – 42, Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0002961/18970708/089/0041.&lt;/ref&gt;{{rp|42, Col. 2c}}&lt;/blockquote&gt;
*&quot;Charles Alias was French and very small. He had started as a traveller in artificial flowers and married a little dressmaker in Long Acre. They started making theatrical costumes and later moved to 36 Soho Square.&quot;&lt;ref&gt;{{Cite book|url=https://books.google.com/books?id=ZJ8fAQAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgMEAI|title=As You Were: Reminiscences|last=Byng|first=Douglas|date=1970|publisher=Duckworth|isbn=978-0-7156-0543-1|language=en}} https://books.google.com/books?id=ZJ8fAQAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgMEAI.&lt;/ref&gt;
* In its Appendix of Royal Warrant Holders, the 1902 ''Debrett's'' also says &quot;Charles Alias, Costumier, 36, Soho Square. W.&quot;&lt;ref&gt;{{Cite book|url=https://books.google.com/books?id=cLc7AQAAMAAJ&amp;pg=RA2-PP7&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgGEAI#v=onepage&amp;q=Alias%20Soho%20dressmaker%20costumier&amp;f=false|title=Debrett's Peerage, Baronetage, Knightage, and Companionage: Comprising Information Concerning All Persons Bearing Hereditary Or Courtesy Titles, Knights, and Companions of All the Various Orders, and the Collateral Branches of All Peers and Baronets|date=1902|publisher=Dean &amp; Son, Limited|language=en}} https://books.google.com/books?id=cLc7AQAAMAAJ&amp;pg=RA2-PP7&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgGEAI#v=onepage&amp;q=Alias%20Soho%20dressmaker%20costumier&amp;f=false.&lt;/ref&gt; (n.p.; end of book)
* The ''Encyclopedia of the Musical Theatre'', Vol. 1, says, &quot;Alias &amp; Co prospered in the 1880s, having a major success with their new costumes for the transferred version of the amazing ''Dorothy'' [a comic opera by Alfred Cellier, libretto by B. C. Stephenson, &quot;transferred&quot; from the Gaiety to the Prince of Wales's Theatre in 1886 and then to the Lyric Theatre in 1888, the most successful of the productions&lt;ref&gt;{{Cite journal|date=2023-03-25|title=Dorothy (opera)|url=https://en.wikipedia.org/w/index.php?title=Dorothy_(opera)&amp;oldid=1146605626|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Dorothy_(opera).&lt;/ref&gt;], and on into the 1890s by which ...&quot;; &quot;The Aliases made their mark in the West End when they provided the costumes for the original London production of La Fille de ...&quot;&lt;ref&gt;{{Cite book|url=https://books.google.com/books?id=2myfAAAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgEEAI|title=The Encyclopedia of the Musical Theatre|last=G?nzl|first=Kurt|date=1994|publisher=Schirmer Books|isbn=978-0-02-871445-5|language=en}} https://books.google.com/books?id=2myfAAAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgEEAI.&lt;/ref&gt; (taking from snippets)
* BNA search: Alias, Costumier, 36, Soho Square, London: 1898 shows a lot of advertisements.
* In 1892 Mr. C. Alias, 36, Soho Square, W., was a director of the 13th Annual Dramatic Ball, at the Freemasons' Tavern.&lt;ref&gt;{{Cite web|url=https://www.britishnewspaperarchive.co.uk/account/register?countrykey=0&amp;showgiftvoucherclaimingoptions=false&amp;gift=false&amp;nextpage=%2faccount%2flogin%3freturnurl%3d%252fviewer%252fbl%252f0001682%252f18920213%252f011%252f0004&amp;rememberme=false&amp;cookietracking=false&amp;partnershipkey=0&amp;newsletter=false&amp;offers=false&amp;registerreason=none&amp;showsubscriptionoptions=false&amp;showcouponmessaging=false&amp;showfreetrialmessaging=false&amp;showregisteroptions=false&amp;showloginoptions=false&amp;showcaptchaerrormessage=false&amp;isonlyupgradeable=false|title=Register {{!}} British Newspaper Archive|website=www.britishnewspaperarchive.co.uk|access-date=2023-04-28}} https://www.britishnewspaperarchive.co.uk/viewer/bl/0001682/18920213/011/0004.&lt;/ref&gt;
* In a gushing piece written for the 15 December 1899 ''Music Hall and Theatre Review'', &quot;The Bohemian Girl&quot; says that Alias executed Comelli designs for a Christmas pantomime ''Triumph of Music''. She goes on to talk about Willie Clarkson's work for another pantomime and a visit by Mrs. Langtry.&lt;ref&gt;&quot;Bohemian Girl, The.&quot; &quot;Preparing for the Pantomime.&quot; ''Music Hall and Theatre Review'' 15 December 1899, Friday: 24 [of 60], Cols. 1b–c and 2b–c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002237/18991215/160/0024.&lt;/ref&gt;
Russell Harris quotes ''The Encyclopedia of the Musical Theatre'' (Blackwell, 1994. Vol. 1, p. 19.):&lt;blockquote&gt;ALIAS, Charles (b France, 184-?; d London, 11 May 1921). The most famous name in British theatrical costumery in the second half of the 19th century.

The son of a French doctor, the young Alias fought alongside his father in the Franco-Prussian war where he is said to have lost the sight in one eye. He visited Britain and the Philharmonic Theatre, Islington, shortly afterwards as a dresser with the French dance troupe, Les Clodoches, and there he met and married Miss Price, the theatre's costumer. Although Alias had no experience in the theatre, he joined his wife in setting up the freelance firm of M et Mme Alias &amp; Co, '''someties''' designing and manufacturing, or more often just making up from the designs of such artists as [Comelli or] Wilhelm or [[Social Victorians/People/Faustin Betbeder|Faustin]], the costumes for an ever-extending series of musical shows.

The Aliases made their mark in the West End when theyprovided the costumes for the original London production of ''La Fille de Madame Angot'' (1873), and thereafter they costumes, either wholly or partly, many of London's most important musical productions including the burlesques at the Gaiety Theatre (''The Bohemian G'yurl, Little Dr Faust, Gulliver, Il Sonnambulo, Pretty Esmeralda'' etc), the Royalty (''Madcap, '''Pluto''''' '''etc'''), and the Strand (''The '''Lying''' Dutchman, L'Africaine, Nemesis, Loo, Antarctic, Champagne, The Baby, Intimidad''), Gilbert's early ''Tospyturveydom'' and ''Princess Toto'', Gilbert and Sullivan premières at the '''OPera''' Comique (''The Pirates of Penzance'') and the Savoy (''Iolanthe''), the vast spectaculars at the Alhambra (''La Poule aux oeufs d'or'' etc) and, most noticeably, the long string of French opéras-bouffes and opéras-comiques which were produced in Britain in the 1870s and 1880s. These included the record-breaking ''Trouillat (La Belle Normande), Le Jour et la nuit (Manola), La Timbale d'argent (The Duke's Daughter), La Marjolaine, Les Prés St Gervais'' and most of the long string of adaptations from the French made by Alias's close friend Henry Farnie, and produced by Alexander Henderson.

Alias maintained a close connection with his homeland. His home at 48 Soho Square became well known as a first stopping place for Frenchmen new to London and a congenial gathering place for theatricals, and he as a useful and friendly intermediary in various theatrical dealings between London and Paris. Hervé, Planquette, Chassaigne, Audran and Lecocq were all guests at Soho Square and the little costumier was said to have been instrumental in the brothers Mansell bringing Hervé and his ''Chilpéric'' (1870) to London, and thus helping set off the craze for opéra-bouffe which dominated the 1870s musical theatre in England. He also encouraged Planquette to work with H B Farnie on an original musical for Britain - the result of which was the enduring ''Rip van Winkle''.

Alias &amp; Co prospered in the 1880s, having a major succss with their new costumes for the transferred version of the amazing ''Dorothy'', and on into the 1890s by which stage they had become largely costume-makers rather than designers. Alias himself had by this time become one of the 'characters' of the London theatre, always anxiously asking 'What time de répétition générale?' as an opening approached, but always punctually ready with the show's costumes on dress-rehearsal night.

When Mme Alias died, Charles remarried and continued the business with his new wife, Mme Marie Wallet Floret from the Paris Opéra wardrobe, up to his death.&lt;ref&gt;Harris, Russell. {{Cite web|url=http://lafayette.org.uk/edw1335.html|title=King Edward VII at the Devonshire House Ball 1897, by Lafayette|website=lafayette.org.uk|access-date=2024-07-23}} Lafayette Negative Archive http://lafayette.org.uk/edw1335.html.  Quoting ''The Encyclopedia of the Musical Theatre'' (Vol. 1, Blackwell, 1994, p. 19).&lt;/ref&gt;&lt;/blockquote&gt;'''Costumes for the Fancy-dress Ball'''

Mr. Alias made costumes for the following guests at the Duchess of Devonshire’s 1897 fancy-dress ball:

# [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]]
# The [[Social Victorians/People/Connaught|Duke of Connaught]]
# The [[Social Victorians/People/George and Mary|Duke of York]]
# Duke of Fife&lt;ref name=&quot;:6&quot;&gt;Harris, Russell. &quot;Costumes by Named Dressmakers.&quot; {{Cite web|url=http://www.rvondeh.dircon.co.uk/incalmprose/|title=The Devonshire House Ball 1897 photographed by Lafayette|website=www.rvondeh.dircon.co.uk|access-date=2024-05-21}} 2011. http://www.rvondeh.dircon.co.uk/incalmprose/.&lt;/ref&gt;
# The Duke of Devonshire&lt;ref name=&quot;:6&quot; /&gt;
# [[Social Victorians/People/Stonor#Julia Caroline Stonor, Marquise of Hautpoul|Julia Stonor, Marquise of Hartpoul]]
# [[Social Victorians/People/Bourke|Hon. Mrs. Gwendolen Bourke]]
# [[Social Victorians/People/Mar and Kellie#Violet, Countess of Mar and Kellie|Violet, Countess of Mar and Kellie]]
# [[Social Victorians/People/Tweedmouth#Fanny, Baroness Tweedmouth|Fanny, Baroness Tweedmouth]]
# [[Social Victorians/People/Victoria of Schleswig-Holstein#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Princess Victoria of Schleswig-Holstein]]
# [[Social Victorians/People/Connaught#Princess Louise, Duchess of Connaught|Princess Louise, Duchess of Connaught]]
# [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton|Mary, Dowager Duchess of Hamilton]]
# [[Social Victorians/People/Portland|The Duchess of Portland]]
# [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]]
# Adolf von André&lt;ref name=&quot;:6&quot; /&gt;
# Lady St. Oswald&lt;ref name=&quot;:6&quot; /&gt;
# Earl of Rosebery&lt;ref name=&quot;:6&quot; /&gt;

=== Faustin Bedbeter ===
[[Social Victorians/People/Faustin Betbeder|Faustin Bedbeter]] was a caricaturist and painter who left France after Bismarck's seige of Paris and settled in London, working for the ''London Figaro'' and ''Punch''. He was a costumier beginning at least in 1875. He designed the costumes for a 1909 revival of [[Social Victorians/People/Gilbert|Gilbert]] and [[Social Victorians/People/Arthur Sullivan|Sullivan]]'s ''The Pirates of Penzance''.

=== Willie Clarkson ===
Mr. W. Clarkson, of Wellington-street

Clarkson is also listed among the [[Social Victorians/People/Dressmakers and Costumiers#Perruquiers|perruquiers]]. Clarkson made the costumes for the following guests at the ball:

* Grand Duke Michael of Russia&lt;ref name=&quot;:0&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4A–8 Col. 2B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;{{rp|p. 8, Col. 2a}}
* The Duke of Manchester&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
* [[Social Victorians/People/Gleichen#Laura, Princess Victor of Hohenlohe Langenburg|Laura, Princess Victor of Hohenlohe]]&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
* Princess Louise&lt;ref name=&quot;:1&quot; /&gt;

=== M. Comelli ===
Attilio Giuseppe de Comelli von Stuckenfeld (1858-1925).

Comelli &quot;was appointed house designer to the Royal Opera House in the 1890s&quot;&lt;ref name=&quot;:2&quot;&gt;&quot;Attilio Comelli Design Collection.&quot; ''Royal Opera House''  https://www.rohcollections.org.uk/collectionComelli.aspx (retrieved February 2024).&lt;/ref&gt; continuing &quot;to the early 1920s.&quot;&lt;ref&gt;{{Citation|title=Drury Lane Design Collection|url=https://collections.vam.ac.uk/item/O1172507/drury-lane-design-collection-costume-design-comelli-attilio/|date=1915|accessdate=2024-02-13|first=Attilio|last=Comelli}}. https://collections.vam.ac.uk/item/O1172507/drury-lane-design-collection-costume-design-comelli-attilio/.&lt;/ref&gt; At the same time, &quot;He was credited as Artist in Chief at the Alhambra, Theatre Royal, Drury Lane and the Royal Opera House in London, and also found time to provide costumes for some of the Savoy operas and for Christmas pantomimes in London and Australia.&quot;&lt;ref name=&quot;:2&quot; /&gt; After coming &quot;to London in the late 19th century [he] quickly established himself as one of the most prolific designers for the London stage.&quot;&lt;ref name=&quot;:2&quot; /&gt;

He described his research process for costume design for the July 1902 ''Cassell's Magazine'':&lt;blockquote&gt;When I get the order to prepare designs for a new play … [sic ellipsis] I first spend some weeks in studying, at the British and South Kensington [now the Victoria &amp; Albert] Museum, every available authority on the period, and I frequently send my brother to Paris and Berlin, if there is a chance of getting information there that is not available in London’. (‘The Art of Theatrical Disguise’ by Sidney Dark, ''Cassell’s Magazine'', July 1902, pp.162–7).&lt;ref name=&quot;:2&quot; /&gt;&lt;/blockquote&gt;According to the Royal Opera House, he &quot;appears to have had several siblings, including possibly Emilio Andrea Comelli (1862–1929).&quot;&lt;ref name=&quot;:2&quot; /&gt;  Also, perhaps another relative, Italian painter Dante Comelli (1880–1958) designed for the Royal Opera House in Covent Garden later.

Comelli's designs for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:
* Comelli designed the costumes that were constructed by [[Social Victorians/People/Dressmakers and Costumiers#Mr. Charles Alias|Mr. Alias of Soho Square]].&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}

* Comelli designed the costumes of the attendants of [[Social Victorians/People/Louisa Montagu Cavendish|Louise, Duchess of Devonshire]] as well as her own costume. Alias did not construct her costume, [[Social Victorians/People/Dressmakers and Costumiers#The House of Worth|the House of Worth]] did.
* Comelli may have designed the costumes of the entourage of [[Social Victorians/People/Pless#Daisy, Princess Henry of Pless|Daisy, Princess of Pless]], although Mrs. Mason made Daisy's dress.&lt;ref&gt;&quot;Dresses Worn at the Duchess of Devonshire's Ball on July 2. Made by Mrs. Mason, 4 New Burlington Street, W.&quot; The ''Queen'' 10 July 1897, Saturday: 48 [of 98 BNA; p. 74 print page), Col. 1a–3c [of 3]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/BL/0002627/18970710/168/0048?browse=true.&lt;/ref&gt; George Cornwallis-West says his costume was &quot;designed by a famous theatrical designer of the day.&quot;&lt;ref&gt;Qtd. in Martin Spies, &quot;&quot;Late Victorian Aristocrats and the Racial Other: The Devonshire House Ball of 1897.&quot; ''Race &amp; Class'' April–June 2016 (57.4): 95–103.&lt;/ref&gt;{{rp|97}}
[[File:Ellen Terry as Lady Macbeth.jpg|thumb|''Ellen Terry as Lady Macbeth'', Sargent 1889]]

=== Alice Comyns Carr and Ada Nettleship ===
According to Smallhythe Place, the &quot;beetle wing dress&quot; for Ellen Terry's 1888 performance as Lady Macbeth was designed by Alice Comyns Carr and constructed by Ada Nettleship, the &quot;team&quot; that made Ellen Terry's costumes for perhaps 2 decades.&lt;ref name=&quot;:14&quot;&gt;&quot;'Beetle Wing Dress' for Lady Macbeth.&quot; Smallhythe Place, Kent. The National Trusts Collections. Object NT 1118839.1 (1888) https://www.nationaltrustcollections.org.uk/object/1118839.1.&lt;/ref&gt; John Singer Sargent's 1889 portrait of Terry in this dress is at right. (Smallhythe Place, Kent, part of the National Trust, was Terry's home from 1899 to her death. This dress is part of that collection.)

Nettleship crocheted the sleeves and skirt of Terry's costume to resemble &quot;soft chain armour,&quot;&lt;ref name=&quot;:14&quot; /&gt; which she overlaid with wing cases from 1,000 beetles.&lt;ref name=&quot;:15&quot;&gt;{{Cite web|url=https://womenwhomeantbusiness.com/2021/01/21/ada-nettleship-1856-1932/|title=Ada Nettleship (1856-1932)|last=B|first=Lizzie|date=2021-01-21|website=Women Who Meant Business|language=en|access-date=2025-06-06}}&lt;/ref&gt;

Comyn Carr and Nettleship's beetle-wing costume was not the only or even the first dress decorated with the iridescent wings. Ada Nettleship had used beetle wings in &quot;an 1886 dress and an 1887 hat for Constance Lloyd that were oversewn with iridescent green beetle wings&quot;&lt;ref name=&quot;:16&quot;&gt;{{Cite journal|date=2025-04-21|title=Ada Nettleship|url=https://en.wikipedia.org/w/index.php?title=Ada_Nettleship&amp;oldid=1286707541|journal=Wikipedia|language=en}}&lt;/ref&gt; — and [[Social Victorians/People/Dressmakers and Costumiers#Mrs Sims' Court Dress Establishment, Dublin|Mrs Sims]] had used some for a dress in c. 1880.&lt;ref name=&quot;:13&quot; /&gt;

==== Personal Details ====
Alice Laura Vansittart Comyns Carr designed costumes, and dressmaker Adaline Cort Nettleship constructed Comyns Carr's designs. They were a &quot;costume team&quot; separate from those who did the costumes for &quot;the rest of the Lyceum company.&quot;&lt;ref name=&quot;:14&quot; /&gt; They appear to have maintained individual establishments, with Nettelship often constructing costumes for Terry that were designed by Comyns Carr.

Alice Comyns Carr (1850–1927) was married to J. Comyns Carr, &quot;drama and art critic, author, playwright and director of the Grosvenor Gallery.&quot;&lt;ref&gt;{{Cite journal|date=2025-04-21|title=Alice Comyns Carr|url=https://en.wikipedia.org/w/index.php?title=Alice_Comyns_Carr&amp;oldid=1286707345|journal=Wikipedia|language=en}}&lt;/ref&gt; She was associated with the [[Social Victorians/Terminology#Progressive Style|aesthetic dress movement]] and was friends with Edward Burne-Jones and John Singer Sargent as well as Lawrence Alma-Tadema, &quot;the writers Robert Browning and Henry James and composers Hubert Parry and [[Social Victorians/People/Arthur Sullivan|Arthur Sullivan]].&quot;&lt;ref name=&quot;:15&quot; /&gt;

Ada (Adaline) Cort Nettleship (1856 – 19 December 1932&lt;ref name=&quot;:16&quot; /&gt;) was married to painter John Trivett Nettleship. Some of her &quot;[n]otable clients included the soprano Marie Tempest, and the actors Ellen Terry, Winifred Emery, Sarah Bernhardt, and Mrs Patrick Campbell.&quot;&lt;ref name=&quot;:16&quot; /&gt; Like Comyns Carr, Nettleship was an advocate of [[Social Victorians/Terminology#Progressive Style|aesthetic dress design]], making dresses for Constance Lloyd in that progressive style, including her dress for her wedding to [[Social Victorians/People/Oscar Wilde|Oscar Wilde]]. Nettleship &quot;in her youth had been a noted ‘art-embroiderer’ in the style of May Morris.&quot;&lt;ref name=&quot;:15&quot; /&gt;

Alice Comyns Carr published her ''Reminiscences'' in 1926, the year before her death. Ada Nettleship was covered by the newspapers from time to time (&quot;''St James Gazette'' 30/5/1883; ''Dundee Evening Telegraph'' 7/7/1884; ''Morning Post'' 16/10/1886; ''The Queen'' 13/8/1887; ‘Ellen Terry’s gowns and the woman who makes them’ by Bessie O’Connor in ''Harpers Bazaar'' 9th Jan 1897; ‘What Actresses Pay For Their Dresses’ in ''New Zealand Herald'' 25/08/1900; ''South Wales Daily News'' 25/1/1902; ''Leeds Mercury'' 13/2/1914.&quot;&lt;ref name=&quot;:15&quot; /&gt;)

=== Miss Mary E. Fisher ===
Mme. or Miss Mary E. Fisher, 26, Bedford-street, Covent-garden&lt;ref name=&quot;:9&quot;&gt;{{Cite book|url=https://books.google.co.in/books?id=cVQZAAAAYAAJ&amp;pg=RA3-PR2&amp;dq=Mr.+May,+Garrick-street,+Covent-garden&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;redir_esc=y|title=The Play-pictorial|date=1908|publisher=Greening &amp; Company, Limited|language=en}} P. ADVT ii. ''Google Books'' https://books.google.com/books?id=cVQZAAAAYAAJ.&lt;/ref&gt; &lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
*Miss Mary E. Fisher is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}

=== Charles H. Fox ===
Fox: &quot;perruquier and costumier Charles H. Fox. Since 1878, Fox had been a major supplier of wigs and costumes for private theatricals and fancy dress balls.&quot;&lt;ref name=&quot;:3&quot;&gt;&quot;B. J. Simmons &amp; Co.: An Inventory of Its Costume Design Records at the Harry Ransom Center.&quot; ''B. J. Simmons &amp; Co. Costume Design Records''. Harry Ransom Center. The University of Texas. 2023. Retrieved February 2024. https://norman.hrc.utexas.edu/fasearch/findingAid.cfm?eadID=01440.&lt;/ref&gt;

=== Harrison ===
Harrison's, Ltd., 31, Bow-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* In a chatty column written as a letter to &quot;Dearest Amy,&quot; the article in ''Truth'' on the ball says, &quot;Princess Henry of Pless was another [Queen of Sheba], and her dress was absolutely magnificent. The conception of it was both poetic and artistic, and is due, I believe, to the genius of Mrs. Harrison.&quot;&lt;ref name=&quot;:12&quot; /&gt;{{rp|42, Col. 1b}}
* There are ads for Harrison's.

=== May ===
Mr. May, Garrick-street, Covent-garden&lt;ref name=&quot;:9&quot; /&gt;

* Mr. May is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}

=== Nathan ===
Messrs. L. and H. Nathan, Coventry-street, Haymarket; 17, Convent-street, Picadilly

*Messrs. L. and H. Nathan is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}
*Mr. Karl, artist, designed the costumes made by Messrs. L. and H. Nathan of Coventry-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} &lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}
*Messrs Nathan made the costumes for the following people:
**[[Social Victorians/People/Harcourt#Elizabeth Harcourt|Elizabeth, Lady Harcourt]]
**[[Social Victorians/People/Rothschild Family#Emma, Lady Rothschildand Nathan Mayer, Lord Rothschild|Emma, Lady Rothschild]]

=== Simmons and Sons ===
Messrs. John Simmons and Sons, Coventry House, Haymarket.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} Simmons, 7 and 8, King Street, Covent Garden.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} Possibly there are 2 Simmonses?

The Harry Ransom Center has a collection on this firm:&lt;blockquote&gt;The London costumier B. J. Simmons &amp; Co. was founded in 1857 by a Mr. B. J. Simmons and operated by his direct descendants well into the 1930s. Simmons' costumes were known for their correctness of period, sophisticated design, and high quality. ... In their busy Covent Garden workshop, dressmakers turned out immaculately constructed stage apparel, often from renderings by leading costume designers. Successful theater managers repeatedly turned to Simmons for historical costumes, especially Herbert Beerbohm Tree whose magnificent stagings of Shakespeare were often outfitted by Simmons.

While best known as a historical costumier for the London stage, Simmons' output was diverse. The company created costumes for a variety of shows in the West End, the provinces, and overseas, ranging from Victorian pantomime to the &quot;kitchen sink&quot; dramas of the 1960s. ... In addition to making new costumes for professional productions, Simmons operated a thriving rental business which allowed operatic and dramatic societies across England to hire beautifully made garments for amateur productions. Like many theatrical costumiers, Simmons maintained a substantial nontheatrical trade.

Simmons began as a family-run outfit known variously as B. J. Simmons, J. B. Simmons, John Simmons &amp; Son/Sons, Simmons/Symmons/Simmonds Brothers, G. B. Simmons, and B. &amp; G. Simmons. The force majeure seems to have been John Simmons, whose name appears in ''The London Stage'' and in London newspapers until 1922. According to J. P. Wearing, between 1890 and 1899 Simmons provided costumes for at least forty-two theatre productions in London.&lt;ref name=&quot;:3&quot; /&gt;&lt;/blockquote&gt;Simmons' contributions to costumes for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:
* Messrs. John Simmons and Son is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}
* Simmons and Sons made costumes for the following guests at the ball:
** [[Social Victorians/People/Ellesmere#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Francis Egerton, 3rd Earl of Ellesmere]]&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** The Duke of Somerset&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** The Marquis of Winchester&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Earl Beauchamp&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Earl Carrington&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Earl Essex&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Viscount Esher&lt;ref name=&quot;:6&quot; /&gt;
** Lord Ampthill&lt;ref name=&quot;:6&quot; /&gt;
** Lady Ampthill&lt;ref name=&quot;:6&quot; /&gt;
Simmons and Sons is also sometimes listed as having made clothing for other social events:

* For the [[Social Victorians/1892-02-10 Alington Leigh Wedding|very fashionable February 1892 wedding between Henry Sturt, Lord Alington and Evelyn Leigh]] — the &quot;most important social event of last week in the social world&quot;&lt;ref name=&quot;:03&quot;&gt;&quot;Lord Alington to Miss Leigh.&quot; ''Gentlewoman'' 20 February 1892, Saturday: 21 [of 46], Cols. 1a–3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18920220/092/0021. Same print title, p. 237.&lt;/ref&gt;{{rp|Col. 1a}} — &quot;Messrs. Simmons &amp; Sons, of Coventry House, Haymarket, made the charming little suits for the pages, which were so much admired.&quot;&lt;ref name=&quot;:03&quot; /&gt;{{rp|Col. 3a}}

=== Smaller Concerns ===
* Mme. Auguste, of Wellington-street&lt;ref name=&quot;:42&quot;&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 42, Col. 3b}}
* Mr. W. Clarkson, 44, Wellington Street (costumes and wigs)&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}

=== Unknown Whether Costumier or Dressmaker ===
*Mme. Ellis: &quot;The pretty costumes of Merlin and Vivian worn by [[Social Victorians/People/Walker|Mr and Mrs Willie Walker]] at the Devonshire House Ball, were made by Mme. Ellis, 16, Upper George-street, Bryanston-square.&quot;&lt;ref&gt;Holt, Ardern. &quot;Dress and Fashion. To Correspondents.&quot; The ''Queen'' 24 July 1897, Saturday: 54 [of 88], Col. 1a [of 3]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18970724/271/0054.&lt;/ref&gt;
* Madame Frederic, of Lower Grosvenor Place
* &quot;and many others&quot;&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}

== Perruquiers ==
Mr. W. Clarkson &quot;supplied the wigs and headdresses for the Royal Family&quot;&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}} for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:&lt;blockquote&gt;At the Duchess of Devonshire's ball, on the 2d inst., the Prince of Wales looked as if he had stepped out of a masterpiece by one of the old painters. His wig, which completed a correct make-up as Knight of Malta, was specially made and fitted by that favoured &quot;Royal Perruquier&quot; Mr Willie Clarkson, who also had the honour of making and fitting the wigs worn by Prince Charles of Denmark, the Duke of York, and the Duke and Duchess of Connaught, and of dressing the hair of the Duchess of York and the Princess Victoria of Schleswig-Holstein. Mr Clarkson also supplied a number of the costumes, including those worn by the Grand Duke Michael of Russia, Princess Louise, and the Duke of Manchester. It would not be safe to say how many crowned heads have literally &quot;passed through the hands&quot; of Mr Clarkson. The art of the perruquier is a very difficult one, requiring historical knowledge, patient research, and great taste. It is most essential to the success of any theatrical performance or of an historical ball.&lt;ref name=&quot;:1&quot;&gt;“Foreign Plays and Players.” ''The Era'' 10 July 1897, Saturday: 15 [of 28], Col. 3c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000053/18970710/032/0015.&lt;/ref&gt;&lt;/blockquote&gt;Clarkson also provided costumes and wigs for the [[Social Victorians/Royals Amateur Theatricals|amateur theatricals]] that the royals took part in to entertain themselves.

== Jewelers ==
After naming costumiers for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]], the ''Gentlewoman'' specifically mentions the Parisian Company for its jewelry and Mr. Norman of Bond Street for the shoes he made:&lt;blockquote&gt;Among other firms [than the costumiers] who lent their aid to make the great ball a huge success was the Parisian Company, whose sparkling gems and jewels, and whose ropes of pearls and precious stones, enhanced the charms of many a fair dame in her dainty old-world costume, and the firm of Mr. Norman, 69, New Bond-street, who designed and made the shoes for the Princess of Wales, the Duchess of Buccleuch, &amp;c., &amp;c.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3c}}&lt;/blockquote&gt;According to the ''Westminster Gazette'', &quot;One very great lady indeed had been lent, by a jeweller, diamonds worth about £13,000.&quot;&lt;ref name=&quot;:4&quot;&gt;“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.&lt;/ref&gt;{{rp|p. 5, Col. 2c}}

== People Who Made Costumes for the Ball ==
The ''Queen'' often mentions the dressmaker or costumier in its reports on the costumes at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball at Devonshire House]] as well as in general.

The ''Gentlewoman'' covered this topic explicitly in its report on the ball:&lt;blockquote&gt;Very great credit is due to the taste and artistic powers of the designers of these dresses, and particular mention must be made of M. Comelli, of Covent Garden Theatre, whose facile pen designed most of the superb toilettes so ably carried out by Messrs. Alias, of Soho-square. Other theatrical costumiers who brought all their special talents to bear on the historical and fancy costumes required for this function were Messrs. Nathan (artist, Mr. Karl), of Coventry-street; Messrs. John Simmons &amp; Sons, Haymarket; Mme. Auguste, of Wellington-street; Harrison's, Ltd., 31, Bow-street; Simmons, 7 and 8, King-street; Mr. Clarkson, 44, Wellington-street; Mme. Fisher, 26, Bedford-street; and many others. A great number of well-known modistes in London were also called upon to supply dresses. Amongst these we chronicle M. Mason, New Burlington-street; M. Machinka, Conduit-street; Paquin, of Dover-street; Jays, Ltd., Regent-street; Messrs. Durrant, 116, Bond-street (who made Lady Londonderry's magnificent gown), and numerous others.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}&lt;/blockquote&gt;The London ''Evening Standard'' cites the sources of its information about the costumes:&lt;blockquote&gt;We are indebted for some of the particulars of the dresses to Mr. Charles Alias, Soho-square; Messrs. L. and H. Nathan, Coventry-street, Haymarket; Messrs. John Simmons and Son, Coventry House, Haymarket; Mr. May, Garrick-street, Covent-garden; Miss Mary E. Fisher, 26 Bedford-street, Covent-garden; and the ''Lady'' newspaper.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}&lt;/blockquote&gt;The ''Morning Post'' also addressed the costumiers. It named Mr. Alias in association with the royals, as well as mentioning several other costumiers by name:&lt;blockquote&gt;The costumes worn by the Prince of Wales, the Duke of York, and the Duchess of Connaught, as well as many others were supplied by Mr. Alias, of Soho-square. Those worn by the Grand Duke Michael of Russia, the Duke of Manchester, Princess Victor of Hohenlohe, and others were made by Mr. W. Clarkson, of Wellington-street, who also supplied the wigs and headdresses for the Royal Family. Messrs. Simmons and Sons, of the Haymarket, made a large number of costumes, including those of the Duke of Somerset, the Marquis of Winchester, Earls Beauchamp, Carrington, Ellesmere, and Essex. Nathan, of Coventry-street, and Simmons, of King-street, Covent-garden; Madame Frederic, of Lower Grosvenor-place, and Mrs. Mason, of New Burlington-street, also made some of the principal costumes.&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}&lt;/blockquote&gt;On 3 July 1897, the day after the ball, the ''Belfast News-letter'' says,&lt;blockquote&gt;For weeks past all the leading London dressmakers and costumiers had been hard at work executing the orders for this great ball. At Alias Nathan's, Clarkson's, Auguste's, and Simmons' all hands set to with a will, and it is gratifying to know that the dresses entrusted to them more than held their own with those sent over from Paris.&lt;ref name=&quot;:10&quot;&gt;&quot;The Duchess of Devonshire's Fancy Dress Ball. Special Telegram.&quot; ''Belfast News-Letter'' Saturday 03 July 1897: 5 [of 8], Col. 9c [of 9]–6, Col. 1a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0000038/18970703/015/0005.&lt;/ref&gt;{{rp|p. 5, Col. 9a}}&lt;/blockquote&gt;

According to the ''Derbyshire Times and Chesterfield Herald'', citing the ''Daily Mail'',
&lt;blockquote&gt;
&lt;p&gt;Lady de Grey is going as Zenobia, and is getting her dress from Doucet, I hear, while Worth also is making a great many costumes; but the greatest number are being made in England. The Duchess of Portland, the Duchess of Hamilton, Lady Mar and Kellie, and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]] are all going to the costumier in Soho-square, and Alias has also been summoned to Marlborough House for a consultation.&lt;/p&gt;
&lt;p&gt;Mr. Caryl Craven, who is so clever in such matters, is helping the Duchess of Leeds with her dress; in fact, everyone seems pressed into the service, and the result will be one of the most brilliant sights that ever was seen.&lt;ref name=&quot;:11&quot; &lt;/p&gt;&lt;/blockquote&gt;
== Notes and Questions ==

# Which costumier was this? &quot;A well-known West End dressmaker booked for the Duchess of Devonshire's fancy dress ball orders representing £27000.&quot;&lt;ref&gt;&quot;London Letter.&quot; ''Western Daily Press'' 15 July 1897, Thursday: 8 [of 8], Col. 7c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000264/18970715/146/0008.&lt;/ref&gt;

== References ==
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      <text bytes="54976" sha1="o65uh772hkfmzb8t49htgchy9hufpwq" xml:space="preserve">== Dressmakers, Modistes, Costumiers, Perruquiers and Jewelers ==

=== Not to Mention Seamstresses, Tailors, Lace-makers, Milliners, and Lady's Maids ===
Dominated as the social world was by women, fashion was an important part of the reportage on social events, with some reporters demonstrating knowledge of fabrics, cuts, laces, and so on. The Victorians had specialized terms for people who designed and made clothing, especially very fashionable clothes or haut couture, and specialized careers for those people who assisted women to acquire, manage and wear that clothing. Because of the popularity of fancy-dress or costume parties, some of the people assisting them were costumiers from the world of theatre and opera. The terminology and examples that follow are generally focused on the end of the 19th century in London.

== Fashion Houses, Couturiers and Modistes ==
The ''Gentlewoman'' says, &quot;A great number of well-known modistes in London were also called upon to supply dresses.&quot;&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} Among those who helped construct the costumes and wigs include the following:

=== Doucet ===
A gossipy article in ''Derbyshire Times and Chesterfield Herald'' (citing the ''Daily Mail'') says, &quot;Lady de Grey is going as Zenobia, and is getting her dress from Doucet, I hear,&quot;&lt;ref name=&quot;:11&quot;&gt;“Derbyshire Sayings and Doings.” ''Derbyshire Times and Chesterfield Herald'' 12 June 1897, Saturday: 5 [of 8], Col. 2A. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000228/18970612/018/0005.&lt;/ref&gt; although she went as Cleopatra and not Zenobia (only the Duchess of Devonshire went as Zenobia).

=== Mme Durrant ===

Mme Durrant's concern, at the end of the 19th century, at least, was at 116 &amp; 117 New Bond-street, London W. An ad in ''The Queen'' says,&lt;blockquote&gt;Court Dressmaker and Milliner. The Latest Paris Models in Morning, Afternoon, Tailor, and Evening Gowns, Millinery, and Mantles.&quot;&lt;ref&gt;&quot;Madame Durrant, Court Dressmaker and Milliner.&quot; ''The Queen'' 15 April 1899, Saturday: 11 [of 88], Cols. 2–3c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18990415/082/0011.&lt;/ref&gt;&lt;/blockquote&gt;Mme Durrant made the costumes for the following guests at the ball:

# [[Social Victorians/People/Londonderry#Theresa, Marchioness of Londonderry|Theresa, Marchioness of Londonderry]]&lt;ref&gt;&quot;Lines for the Ladies.&quot; ''Daily Gazette for Middlesbrough'' Thursday 16 June 1898: 4 [of 4], Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000159/18980616/060/0004.&lt;/ref&gt; The dress and fabrics for the Marchioness of Londonderry as well as her quadrille, were made in Britain or Ireland.&lt;ref name=&quot;:02&quot;&gt;&quot;This Morning’s News.&quot; London ''Daily News'' 6 July 1897, Tuesday: 7 [of 12], Col. 3b. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970706/038/0007.&lt;/ref&gt;

Mme Durrant made at least a couple of dresses for Queen Mary (early 20th century).&lt;ref&gt;{{Cite web|url=https://tr.pinterest.com/pin/278730664423122186/|title=1900 - 1919 Clothing panosundaki Pin|website=Pinterest|language=en|access-date=2023-03-08}} https://pin.it/2GUiBm7 and https://pin.it/2GUiBm7.&lt;/ref&gt; Also, perhaps early 20th-c, Durrant had an address on Dover Street.&lt;ref&gt;{{Cite web|url=http://www.elisarolle.com/queerplaces/ch-d-e/Edwin%20Hardy%20Amies.html|title=queerplaces - Sir Edwin Hardy Amies|website=www.elisarolle.com|access-date=2023-03-08}} http://www.elisarolle.com/queerplaces/ch-d-e/Edwin%20Hardy%20Amies.html.&lt;/ref&gt; ''The Queen'' also has ads for a &quot;Mr. Durrrant's Ladies' Taylor and Habit Maker&quot; in Edinburgh and Glasgow in 1892.&lt;ref&gt;&quot;Durrant Ladies' Taylor and Habit Maker.&quot; [advertisement] ''The Queen'' 06 February 1892, Saturday: 5 [of 81], Cols. 2–3c [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18920206/043/0005.&lt;/ref&gt;

=== Mrs. Mason ===
M. or Mrs. Mason, of 4, New Burlington Street, W.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* &quot;Dress and Fashion&quot; answer by Adern Holt in the ''Queen'' to queries posed by &quot;Correspondents&quot;: &quot;F&lt;small&gt;ANCY&lt;/small&gt; D&lt;small&gt;RESS&lt;/small&gt;. — For the beautiful ball such as you describe you cannot do better than go to Mrs Mason, New Burlington-street, for the costume about which you inquire. It needs very careful making and the most artistic designs, and these you would be sure to obtain there, for the dresses she made for the Duchess of Devonshire's ball were quite artistic masterpieces.&quot;&lt;ref&gt;Holt, Ardern. &quot;Dress and Fashion. To Correspondents.&quot; The ''Queen'' 17 July 1897, Saturday: 48 [of 97], Col. 1a [of 3]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18970717/231/0049.&lt;/ref&gt;
Mrs. Mason made costumes for the following guests at the ball:

# [[Social Victorians/People/Pless|Daisy, Princess of Pless]]
# [[Social Victorians/People/Ashburton#Mabel, Lady Ashburton|Mabel, Lady Ashburton]]
# [[Social Victorians/People/de Trafford#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Violet, Lady de Trafford]]
# [[Social Victorians/People/Cadogan#Lady Sophie Scott|Lady Sophie Scott]]
# Lady Lurgan&lt;ref name=&quot;:6&quot; /&gt;
# [[Social Victorians/People/Leeds#Katherine, Duchess of Leeds|Katherine, Duchess of Leeds]]
# [[Social Victorians/People/Sutherland#Millicent, Duchess of Sutherland|Millicent, Duchess of Sutherland]]
# [[Social Victorians/People/Meysey-Thompson#Lady Ethel Meysey Thompson|Lady Ethel Meysey Thompson]]
# [[Social Victorians/People/Muriel Wilson|Muriel Wilson]]
# [[Social Victorians/People/Edmonstone#Lady Ida Edmonstone|Lady Ida Edmonstone]]
# [[Social Victorians/People/Goelet#Costumes at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Mary Goelet]]
#[[Social Victorians/People/Cavendish#Lady Edward Cavendish|Lady Edward Cavendish]]
#[[Social Victorians/People/Sarah Spencer-Churchill Wilson#Lady Sarah Wilson|Lady Sarah Wilson]]
#[[Social Victorians/People/Derby#Constance Villiers Stanley, Countess of Derby|Countess of Derby]]
#Mrs [[Social Victorians/People/Bourke|Gwendolen Bourke]]&lt;ref name=&quot;:6&quot; /&gt;
#Duchess of Roxburghe&lt;ref name=&quot;:6&quot; /&gt;

=== Morin-Blossier ===
The French &quot;tailoring workshop&quot;&lt;ref&gt;{{Cite web|url=https://fashion.mam-e.it/morin-blossier/|title=Morin-Blossier -|date=2016-02-05|language=it-IT|access-date=2022-04-07}}&lt;/ref&gt; of Morin-Blossier &quot;possibly&quot;&lt;ref name=&quot;:6&quot; /&gt; made the dress worn to  the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball]] by

* Alexandra, Princess of Wales&lt;ref name=&quot;:6&quot; /&gt;
* [[Social Victorians/People/Prince Charles of Denmark|Princess Maud of Wales]] (Princess Charles of Denmark)&lt;ref name=&quot;:43&quot;&gt;Harris, Russell. &quot;Prince and Princess Carl of Denmark, later King Haakon VII (1872-1957) and Queen Maud of Norway (1869-1938),  and Princess Victoria of Wales (1868-1935), as a 16th century Danish courtier, and Ladies-in-Waiting at to Marguerite de Valois.&quot; &quot;List of Sitters.&quot; ''In Calm Prose''. 2011 http://www.rvondeh.dircon.co.uk/incalmprose/denmark.html.&lt;/ref&gt;
* Duchess of York&lt;ref name=&quot;:6&quot; /&gt;
* Princess Victoria&lt;ref name=&quot;:6&quot; /&gt;

=== Messrs Russell and Allen ===
Old Bond-street., W.

Made presentation dresses for 8 of the following in 1913&lt;ref&gt;&quot;Their Majesties' Court.&quot; ''Lady's Pictorial'' 17 May 1913, Saturday: 35 [of 64], Col. 2c [of 3]. ''British Newspaper Archive''https://www.britishnewspaperarchive.co.uk/viewer/bl/0005980/19130517/296/0035. Same print title, p. 787.&lt;/ref&gt;:

* Mrs. A. C. Hardy, of Montreal
* Mrs. Thorburn
* Mrs. Ralph Berners
* Miss Spencer Warwick
* [[Social Victorians/People/Bourke|Miss [Daphne] Bourke]]
* Mrs. Henry Barran
* Miss D. Hickman
* Hon. Irene Molesworth
* The Hon. Edith Winn
* The Hon. Hilaria St. Aubyn
* The Hon. Mary Charteris
* Miss Grace Holley

=== Mrs Sims' Court Dress Establishment, Dublin ===
Mrs Mary Sims, Dawson Street, Dublin

Mrs Sims made a dress decorated with beetle wings in c. 1880; this dress still exists and, according to Elaine Hewitt, is in the NMI collections.&lt;ref name=&quot;:13&quot;&gt;Objects in Focus: New Research Seminar, Naional Museum of Ireland, Decoraive Arts and History, Collins Barracks. Saturday 16th February 2013. https://www.academia.edu/2455567/The_material_culture_of_infancy_and_early_childhood_in_Ireland_c_1680_1830?auto=download.&lt;/ref&gt; Hewitt's precis for an exhibit called ''Objects in Focus: New Research Seminar, National Museum of Ireland, Decoraive Arts and History, Collins Barracks'' says, &quot;Mary Sims was a court dressmaker by Royal appointment, who established herself from 1863 as the most prominent dressmaker in Dublin.&quot;

Mrs Sims made costumes for the following guests at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:

* [[Social Victorians/People/Cadogan#Lady Beatrix, Countess Cadogan|Lady Beatrix, Countess Cadogan]]

Other people Mrs Sims made clothes for:

* Alexandra, Princess of Wales, 1885: Kate Strasdin offers an example of Alexandra's strategic use of clothing: a gown Alexandra wore to a Drawing Room at Buckingham Palace was, according to the ''Times'', &quot;a dress of rich yellow satin and silver brocade, draped with silver lace, corsage to correspond, made by Mrs Sims of Dublin.&quot;{{rp|1885, p. 11}} What is strategic is the release of Mrs Sims's name, according to Strasdin, since &quot;[t]he communication of this detail can only have come from the royal household itself, demonstrating the control that Alexandra exerted over details released to the press relating to her appearance.&quot;&lt;ref&gt;Strasdin, Kate, &quot;Reporting Royal Dress: Queen Alexandra and Royal Image Making.&quot; Falmouth University Research Repository. http://repository.falmouth.ac.uk.&lt;/ref&gt;
* Ishbel, Marchioness Aberdeen, 1886: &quot;Ishbel, Lady Aberdeen (1857–1939), [wore a &quot;costume of an Irish lady in the thirteenth century&quot;] in 1886 while presiding over a garden party at the Vice Regal Lodge in the Phoenix Park in Dublin, an event to which the 2,000 invited guests were expected to wear clothes of Irish manufacture.&quot;&lt;ref&gt;Alex Ward, &quot;Dress and National Identity: Women’s Clothing and the Celtic Revival,&quot; ''Costume'', 48:2, 2014, 193-212, DOI: https://doi.org/10.1179/0590887614Z.00000000050.&lt;/ref&gt;{{rp|199}}

=== Smaller Concerns ===
* Madame Fréderic: made the costume for Princess Mary of Teck&lt;ref name=&quot;:6&quot; /&gt;
* Jays, Ltd., Regent-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* M. Machinka, Conduit-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* Maison Lucille: made Mrs. James's costume&lt;ref name=&quot;:6&quot; /&gt;
* Mrs. Nettleship: made the Countess of Yarborough's costume&lt;ref name=&quot;:6&quot; /&gt;
* Paquin, of Dover-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}: made the dress of Madame von André&lt;ref name=&quot;:6&quot; /&gt;

=== Worth, of Paris ===
Located in Paris, Maison Worth or the House of Worth — named for owner and designer Englishman Charles Frederick Worth — was a very influential couturier in the 2nd half of the 19th and the first quarter of the 20th centuries.&lt;blockquote&gt;Worth’s designs are notable for his use of lavish fabrics and trimmings, his incorporation of elements of historic dress, and his attention to fit. While the designer still created one-of-a-kind pieces for his most important clients, he is especially known for preparing a variety of designs that were shown on live models at the House of Worth. Clients made their selections and had garments tailor-made in Worth’s workshop.&lt;ref name=&quot;:7&quot;&gt;{{Cite web|url=https://www.metmuseum.org/toah/hd/wrth/hd_wrth.htm|title=Charles Frederick Worth (1825–1895) and the House of Worth {{!}} Essay {{!}} The Metropolitan Museum of Art {{!}} Heilbrunn Timeline of Art History|last=Krick|first=Authors: Jessa|website=The Met’s Heilbrunn Timeline of Art History|language=en|access-date=2024-07-12}} https://www.metmuseum.org/toah/hd/wrth/hd_wrth.htm.&lt;/ref&gt;&lt;/blockquote&gt;After having won design prizes at the 1851 Great Exhibition in London, which was housed at the Crystal Palace, and the 1854 Exposition Universelle in Paris, Worth opened his own design house in Paris in 1858.&lt;ref name=&quot;:7&quot; /&gt; The Empress Eugénie appointed him designer to the court of France&lt;ref&gt;{{Cite journal|date=2024-07-03|title=House of Worth|url=https://en.wikipedia.org/w/index.php?title=House_of_Worth&amp;oldid=1232307431|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/House_of_Worth.&lt;/ref&gt;:&lt;blockquote&gt;Worth’s rise as a designer coincided with the establishment of the Second Empire in France. The restoration of a royal house in 1852, with Napoleon III (1808–1873) as the new emperor, once again made Paris an imperial capital and the setting for numerous state occasions. Napoleon III implemented a grand vision for both Paris and France, initiating changes and modernization that revitalized the French economy and made Paris into a showpiece of Europe. The demand for luxury goods, including textiles and fashionable dress, reached levels that had not been seen since before the French Revolution (1789–99). When Napoleon III married Empress Eugénie (1826–1920), her tastes set the style at court .... The empress’ patronage ensured Worth’s success as a popular dressmaker from the 1860s onward.&lt;ref name=&quot;:7&quot; /&gt;&lt;/blockquote&gt;Other patrons included women from Empress Eugénie's court, &quot;Elizabeth of Austria, Margherita of Italy, Mme. de Castiglione, Mme. de Pourtales, and every reigning star in the theatrical and operatic world.&quot;&lt;ref&gt;[Worth, House of.] {{Cite book|url=http://archive.org/details/AHistoryOfFeminineFashion|title=A History Of Feminine Fashion (1800s to 1920s)}} Before 1927. [Likely commissioned by Worth. Link is to Archive.org; info from Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Worth_Biarritz_salon.jpg.]&lt;/ref&gt; (6) By the end of the 19th century, wealthy women from the US, the UK and around Europe were making their way to Maison Worth in Paris.

Besides his contributions to in developments in models of promotion and business for the couture fashion house, Worth's real influence took the form of a particular look, which for the end of the century we call the [[Social Victorians/Terminology#Traditional Style|traditional Victorian style]]. After Charles Worth's death in 1895, his sons Gaston-Lucien and Jean-Philippe &quot;succeeded in maintaining his high standards,&quot; and Jean-Philippe especially &quot;follow[ed] his father’s aesthetic, with his use of dramatic fabrics and lavish trimmings.&quot;&lt;ref name=&quot;:7&quot; /&gt; While we associate a particular look with it, the House of Worth designed its clothing for its customers, whose relationship with the traditional style could be nuanced and fluctuating. For example, Lillie Langtry sometimes purchased her gowns at Maison Worth, even at the time she was known not to be corseted, so the style of the House of Worth is also less static and extreme than the gowns of some of its customers might suggest.

==== Costumes for the Fancy-dress Ball ====
The House of Worth made costumes for the following guests at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:

# [[Social Victorians/People/Louisa Montagu Cavendish|Louise, Duchess of Devonshire]], although the costume was designed by [[Social Victorians/People/Dressmakers and Costumiers#M. Comelli|Attilio Comelli]].
# Lady Randolph Churchill&lt;ref name=&quot;:6&quot; /&gt;
# Mrs. Arthur Paget&lt;ref name=&quot;:6&quot; /&gt;
# Daisy, Countess of Warwick&lt;ref name=&quot;:6&quot; /&gt;

== Costumiers for Theatres and Operas ==
At the end of the 19th century, the profession of costumier depended on a knowledge of the history of clothing, although the costumiers themselves  generally did not feel constrained by notions of [[Social Victorians/Terminology#Historical Accuracy|historical accuracy]] for the productions they designed for. ['''until the industrial revolution women made fabrics and clothing, plus ppl wore clothing every day, so clothing was not considered important. Planché; actual history of clothing vs just looking at portraits. History of clothing: foundation garments, items specific to a particular time like a codpiece, fabrics changed and evolved over time, plus a greater variety of fabrics; fabric and empires. The idea of a coherent production design with costumes designed for the particular actor in that production may have been changing about this time; before this actors provided their own costumes; Ellen Terry was probably part of this, Gilbert and Sullivan.''']

Not present at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] but certainly very involved in it were the people who made or provided the clothing, hats, wigs, jewelry, and other accessories. Besides people who made the costumes (costumiers, dressmakers, and modistes) and wigs (perruquiers), embroiderers, jewelers and shoemakers are occasionally mentioned although almost never named in the newspaper accounts.

Not all of these may have been costumiers, at least professional ones; some of the less well known might have been [[Social Victorians/People/Dressmakers and Costumiers#Fashion Houses, Couturiers and Modistes|clothiers]] instead.

=== Mr. Charles Alias ===
Mr. Charles Alias, 36 Soho Square

==== Personal Details ====

* Charles Georges Alias (1852 – 11 May 1921&lt;ref name=&quot;:5&quot;&gt;Principal Probate Registry. ''Calendar of the Grants of Probate and Letters of Administration made in the Probate Registries of the High Court of Justice in England''. London, England © Crown copyright. Ancestry.com. ''England &amp; Wales, National Probate Calendar (Index of Wills and Administrations), 1858-1995'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt;)
* Sarah Alias ()

Notes

# Will probated on 6 October 1921, effects of £6376 18s. 5d. to Marie Alias, widow.&lt;ref name=&quot;:5&quot; /&gt;
# 1881 Census: Charles Alias was born in France; they lived at 114 St Martins Lane in St Martin in the Fields; his occupation is listed as Costumier (Milliner); 2 boarders and a servant were living with them: Robert Soutar (age 51, comedian/actor), Harriet Morgan (age 28, comedian/actor) and the general domestic servant Lucy Ann Hewitt (age 23). Other servants' names follow, but apparently they were not living in 114 St Martins Lane.&lt;ref&gt;''Census Returns of England and Wales, 1881''. Kew, Surrey, England: The National Archives of the UK (TNA): Public Record Office (PRO), 1881. Class: ''RG11''; Piece: ''328''; Folio: ''42''; Page: ''27''; GSU roll: ''1341071''. Ancestry.com and The Church of Jesus Christ of Latter-day Saints. ''1881 England Census'' [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2004.&lt;/ref&gt;
# 1891 Census: Charles Alias was born in France; they lived at 36 Soho Square; his occupation is listed as Theatrical Costumier;

==== Costumier ====
[[Social Victorians/People/Dressmakers and Costumiers#Comelli|M. Comelli]], designer and costumier at Covent Garden, designed the costumes that were constructed by Mr. Alias of Soho Square.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* Several newspapers specifically name Mr. Alias as one of their sources of information about the costumes for the Duchess of Devonshire's ball: The London ''Echo''&lt;ref&gt;“A Jubilee Ball. Brilliant Scene at Devonshire House. Some of the Costumes Worn.” The London ''Echo'' 3 July 1897, Saturday: 2 [of 4], Cols. 6a – 7a [of 7]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0004596/18970703/027/0002.&lt;/ref&gt;{{rp|p. 2, Col. 6a}}; the London ''Evening Standard'' &lt;ref name=&quot;:8&quot;&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 5b}}
* The column &quot;Girls' Gossip&quot; names M. Alias in its discussion of the costumes:&lt;blockquote&gt;Herr von André was a splendid Benvenuto Cellini in brown and crimson, a perfect triumph of M. Alias's art. In fact, it was owing to the studious research and historical accuracy displayed by this clever costumier that so many of the dresses were so realistically pictorial. Alias dressed the Prince of Wales, the Duke and Duchess of Connaught, Duke of York, Prince Christian, Lord Lathom, and about a hundred other great ones of our island for the occasion.&lt;ref name=&quot;:12&quot;&gt;“Girls’ Gossip.” ''Truth'' 8 July 1897, Thursday: 41 [of 70], Col. 1b – 42, Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0002961/18970708/089/0041.&lt;/ref&gt;{{rp|42, Col. 2c}}&lt;/blockquote&gt;
*&quot;Charles Alias was French and very small. He had started as a traveller in artificial flowers and married a little dressmaker in Long Acre. They started making theatrical costumes and later moved to 36 Soho Square.&quot;&lt;ref&gt;{{Cite book|url=https://books.google.com/books?id=ZJ8fAQAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgMEAI|title=As You Were: Reminiscences|last=Byng|first=Douglas|date=1970|publisher=Duckworth|isbn=978-0-7156-0543-1|language=en}} https://books.google.com/books?id=ZJ8fAQAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgMEAI.&lt;/ref&gt;
* In its Appendix of Royal Warrant Holders, the 1902 ''Debrett's'' also says &quot;Charles Alias, Costumier, 36, Soho Square. W.&quot;&lt;ref&gt;{{Cite book|url=https://books.google.com/books?id=cLc7AQAAMAAJ&amp;pg=RA2-PP7&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgGEAI#v=onepage&amp;q=Alias%20Soho%20dressmaker%20costumier&amp;f=false|title=Debrett's Peerage, Baronetage, Knightage, and Companionage: Comprising Information Concerning All Persons Bearing Hereditary Or Courtesy Titles, Knights, and Companions of All the Various Orders, and the Collateral Branches of All Peers and Baronets|date=1902|publisher=Dean &amp; Son, Limited|language=en}} https://books.google.com/books?id=cLc7AQAAMAAJ&amp;pg=RA2-PP7&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgGEAI#v=onepage&amp;q=Alias%20Soho%20dressmaker%20costumier&amp;f=false.&lt;/ref&gt; (n.p.; end of book)
* The ''Encyclopedia of the Musical Theatre'', Vol. 1, says, &quot;Alias &amp; Co prospered in the 1880s, having a major success with their new costumes for the transferred version of the amazing ''Dorothy'' [a comic opera by Alfred Cellier, libretto by B. C. Stephenson, &quot;transferred&quot; from the Gaiety to the Prince of Wales's Theatre in 1886 and then to the Lyric Theatre in 1888, the most successful of the productions&lt;ref&gt;{{Cite journal|date=2023-03-25|title=Dorothy (opera)|url=https://en.wikipedia.org/w/index.php?title=Dorothy_(opera)&amp;oldid=1146605626|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Dorothy_(opera).&lt;/ref&gt;], and on into the 1890s by which ...&quot;; &quot;The Aliases made their mark in the West End when they provided the costumes for the original London production of La Fille de ...&quot;&lt;ref&gt;{{Cite book|url=https://books.google.com/books?id=2myfAAAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgEEAI|title=The Encyclopedia of the Musical Theatre|last=G?nzl|first=Kurt|date=1994|publisher=Schirmer Books|isbn=978-0-02-871445-5|language=en}} https://books.google.com/books?id=2myfAAAAMAAJ&amp;q=Alias+Soho+dressmaker+costumier&amp;dq=Alias+Soho+dressmaker+costumier&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;ved=2ahUKEwjpr_zTzc3-AhXwlIkEHZ8wDHYQ6AF6BAgEEAI.&lt;/ref&gt; (taking from snippets)
* BNA search: Alias, Costumier, 36, Soho Square, London: 1898 shows a lot of advertisements.
* In 1892 Mr. C. Alias, 36, Soho Square, W., was a director of the 13th Annual Dramatic Ball, at the Freemasons' Tavern.&lt;ref&gt;{{Cite web|url=https://www.britishnewspaperarchive.co.uk/account/register?countrykey=0&amp;showgiftvoucherclaimingoptions=false&amp;gift=false&amp;nextpage=%2faccount%2flogin%3freturnurl%3d%252fviewer%252fbl%252f0001682%252f18920213%252f011%252f0004&amp;rememberme=false&amp;cookietracking=false&amp;partnershipkey=0&amp;newsletter=false&amp;offers=false&amp;registerreason=none&amp;showsubscriptionoptions=false&amp;showcouponmessaging=false&amp;showfreetrialmessaging=false&amp;showregisteroptions=false&amp;showloginoptions=false&amp;showcaptchaerrormessage=false&amp;isonlyupgradeable=false|title=Register {{!}} British Newspaper Archive|website=www.britishnewspaperarchive.co.uk|access-date=2023-04-28}} https://www.britishnewspaperarchive.co.uk/viewer/bl/0001682/18920213/011/0004.&lt;/ref&gt;
* In a gushing piece written for the 15 December 1899 ''Music Hall and Theatre Review'', &quot;The Bohemian Girl&quot; says that Alias executed Comelli designs for a Christmas pantomime ''Triumph of Music''. She goes on to talk about Willie Clarkson's work for another pantomime and a visit by Mrs. Langtry.&lt;ref&gt;&quot;Bohemian Girl, The.&quot; &quot;Preparing for the Pantomime.&quot; ''Music Hall and Theatre Review'' 15 December 1899, Friday: 24 [of 60], Cols. 1b–c and 2b–c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002237/18991215/160/0024.&lt;/ref&gt;
Russell Harris quotes ''The Encyclopedia of the Musical Theatre'' (Blackwell, 1994. Vol. 1, p. 19.):&lt;blockquote&gt;ALIAS, Charles (b France, 184-?; d London, 11 May 1921). The most famous name in British theatrical costumery in the second half of the 19th century.

The son of a French doctor, the young Alias fought alongside his father in the Franco-Prussian war where he is said to have lost the sight in one eye. He visited Britain and the Philharmonic Theatre, Islington, shortly afterwards as a dresser with the French dance troupe, Les Clodoches, and there he met and married Miss Price, the theatre's costumer. Although Alias had no experience in the theatre, he joined his wife in setting up the freelance firm of M et Mme Alias &amp; Co, '''someties''' designing and manufacturing, or more often just making up from the designs of such artists as [Comelli or] Wilhelm or [[Social Victorians/People/Faustin Betbeder|Faustin]], the costumes for an ever-extending series of musical shows.

The Aliases made their mark in the West End when theyprovided the costumes for the original London production of ''La Fille de Madame Angot'' (1873), and thereafter they costumes, either wholly or partly, many of London's most important musical productions including the burlesques at the Gaiety Theatre (''The Bohemian G'yurl, Little Dr Faust, Gulliver, Il Sonnambulo, Pretty Esmeralda'' etc), the Royalty (''Madcap, '''Pluto''''' '''etc'''), and the Strand (''The '''Lying''' Dutchman, L'Africaine, Nemesis, Loo, Antarctic, Champagne, The Baby, Intimidad''), Gilbert's early ''Tospyturveydom'' and ''Princess Toto'', Gilbert and Sullivan premières at the '''OPera''' Comique (''The Pirates of Penzance'') and the Savoy (''Iolanthe''), the vast spectaculars at the Alhambra (''La Poule aux oeufs d'or'' etc) and, most noticeably, the long string of French opéras-bouffes and opéras-comiques which were produced in Britain in the 1870s and 1880s. These included the record-breaking ''Trouillat (La Belle Normande), Le Jour et la nuit (Manola), La Timbale d'argent (The Duke's Daughter), La Marjolaine, Les Prés St Gervais'' and most of the long string of adaptations from the French made by Alias's close friend Henry Farnie, and produced by Alexander Henderson.

Alias maintained a close connection with his homeland. His home at 48 Soho Square became well known as a first stopping place for Frenchmen new to London and a congenial gathering place for theatricals, and he as a useful and friendly intermediary in various theatrical dealings between London and Paris. Hervé, Planquette, Chassaigne, Audran and Lecocq were all guests at Soho Square and the little costumier was said to have been instrumental in the brothers Mansell bringing Hervé and his ''Chilpéric'' (1870) to London, and thus helping set off the craze for opéra-bouffe which dominated the 1870s musical theatre in England. He also encouraged Planquette to work with H B Farnie on an original musical for Britain - the result of which was the enduring ''Rip van Winkle''.

Alias &amp; Co prospered in the 1880s, having a major succss with their new costumes for the transferred version of the amazing ''Dorothy'', and on into the 1890s by which stage they had become largely costume-makers rather than designers. Alias himself had by this time become one of the 'characters' of the London theatre, always anxiously asking 'What time de répétition générale?' as an opening approached, but always punctually ready with the show's costumes on dress-rehearsal night.

When Mme Alias died, Charles remarried and continued the business with his new wife, Mme Marie Wallet Floret from the Paris Opéra wardrobe, up to his death.&lt;ref&gt;Harris, Russell. {{Cite web|url=http://lafayette.org.uk/edw1335.html|title=King Edward VII at the Devonshire House Ball 1897, by Lafayette|website=lafayette.org.uk|access-date=2024-07-23}} Lafayette Negative Archive http://lafayette.org.uk/edw1335.html.  Quoting ''The Encyclopedia of the Musical Theatre'' (Vol. 1, Blackwell, 1994, p. 19).&lt;/ref&gt;&lt;/blockquote&gt;'''Costumes for the Fancy-dress Ball'''

Mr. Alias made costumes for the following guests at the Duchess of Devonshire’s 1897 fancy-dress ball:

# [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]]
# The [[Social Victorians/People/Connaught|Duke of Connaught]]
# The [[Social Victorians/People/George and Mary|Duke of York]]
# Duke of Fife&lt;ref name=&quot;:6&quot;&gt;Harris, Russell. &quot;Costumes by Named Dressmakers.&quot; {{Cite web|url=http://www.rvondeh.dircon.co.uk/incalmprose/|title=The Devonshire House Ball 1897 photographed by Lafayette|website=www.rvondeh.dircon.co.uk|access-date=2024-05-21}} 2011. http://www.rvondeh.dircon.co.uk/incalmprose/.&lt;/ref&gt;
# The Duke of Devonshire&lt;ref name=&quot;:6&quot; /&gt;
# [[Social Victorians/People/Stonor#Julia Caroline Stonor, Marquise of Hautpoul|Julia Stonor, Marquise of Hartpoul]]
# [[Social Victorians/People/Bourke|Hon. Mrs. Gwendolen Bourke]]
# [[Social Victorians/People/Mar and Kellie#Violet, Countess of Mar and Kellie|Violet, Countess of Mar and Kellie]]
# [[Social Victorians/People/Tweedmouth#Fanny, Baroness Tweedmouth|Fanny, Baroness Tweedmouth]]
# [[Social Victorians/People/Victoria of Schleswig-Holstein#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Princess Victoria of Schleswig-Holstein]]
# [[Social Victorians/People/Connaught#Princess Louise, Duchess of Connaught|Princess Louise, Duchess of Connaught]]
# [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton|Mary, Dowager Duchess of Hamilton]]
# [[Social Victorians/People/Portland|The Duchess of Portland]]
# [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]]
# Adolf von André&lt;ref name=&quot;:6&quot; /&gt;
# Lady St. Oswald&lt;ref name=&quot;:6&quot; /&gt;
# Earl of Rosebery&lt;ref name=&quot;:6&quot; /&gt;

=== Faustin Bedbeter ===
[[Social Victorians/People/Faustin Betbeder|Faustin Bedbeter]] was a caricaturist and painter who left France after Bismarck's seige of Paris and settled in London, working for the ''London Figaro'' and ''Punch''. He was a costumier beginning at least in 1875. He designed the costumes for a 1909 revival of [[Social Victorians/People/Gilbert|Gilbert]] and [[Social Victorians/People/Arthur Sullivan|Sullivan]]'s ''The Pirates of Penzance''.

=== Willie Clarkson ===
Mr. W. Clarkson, of Wellington-street

Clarkson is also listed among the [[Social Victorians/People/Dressmakers and Costumiers#Perruquiers|perruquiers]]. Clarkson made the costumes for the following guests at the ball:

* Grand Duke Michael of Russia&lt;ref name=&quot;:0&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4A–8 Col. 2B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;{{rp|p. 8, Col. 2a}}
* The Duke of Manchester&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
* [[Social Victorians/People/Gleichen#Laura, Princess Victor of Hohenlohe Langenburg|Laura, Princess Victor of Hohenlohe]]&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
* Princess Louise&lt;ref name=&quot;:1&quot; /&gt;

=== M. Comelli ===
Attilio Giuseppe de Comelli von Stuckenfeld (1858-1925).

Comelli &quot;was appointed house designer to the Royal Opera House in the 1890s&quot;&lt;ref name=&quot;:2&quot;&gt;&quot;Attilio Comelli Design Collection.&quot; ''Royal Opera House''  https://www.rohcollections.org.uk/collectionComelli.aspx (retrieved February 2024).&lt;/ref&gt; continuing &quot;to the early 1920s.&quot;&lt;ref&gt;{{Citation|title=Drury Lane Design Collection|url=https://collections.vam.ac.uk/item/O1172507/drury-lane-design-collection-costume-design-comelli-attilio/|date=1915|accessdate=2024-02-13|first=Attilio|last=Comelli}}. https://collections.vam.ac.uk/item/O1172507/drury-lane-design-collection-costume-design-comelli-attilio/.&lt;/ref&gt; At the same time, &quot;He was credited as Artist in Chief at the Alhambra, Theatre Royal, Drury Lane and the Royal Opera House in London, and also found time to provide costumes for some of the Savoy operas and for Christmas pantomimes in London and Australia.&quot;&lt;ref name=&quot;:2&quot; /&gt; After coming &quot;to London in the late 19th century [he] quickly established himself as one of the most prolific designers for the London stage.&quot;&lt;ref name=&quot;:2&quot; /&gt;

He described his research process for costume design for the July 1902 ''Cassell's Magazine'':&lt;blockquote&gt;When I get the order to prepare designs for a new play … [sic ellipsis] I first spend some weeks in studying, at the British and South Kensington [now the Victoria &amp; Albert] Museum, every available authority on the period, and I frequently send my brother to Paris and Berlin, if there is a chance of getting information there that is not available in London’. (‘The Art of Theatrical Disguise’ by Sidney Dark, ''Cassell’s Magazine'', July 1902, pp.162–7).&lt;ref name=&quot;:2&quot; /&gt;&lt;/blockquote&gt;According to the Royal Opera House, he &quot;appears to have had several siblings, including possibly Emilio Andrea Comelli (1862–1929).&quot;&lt;ref name=&quot;:2&quot; /&gt;  Also, perhaps another relative, Italian painter Dante Comelli (1880–1958) designed for the Royal Opera House in Covent Garden later.

Comelli's designs for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:
* Comelli designed the costumes that were constructed by [[Social Victorians/People/Dressmakers and Costumiers#Mr. Charles Alias|Mr. Alias of Soho Square]].&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}

* Comelli designed the costumes of the attendants of [[Social Victorians/People/Louisa Montagu Cavendish|Louise, Duchess of Devonshire]] as well as her own costume. Alias did not construct her costume, [[Social Victorians/People/Dressmakers and Costumiers#The House of Worth|the House of Worth]] did.
* Comelli may have designed the costumes of the entourage of [[Social Victorians/People/Pless#Daisy, Princess Henry of Pless|Daisy, Princess of Pless]], although Mrs. Mason made Daisy's dress.&lt;ref&gt;&quot;Dresses Worn at the Duchess of Devonshire's Ball on July 2. Made by Mrs. Mason, 4 New Burlington Street, W.&quot; The ''Queen'' 10 July 1897, Saturday: 48 [of 98 BNA; p. 74 print page), Col. 1a–3c [of 3]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/BL/0002627/18970710/168/0048?browse=true.&lt;/ref&gt; George Cornwallis-West says his costume was &quot;designed by a famous theatrical designer of the day.&quot;&lt;ref&gt;Qtd. in Martin Spies, &quot;&quot;Late Victorian Aristocrats and the Racial Other: The Devonshire House Ball of 1897.&quot; ''Race &amp; Class'' April–June 2016 (57.4): 95–103.&lt;/ref&gt;{{rp|97}}
[[File:Ellen Terry as Lady Macbeth.jpg|thumb|''Ellen Terry as Lady Macbeth'', Sargent 1889]]

=== Alice Comyns Carr and Ada Nettleship ===
According to Smallhythe Place, the &quot;beetle wing dress&quot; for Ellen Terry's 1888 performance as Lady Macbeth was designed by Alice Comyns Carr and constructed by Ada Nettleship, the &quot;team&quot; that made Ellen Terry's costumes for perhaps 2 decades.&lt;ref name=&quot;:14&quot;&gt;&quot;'Beetle Wing Dress' for Lady Macbeth.&quot; Smallhythe Place, Kent. The National Trusts Collections. Object NT 1118839.1 (1888) https://www.nationaltrustcollections.org.uk/object/1118839.1.&lt;/ref&gt; John Singer Sargent's 1889 portrait of Terry in this dress is at right. (Smallhythe Place, Kent, part of the National Trust, was Terry's home from 1899 to her death. This dress is part of that collection.)

Nettleship crocheted the sleeves and skirt of Terry's costume to resemble &quot;soft chain armour,&quot;&lt;ref name=&quot;:14&quot; /&gt; which she overlaid with wing cases from 1,000 beetles.&lt;ref name=&quot;:15&quot;&gt;{{Cite web|url=https://womenwhomeantbusiness.com/2021/01/21/ada-nettleship-1856-1932/|title=Ada Nettleship (1856-1932)|last=B|first=Lizzie|date=2021-01-21|website=Women Who Meant Business|language=en|access-date=2025-06-06}}&lt;/ref&gt;

Comyn Carr and Nettleship's beetle-wing costume was not the only or even the first dress decorated with the iridescent wings. Ada Nettleship had used beetle wings in &quot;an 1886 dress and an 1887 hat for Constance Lloyd that were oversewn with iridescent green beetle wings&quot;&lt;ref name=&quot;:16&quot;&gt;{{Cite journal|date=2025-04-21|title=Ada Nettleship|url=https://en.wikipedia.org/w/index.php?title=Ada_Nettleship&amp;oldid=1286707541|journal=Wikipedia|language=en}}&lt;/ref&gt; — and [[Social Victorians/People/Dressmakers and Costumiers#Mrs Sims' Court Dress Establishment, Dublin|Mrs Sims]] had used some for a dress in c. 1880.&lt;ref name=&quot;:13&quot; /&gt;

==== Personal Details ====
Alice Laura Vansittart Comyns Carr designed costumes, and dressmaker Adaline Cort Nettleship constructed Comyns Carr's designs. They were a &quot;costume team&quot; separate from those who did the costumes for &quot;the rest of the Lyceum company.&quot;&lt;ref name=&quot;:14&quot; /&gt; They appear to have maintained individual establishments, with Nettelship often constructing costumes for Terry that were designed by Comyns Carr.

Alice Comyns Carr (1850–1927) was married to J. Comyns Carr, &quot;drama and art critic, author, playwright and director of the Grosvenor Gallery.&quot;&lt;ref&gt;{{Cite journal|date=2025-04-21|title=Alice Comyns Carr|url=https://en.wikipedia.org/w/index.php?title=Alice_Comyns_Carr&amp;oldid=1286707345|journal=Wikipedia|language=en}}&lt;/ref&gt; She was associated with the [[Social Victorians/Terminology#Progressive Style|aesthetic dress movement]] and was friends with Edward Burne-Jones and John Singer Sargent as well as Lawrence Alma-Tadema, &quot;the writers Robert Browning and Henry James and composers Hubert Parry and [[Social Victorians/People/Arthur Sullivan|Arthur Sullivan]].&quot;&lt;ref name=&quot;:15&quot; /&gt;

Ada (Adaline) Cort Nettleship (1856 – 19 December 1932&lt;ref name=&quot;:16&quot; /&gt;) was married to painter John Trivett Nettleship. Some of her &quot;[n]otable clients included the soprano Marie Tempest, and the actors Ellen Terry, Winifred Emery, Sarah Bernhardt, and Mrs Patrick Campbell.&quot;&lt;ref name=&quot;:16&quot; /&gt; Like Comyns Carr, Nettleship was an advocate of [[Social Victorians/Terminology#Progressive Style|aesthetic dress design]], making dresses for Constance Lloyd in that progressive style, including her dress for her wedding to [[Social Victorians/People/Oscar Wilde|Oscar Wilde]]. Nettleship &quot;in her youth had been a noted ‘art-embroiderer’ in the style of May Morris.&quot;&lt;ref name=&quot;:15&quot; /&gt;

Alice Comyns Carr published her ''Reminiscences'' in 1926, the year before her death. Ada Nettleship was covered by the newspapers from time to time (&quot;''St James Gazette'' 30/5/1883; ''Dundee Evening Telegraph'' 7/7/1884; ''Morning Post'' 16/10/1886; ''The Queen'' 13/8/1887; ‘Ellen Terry’s gowns and the woman who makes them’ by Bessie O’Connor in ''Harpers Bazaar'' 9th Jan 1897; ‘What Actresses Pay For Their Dresses’ in ''New Zealand Herald'' 25/08/1900; ''South Wales Daily News'' 25/1/1902; ''Leeds Mercury'' 13/2/1914.&quot;&lt;ref name=&quot;:15&quot; /&gt;)

=== Miss Mary E. Fisher ===
Mme. or Miss Mary E. Fisher, 26, Bedford-street, Covent-garden&lt;ref name=&quot;:9&quot;&gt;{{Cite book|url=https://books.google.co.in/books?id=cVQZAAAAYAAJ&amp;pg=RA3-PR2&amp;dq=Mr.+May,+Garrick-street,+Covent-garden&amp;hl=en&amp;newbks=1&amp;newbks_redir=0&amp;sa=X&amp;redir_esc=y|title=The Play-pictorial|date=1908|publisher=Greening &amp; Company, Limited|language=en}} P. ADVT ii. ''Google Books'' https://books.google.com/books?id=cVQZAAAAYAAJ.&lt;/ref&gt; &lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
*Miss Mary E. Fisher is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}

=== Charles H. Fox ===
Fox: &quot;perruquier and costumier Charles H. Fox. Since 1878, Fox had been a major supplier of wigs and costumes for private theatricals and fancy dress balls.&quot;&lt;ref name=&quot;:3&quot;&gt;&quot;B. J. Simmons &amp; Co.: An Inventory of Its Costume Design Records at the Harry Ransom Center.&quot; ''B. J. Simmons &amp; Co. Costume Design Records''. Harry Ransom Center. The University of Texas. 2023. Retrieved February 2024. https://norman.hrc.utexas.edu/fasearch/findingAid.cfm?eadID=01440.&lt;/ref&gt;

=== Harrison ===
Harrison's, Ltd., 31, Bow-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}
* In a chatty column written as a letter to &quot;Dearest Amy,&quot; the article in ''Truth'' on the ball says, &quot;Princess Henry of Pless was another [Queen of Sheba], and her dress was absolutely magnificent. The conception of it was both poetic and artistic, and is due, I believe, to the genius of Mrs. Harrison.&quot;&lt;ref name=&quot;:12&quot; /&gt;{{rp|42, Col. 1b}}
* There are ads for Harrison's.

=== May ===
Mr. May, Garrick-street, Covent-garden&lt;ref name=&quot;:9&quot; /&gt;

* Mr. May is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}

=== Nathan ===
Messrs. L. and H. Nathan, Coventry-street, Haymarket; 17, Convent-street, Picadilly

*Messrs. L. and H. Nathan is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}
*Mr. Karl, artist, designed the costumes made by Messrs. L. and H. Nathan of Coventry-street&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} &lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}
*Messrs Nathan made the costumes for the following people:
**[[Social Victorians/People/Harcourt#Elizabeth Harcourt|Elizabeth, Lady Harcourt]]
**[[Social Victorians/People/Rothschild Family#Emma, Lady Rothschildand Nathan Mayer, Lord Rothschild|Emma, Lady Rothschild]]

=== Simmons and Sons ===
Messrs. John Simmons and Sons, Coventry House, Haymarket.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} Simmons, 7 and 8, King Street, Covent Garden.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}} Possibly there are 2 Simmonses?

The Harry Ransom Center has a collection on this firm:&lt;blockquote&gt;The London costumier B. J. Simmons &amp; Co. was founded in 1857 by a Mr. B. J. Simmons and operated by his direct descendants well into the 1930s. Simmons' costumes were known for their correctness of period, sophisticated design, and high quality. ... In their busy Covent Garden workshop, dressmakers turned out immaculately constructed stage apparel, often from renderings by leading costume designers. Successful theater managers repeatedly turned to Simmons for historical costumes, especially Herbert Beerbohm Tree whose magnificent stagings of Shakespeare were often outfitted by Simmons.

While best known as a historical costumier for the London stage, Simmons' output was diverse. The company created costumes for a variety of shows in the West End, the provinces, and overseas, ranging from Victorian pantomime to the &quot;kitchen sink&quot; dramas of the 1960s. ... In addition to making new costumes for professional productions, Simmons operated a thriving rental business which allowed operatic and dramatic societies across England to hire beautifully made garments for amateur productions. Like many theatrical costumiers, Simmons maintained a substantial nontheatrical trade.

Simmons began as a family-run outfit known variously as B. J. Simmons, J. B. Simmons, John Simmons &amp; Son/Sons, Simmons/Symmons/Simmonds Brothers, G. B. Simmons, and B. &amp; G. Simmons. The force majeure seems to have been John Simmons, whose name appears in ''The London Stage'' and in London newspapers until 1922. According to J. P. Wearing, between 1890 and 1899 Simmons provided costumes for at least forty-two theatre productions in London.&lt;ref name=&quot;:3&quot; /&gt;&lt;/blockquote&gt;Simmons' contributions to costumes for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:
* Messrs. John Simmons and Son is cited as one of the sources of its information about the costumes by the London ''Evening Standard''.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}
* Simmons and Sons made costumes for the following guests at the ball:
** [[Social Victorians/People/Ellesmere#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Francis Egerton, 3rd Earl of Ellesmere]]&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** The Duke of Somerset&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** The Marquis of Winchester&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Earl Beauchamp&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Earl Carrington&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Earl Essex&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}
** Viscount Esher&lt;ref name=&quot;:6&quot; /&gt;
** Lord Ampthill&lt;ref name=&quot;:6&quot; /&gt;
** Lady Ampthill&lt;ref name=&quot;:6&quot; /&gt;
Simmons and Sons is also sometimes listed as having made clothing for other social events:

* For the [[Social Victorians/1892-02-10 Alington Leigh Wedding|very fashionable February 1892 wedding between Henry Sturt, Lord Alington and Evelyn Leigh]] — the &quot;most important social event of last week in the social world&quot;&lt;ref name=&quot;:03&quot;&gt;&quot;Lord Alington to Miss Leigh.&quot; ''Gentlewoman'' 20 February 1892, Saturday: 21 [of 46], Cols. 1a–3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18920220/092/0021. Same print title, p. 237.&lt;/ref&gt;{{rp|Col. 1a}} — &quot;Messrs. Simmons &amp; Sons, of Coventry House, Haymarket, made the charming little suits for the pages, which were so much admired.&quot;&lt;ref name=&quot;:03&quot; /&gt;{{rp|Col. 3a}}

=== Smaller Concerns ===
* Mme. Auguste, of Wellington-street&lt;ref name=&quot;:42&quot;&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 42, Col. 3b}}
* Mr. W. Clarkson, 44, Wellington Street (costumes and wigs)&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}

=== Unknown Whether Costumier or Dressmaker ===
*Mme. Ellis: &quot;The pretty costumes of Merlin and Vivian worn by [[Social Victorians/People/Walker|Mr and Mrs Willie Walker]] at the Devonshire House Ball, were made by Mme. Ellis, 16, Upper George-street, Bryanston-square.&quot;&lt;ref&gt;Holt, Ardern. &quot;Dress and Fashion. To Correspondents.&quot; The ''Queen'' 24 July 1897, Saturday: 54 [of 88], Col. 1a [of 3]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18970724/271/0054.&lt;/ref&gt;
* Madame Frederic, of Lower Grosvenor Place
* &quot;and many others&quot;&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}

== Perruquiers ==
Mr. W. Clarkson &quot;supplied the wigs and headdresses for the Royal Family&quot;&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}} for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]]:&lt;blockquote&gt;At the Duchess of Devonshire's ball, on the 2d inst., the Prince of Wales looked as if he had stepped out of a masterpiece by one of the old painters. His wig, which completed a correct make-up as Knight of Malta, was specially made and fitted by that favoured &quot;Royal Perruquier&quot; Mr Willie Clarkson, who also had the honour of making and fitting the wigs worn by Prince Charles of Denmark, the Duke of York, and the Duke and Duchess of Connaught, and of dressing the hair of the Duchess of York and the Princess Victoria of Schleswig-Holstein. Mr Clarkson also supplied a number of the costumes, including those worn by the Grand Duke Michael of Russia, Princess Louise, and the Duke of Manchester. It would not be safe to say how many crowned heads have literally &quot;passed through the hands&quot; of Mr Clarkson. The art of the perruquier is a very difficult one, requiring historical knowledge, patient research, and great taste. It is most essential to the success of any theatrical performance or of an historical ball.&lt;ref name=&quot;:1&quot;&gt;“Foreign Plays and Players.” ''The Era'' 10 July 1897, Saturday: 15 [of 28], Col. 3c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000053/18970710/032/0015.&lt;/ref&gt;&lt;/blockquote&gt;Clarkson also provided costumes and wigs for the [[Social Victorians/Royals Amateur Theatricals|amateur theatricals]] that the royals took part in to entertain themselves.

== Jewelers ==
After naming costumiers for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]], the ''Gentlewoman'' specifically mentions the Parisian Company for its jewelry and Mr. Norman of Bond Street for the shoes he made:&lt;blockquote&gt;Among other firms [than the costumiers] who lent their aid to make the great ball a huge success was the Parisian Company, whose sparkling gems and jewels, and whose ropes of pearls and precious stones, enhanced the charms of many a fair dame in her dainty old-world costume, and the firm of Mr. Norman, 69, New Bond-street, who designed and made the shoes for the Princess of Wales, the Duchess of Buccleuch, &amp;c., &amp;c.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3c}}&lt;/blockquote&gt;According to the ''Westminster Gazette'', &quot;One very great lady indeed had been lent, by a jeweller, diamonds worth about £13,000.&quot;&lt;ref name=&quot;:4&quot;&gt;“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.&lt;/ref&gt;{{rp|p. 5, Col. 2c}}

== People Who Made Costumes for the Ball ==
The ''Queen'' often mentions the dressmaker or costumier in its reports on the costumes at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball at Devonshire House]] as well as in general.

The ''Gentlewoman'' covered this topic explicitly in its report on the ball:&lt;blockquote&gt;Very great credit is due to the taste and artistic powers of the designers of these dresses, and particular mention must be made of M. Comelli, of Covent Garden Theatre, whose facile pen designed most of the superb toilettes so ably carried out by Messrs. Alias, of Soho-square. Other theatrical costumiers who brought all their special talents to bear on the historical and fancy costumes required for this function were Messrs. Nathan (artist, Mr. Karl), of Coventry-street; Messrs. John Simmons &amp; Sons, Haymarket; Mme. Auguste, of Wellington-street; Harrison's, Ltd., 31, Bow-street; Simmons, 7 and 8, King-street; Mr. Clarkson, 44, Wellington-street; Mme. Fisher, 26, Bedford-street; and many others. A great number of well-known modistes in London were also called upon to supply dresses. Amongst these we chronicle M. Mason, New Burlington-street; M. Machinka, Conduit-street; Paquin, of Dover-street; Jays, Ltd., Regent-street; Messrs. Durrant, 116, Bond-street (who made Lady Londonderry's magnificent gown), and numerous others.&lt;ref name=&quot;:42&quot; /&gt;{{rp|p. 42, Col. 3b}}&lt;/blockquote&gt;The London ''Evening Standard'' cites the sources of its information about the costumes:&lt;blockquote&gt;We are indebted for some of the particulars of the dresses to Mr. Charles Alias, Soho-square; Messrs. L. and H. Nathan, Coventry-street, Haymarket; Messrs. John Simmons and Son, Coventry House, Haymarket; Mr. May, Garrick-street, Covent-garden; Miss Mary E. Fisher, 26 Bedford-street, Covent-garden; and the ''Lady'' newspaper.&lt;ref name=&quot;:8&quot; /&gt;{{rp|p. 3, Col. 5b}}&lt;/blockquote&gt;The ''Morning Post'' also addressed the costumiers. It named Mr. Alias in association with the royals, as well as mentioning several other costumiers by name:&lt;blockquote&gt;The costumes worn by the Prince of Wales, the Duke of York, and the Duchess of Connaught, as well as many others were supplied by Mr. Alias, of Soho-square. Those worn by the Grand Duke Michael of Russia, the Duke of Manchester, Princess Victor of Hohenlohe, and others were made by Mr. W. Clarkson, of Wellington-street, who also supplied the wigs and headdresses for the Royal Family. Messrs. Simmons and Sons, of the Haymarket, made a large number of costumes, including those of the Duke of Somerset, the Marquis of Winchester, Earls Beauchamp, Carrington, Ellesmere, and Essex. Nathan, of Coventry-street, and Simmons, of King-street, Covent-garden; Madame Frederic, of Lower Grosvenor-place, and Mrs. Mason, of New Burlington-street, also made some of the principal costumes.&lt;ref name=&quot;:0&quot; /&gt;{{rp|p. 8, Col. 2a}}&lt;/blockquote&gt;On 3 July 1897, the day after the ball, the ''Belfast News-letter'' says,&lt;blockquote&gt;For weeks past all the leading London dressmakers and costumiers had been hard at work executing the orders for this great ball. At Alias Nathan's, Clarkson's, Auguste's, and Simmons' all hands set to with a will, and it is gratifying to know that the dresses entrusted to them more than held their own with those sent over from Paris.&lt;ref name=&quot;:10&quot;&gt;&quot;The Duchess of Devonshire's Fancy Dress Ball. Special Telegram.&quot; ''Belfast News-Letter'' Saturday 03 July 1897: 5 [of 8], Col. 9c [of 9]–6, Col. 1a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0000038/18970703/015/0005.&lt;/ref&gt;{{rp|p. 5, Col. 9a}}&lt;/blockquote&gt;

According to the ''Derbyshire Times and Chesterfield Herald'', citing the ''Daily Mail'',
&lt;blockquote&gt;
&lt;p&gt;Lady de Grey is going as Zenobia, and is getting her dress from Doucet, I hear, while Worth also is making a great many costumes; but the greatest number are being made in England. The Duchess of Portland, the Duchess of Hamilton, Lady Mar and Kellie, and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]] are all going to the costumier in Soho-square, and Alias has also been summoned to Marlborough House for a consultation.&lt;/p&gt;
&lt;p&gt;Mr. Caryl Craven, who is so clever in such matters, is helping the Duchess of Leeds with her dress; in fact, everyone seems pressed into the service, and the result will be one of the most brilliant sights that ever was seen.&lt;ref name=&quot;:11&quot; 
== Notes and Questions ==

# Which costumier was this? &quot;A well-known West End dressmaker booked for the Duchess of Devonshire's fancy dress ball orders representing £27000.&quot;&lt;ref&gt;&quot;London Letter.&quot; ''Western Daily Press'' 15 July 1897, Thursday: 8 [of 8], Col. 7c. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000264/18970715/146/0008.&lt;/ref&gt;&lt;/p&gt;&lt;/blockquote&gt;

== References ==
{{reflist}}</text>
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  <page>
    <title>24-cell</title>
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      <text bytes="248351" sha1="g196cowdrq3a6xe2yvhiuuag4q1zvvj" xml:space="preserve">{{Short description|Regular object in four dimensional geometry}}
{{Polyscheme|radius=an '''expanded version''' of|active=is the focus of active research}}
{{Infobox 4-polytope
 | Name=24-cell
 | Image_File=Schlegel wireframe 24-cell.png
 | Image_Caption=[[W:Schlegel diagram|Schlegel diagram]]&lt;br&gt;(vertices and edges)
 | Type=[[W:Convex regular 4-polytope|Convex regular 4-polytope]]
 | Last=[[W:Omnitruncated tesseract|21]]
 | Index=22
 | Next=[[W:Rectified 24-cell|23]]
 | Schläfli={3,4,3}&lt;br&gt;r{3,3,4} = &lt;math&gt;\left\{\begin{array}{l}3\\3,4\end{array}\right\}&lt;/math&gt;&lt;br&gt;{3&lt;sup&gt;1,1,1&lt;/sup&gt;} = &lt;math&gt;\left\{\begin{array}{l}3\\3\\3\end{array}\right\}&lt;/math&gt;
 | CD={{Coxeter–Dynkin diagram|node_1|3|node|4|node|3|node}}&lt;br&gt;{{Coxeter–Dynkin diagram|node|3|node_1|3|node|4|node}} or {{Coxeter–Dynkin diagram|node_1|split1|nodes|4a|nodea}}&lt;br&gt;{{Coxeter–Dynkin diagram|node|3|node_1|split1|nodes}} or {{Coxeter–Dynkin diagram|node_1|splitsplit1|branch3|node}}
 | Cell_List=24 [[W:Octahedron|{3,4}]] [[File:Octahedron.png|20px]]
 | Face_List=96 [[W:Triangle|{3}]]
 | Edge_Count=96
 | Vertex_Count= 24
 | Petrie_Polygon=[[W:Dodecagon|{12}]]
 | Coxeter_Group=[[W:F4 (mathematics)|F&lt;sub&gt;4&lt;/sub&gt;]], [3,4,3], order 1152&lt;br&gt;B&lt;sub&gt;4&lt;/sub&gt;, [4,3,3], order 384&lt;br&gt;D&lt;sub&gt;4&lt;/sub&gt;, [3&lt;sup&gt;1,1,1&lt;/sup&gt;], order 192
 | Vertex_Figure=[[W:Cube|cube]]
 | Dual=[[W:Polytope#Self-dual polytopes|self-dual]]
 | Property_List=[[W:Convex polytope|convex]], [[W:Isogonal figure|isogonal]], [[W:Isotoxal figure|isotoxal]], [[W:Isohedral figure|isohedral]]
}}
[[File:24-cell net.png|thumb|right|[[W:Net (polyhedron)|Net]]]]
In [[W:four-dimensional space|four-dimensional geometry]], the '''24-cell''' is the convex [[W:Regular 4-polytope|regular 4-polytope]]{{Sfn|Coxeter|1973|p=118|loc=Chapter VII: Ordinary Polytopes in Higher Space}} (four-dimensional analogue of a [[W:Platonic solid|Platonic solid]]]) with [[W:Schläfli symbol|Schläfli symbol]] {3,4,3}. It is also called '''C&lt;sub&gt;24&lt;/sub&gt;''', or the '''icositetrachoron''',{{Sfn|Johnson|2018|p=249|loc=11.5}} '''octaplex''' (short for &quot;octahedral complex&quot;), '''icosatetrahedroid''',{{sfn|Ghyka|1977|p=68}} '''[[W:Octacube (sculpture)|octacube]]''', '''hyper-diamond''' or '''polyoctahedron''', being constructed of [[W:Octahedron|octahedral]] [[W:Cell (geometry)|cells]].

The boundary of the 24-cell is composed of 24 [[W:Octahedron|octahedral]] cells with six meeting at each vertex, and three at each edge. Together they have 96 triangular faces, 96 edges, and 24 vertices. The [[W:Vertex figure|vertex figure]] is a [[W:Cube|cube]]. The 24-cell is [[W:Self-dual polyhedron|self-dual]].{{Efn|The 24-cell is one of only three self-dual regular Euclidean polytopes which are neither a [[W:Polygon|polygon]] nor a [[W:Simplex|simplex]]. The other two are also 4-polytopes, but not convex: the [[W:Grand stellated 120-cell|grand stellated 120-cell]] and the [[W:Great 120-cell|great 120-cell]]. The 24-cell is nearly unique among self-dual regular convex polytopes in that it and the even polygons are the only such polytopes where a face is not opposite an edge.|name=|group=}} The 24-cell and the [[W:Tesseract|tesseract]] are the only convex regular 4-polytopes in which the edge length equals the radius.{{Efn||name=radially equilateral|group=}}

The 24-cell does not have a regular analogue in [[W:Three dimensions|three dimensions]] or any other number of dimensions, either below or above.{{Sfn|Coxeter|1973|p=289|loc=Epilogue|ps=; &quot;Another peculiarity of four-dimensional space is the occurrence of the 24-cell {3,4,3}, which stands quite alone, having no analogue above or below.&quot;}} It is the only one of the six convex regular 4-polytopes which is not the analogue of one of the five Platonic solids. However, it can be seen as the analogue of a pair of irregular solids: the [[W:Cuboctahedron|cuboctahedron]] and its dual the [[W:Rhombic dodecahedron|rhombic dodecahedron]].{{Sfn|Coxeter|1995|loc=(Paper 3) ''Two aspects of the regular 24-cell in four dimensions''|p=25}}

Translated copies of the 24-cell can [[W:Tesselate|tesselate]] four-dimensional space face-to-face, forming the [[W:24-cell honeycomb|24-cell honeycomb]]. As a polytope that can tile by translation, the 24-cell is an example of a [[W:Parallelohedron|parallelotope]], the simplest one that is not also a [[W:Zonotope|zonotope]].{{Sfn|Coxeter|1968|p=70|loc=§4.12 The Classification of Zonohedra}}

==Geometry==
The 24-cell incorporates the geometries of every convex regular polytope in the first four dimensions, except the 5-cell, those with a 5 in their Schlӓfli symbol,{{Efn|The convex regular polytopes in the first four dimensions with a 5 in their Schlӓfli symbol are the [[W:Pentagon|pentagon]] {5}, the [[W:Icosahedron|icosahedron]] {3, 5}, the [[W:Dodecahedron|dodecahedron]] {5, 3}, the [[600-cell]] {3,3,5} and the [[120-cell]] {5,3,3}. The [[5-cell]] {3, 3, 3} is also pentagonal in the sense that its [[W:Petrie polygon|Petrie polygon]] is the pentagon.|name=pentagonal polytopes|group=}} and the regular polygons with 7 or more sides. In other words, the 24-cell contains ''all'' of the regular polytopes made of triangles and squares that exist in four dimensions except the regular 5-cell, but ''none'' of the pentagonal polytopes. It is especially useful to explore the 24-cell, because one can see the geometric relationships among all of these regular polytopes in a single 24-cell or [[W:24-cell honeycomb|its honeycomb]].

The 24-cell is the fourth in the sequence of six [[W:Convex regular 4-polytope|convex regular 4-polytope]]s (in order of size and complexity).{{Efn|name=4-polytopes ordered by size and complexity}}{{Sfn|Goucher|2020|loc=Subsumptions of regular polytopes}} It can be deconstructed into 3 overlapping instances of its predecessor the [[W:Tesseract|tesseract]] (8-cell), as the 8-cell can be deconstructed into 2 instances of its predecessor the [[16-cell]].{{Sfn|Coxeter|1973|p=302|pp=|loc=Table VI (ii): 𝐈𝐈 = {3,4,3}|ps=: see Result column}} The reverse procedure to construct each of these from an instance of its predecessor preserves the radius of the predecessor, but generally produces a successor with a smaller edge length.{{Efn|name=edge length of successor}}

=== Coordinates ===
The 24-cell has two natural systems of Cartesian coordinates, which reveal distinct structure.

==== Great squares ====
The 24-cell is the [[W:Convex hull|convex hull]] of its vertices which can be described as the 24 coordinate [[W:Permutation|permutation]]s of:

&lt;math display=&quot;block&quot;&gt;(\pm1, \pm 1, 0, 0) \in \mathbb{R}^4 .&lt;/math&gt;

Those coordinates{{Sfn|Coxeter|1973|p=156|loc=§8.7. Cartesian Coordinates}} can be constructed as {{Coxeter–Dynkin diagram|node|3|node_1|3|node|4|node}}, [[W:Rectification (geometry)|rectifying]] the [[16-cell]] {{Coxeter–Dynkin diagram|node_1|3|node|3|node|4|node}} with the 8 vertices that are permutations of (±2,0,0,0). The vertex figure of a 16-cell is the [[W:Octahedron|octahedron]]; thus, cutting the vertices of the 16-cell at the midpoint of its incident edges produces 8 octahedral cells. This process{{Sfn|Coxeter|1973|p=|pp=145-146|loc=§8.1 The simple truncations of the general regular polytope}} also rectifies the tetrahedral cells of the 16-cell which become 16 octahedra, giving the 24-cell 24 octahedral cells.

In this frame of reference the 24-cell has edges of length {{sqrt|2}} and is inscribed in a [[W:3-sphere|3-sphere]] of radius {{sqrt|2}}. Remarkably, the edge length equals the circumradius, as in the [[W:Hexagon|hexagon]], or the [[W:Cuboctahedron|cuboctahedron]]. Such polytopes are ''radially equilateral''.{{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}}

{{Regular convex 4-polytopes|wiki=W:|radius={{radic|2}}}}

The 24 vertices form 18 great squares{{Efn|The edges of six of the squares are aligned with the grid lines of the ''{{radic|2}} radius coordinate system''. For example:
{{indent|5}}({{spaces|2}}0, −1,{{spaces|2}}1,{{spaces|2}}0){{spaces|3}}({{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}0, −1, −1,{{spaces|2}}0){{spaces|3}}({{spaces|2}}0,{{spaces|2}}1, −1,{{spaces|2}}0)&lt;br&gt;
is the square in the ''xy'' plane. The edges of the squares are not 24-cell edges, they are interior chords joining two vertices 90&lt;sup&gt;o&lt;/sup&gt; distant from each other; so the squares are merely invisible configurations of four of the 24-cell's vertices, not visible 24-cell features.|name=|group=}} (3 sets of 6 orthogonal{{Efn|Up to 6 planes can be mutually orthogonal in 4 dimensions. 3 dimensional space accommodates only 3 perpendicular axes and 3 perpendicular planes through a single point. In 4 dimensional space we may have 4 perpendicular axes and 6 perpendicular planes through a point (for the same reason that the tetrahedron has 6 edges, not 4): there are 6 ways to take 4 dimensions 2 at a time.{{Efn|name=Six orthogonal planes of the Cartesian basis}} Three such perpendicular planes (pairs of axes) meet at each vertex of the 24-cell (for the same reason that three edges meet at each vertex of the tetrahedron). Each of the 6 planes is [[W:Completely orthogonal|completely orthogonal]] to just one of the other planes: the only one with which it does not share a line (for the same reason that each edge of the tetrahedron is orthogonal to just one of the other edges: the only one with which it does not share a point). Two completely orthogonal planes are perpendicular and opposite each other, as two edges of the tetrahedron are perpendicular and opposite.|name=six orthogonal planes tetrahedral symmetry}} central squares), 3 of which intersect at each vertex. By viewing just one square at each vertex, the 24-cell can be seen as the vertices of 3 pairs of [[W:Completely orthogonal|completely orthogonal]] great squares which intersect{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} if they are [[W:Completely orthogonal|completely orthogonal]].|name=how planes intersect}} at no vertices.{{Efn|name=three square fibrations}}

==== Great hexagons ====
The 24-cell is [[W:Self-dual|self-dual]], having the same number of vertices (24) as cells and the same number of edges (96) as faces.

If the dual of the above 24-cell of edge length {{sqrt|2}} is taken by reciprocating it about its ''inscribed'' sphere, another 24-cell is found which has edge length and circumradius 1, and its coordinates reveal more structure. In this frame of reference the 24-cell lies vertex-up, and its vertices can be given as follows:

8 vertices obtained by permuting the ''integer'' coordinates:

&lt;math display=&quot;block&quot;&gt;\left( \pm 1, 0, 0, 0 \right)&lt;/math&gt;

and 16 vertices with ''half-integer'' coordinates of the form:

&lt;math display=&quot;block&quot;&gt;\left( \pm \tfrac{1}{2}, \pm \tfrac{1}{2}, \pm \tfrac{1}{2}, \pm \tfrac{1}{2} \right)&lt;/math&gt;

all 24 of which lie at distance 1 from the origin.

[[#Quaternionic interpretation|Viewed as quaternions]],{{Efn|name=quaternions}} these are the unit [[W:Hurwitz quaternions|Hurwitz quaternions]].

The 24-cell has unit radius and unit edge length{{Efn||name=radially equilateral}} in this coordinate system. We refer to the system as ''unit radius coordinates'' to distinguish it from others, such as the {{sqrt|2}} radius coordinates used [[#Great squares|above]].{{Efn|The edges of the orthogonal great squares are ''not'' aligned with the grid lines of the ''unit radius coordinate system''. Six of the squares do lie in the 6 orthogonal planes of this coordinate system, but their edges are the {{sqrt|2}} ''diagonals'' of unit edge length squares of the coordinate lattice. For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}0, −1,{{spaces|2}}0,{{spaces|2}}0){{spaces|3}}({{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0,{{spaces|2}}0)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0, −1,{{spaces|2}}0)&lt;br&gt;
is the square in the ''xy'' plane. Notice that the 8 ''integer'' coordinates comprise the vertices of the 6 orthogonal squares.|name=orthogonal squares|group=}}

{{Regular convex 4-polytopes|wiki=W:|radius=1}}

The 24 vertices and 96 edges form 16 non-orthogonal great hexagons,{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(−&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(−&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0, −1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} four of which intersect{{Efn||name=how planes intersect}} at each vertex.{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:Cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:Cubic pyramid|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} By viewing just one hexagon at each vertex, the 24-cell can be seen as the 24 vertices of 4 non-intersecting hexagonal great circles which are [[W:Clifford parallel|Clifford parallel]] to each other.{{Efn|name=four hexagonal fibrations}}

The 12 axes and 16 hexagons of the 24-cell constitute a [[W:Reye configuration|Reye configuration]], which in the language of [[W:Configuration (geometry)|configurations]] is written as 12&lt;sub&gt;4&lt;/sub&gt;16&lt;sub&gt;3&lt;/sub&gt; to indicate that each axis belongs to 4 hexagons, and each hexagon contains 3 axes.{{Sfn|Waegell|Aravind|2009|loc=§3.4 The 24-cell: points, lines and Reye's configuration|pp=4-5|ps=; In the 24-cell Reye's &quot;points&quot; and &quot;lines&quot; are axes and hexagons, respectively.}}

==== Great triangles ====
The 24 vertices form 32 equilateral great triangles, of edge length {{radic|3}} in the unit-radius 24-cell,{{Efn|These triangles' edges of length {{sqrt|3}} are the diagonals{{Efn|name=missing the nearest vertices}} of cubical cells of unit edge length found within the 24-cell, but those cubical (tesseract){{Efn|name=three 8-cells}} cells are not cells of the unit radius coordinate lattice.|name=cube diagonals}} inscribed in the 16 great hexagons.{{Efn|These triangles lie in the same planes containing the hexagons;{{Efn|name=non-orthogonal hexagons}} two triangles of edge length {{sqrt|3}} are inscribed in each hexagon.  For example, in unit radius coordinates:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(−&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(−&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0, −1,{{spaces|2}}0)&lt;br&gt;
are two opposing central triangles on the ''y'' axis, with each triangle formed by the vertices in alternating rows. Unlike the hexagons, the {{sqrt|3}} triangles are not made of actual 24-cell edges, so they are invisible features of the 24-cell, like the {{sqrt|2}} squares.|name=central triangles|group=}} Each great triangle is a ring linking three completely disjoint{{Efn|name=completely disjoint}} great squares.{{Efn|The 18 great squares of the 24-cell occur as three sets of 6 orthogonal great squares,{{Efn|name=Six orthogonal planes of the Cartesian basis}} each forming a [[16-cell]].{{Efn|name=three isoclinic 16-cells}} The three 16-cells are completely disjoint (and [[#Clifford parallel polytopes|Clifford parallel]]): each has its own 8 vertices (on 4 orthogonal axes) and its own 24 edges (of length {{radic|2}}). The 18 square great circles are crossed by 16 hexagonal great circles; each hexagon has one axis (2 vertices) in each 16-cell.{{Efn|name=non-orthogonal hexagons}} The two great triangles inscribed in each great hexagon (occupying its alternate vertices, and with edges that are its {{radic|3}} chords) have one vertex in each 16-cell. Thus ''each great triangle is a ring linking the three completely disjoint 16-cells''. There are four different ways (four different ''fibrations'' of the 24-cell) in which the 8 vertices of the 16-cells correspond by being triangles of vertices {{radic|3}} apart: there are 32 distinct linking triangles. Each ''pair'' of 16-cells forms a tesseract (8-cell).{{Efn|name=three 16-cells form three tesseracts}} Each great triangle has one {{radic|3}} edge in each tesseract, so it is also a ring linking the three tesseracts.|name=great linking triangles}}

==== Hypercubic chords ====
[[File:24-cell vertex geometry.png|thumb|Vertex geometry of the radially equilateral{{Efn||name=radially equilateral|group=}} 24-cell, showing the 3 great circle polygons and the 4 vertex-to-vertex chord lengths.|alt=]]
The 24 vertices of the 24-cell are distributed{{Sfn|Coxeter|1973|p=298|loc=Table V: The Distribution of Vertices of Four-Dimensional Polytopes in Parallel Solid Sections (§13.1); (i) Sections of {3,4,3} (edge 2) beginning with a vertex; see column ''a''|5=}} at four different [[W:Chord (geometry)|chord]] lengths from each other: {{sqrt|1}}, {{sqrt|2}},  {{sqrt|3}} and {{sqrt|4}}. The {{sqrt|1}} chords (the 24-cell edges) are the edges of central hexagons, and the {{sqrt|3}} chords are the diagonals of central hexagons. The {{sqrt|2}} chords are the edges of central squares, and the {{sqrt|4}} chords are the diagonals of central squares.

Each vertex is joined to 8 others{{Efn|The 8 nearest neighbor vertices surround the vertex (in the curved 3-dimensional space of the 24-cell's boundary surface) the way a cube's 8 corners surround its center. (The [[W:Vertex figure|vertex figure]] of the 24-cell is a cube.)|name=8 nearest vertices}} by an edge of length 1, spanning 60° = &lt;small&gt;{{sfrac|{{pi}}|3}}&lt;/small&gt; of arc. Next nearest are 6 vertices{{Efn|The 6 second-nearest neighbor vertices surround the vertex in curved 3-dimensional space the way an octahedron's 6 corners surround its center.|name=6 second-nearest vertices}} located 90° = &lt;small&gt;{{sfrac|{{pi}}|2}}&lt;/small&gt; away, along an interior chord of length {{sqrt|2}}. Another 8 vertices lie 120° = &lt;small&gt;{{sfrac|2{{pi}}|3}}&lt;/small&gt; away, along an interior chord of length {{sqrt|3}}.{{Efn|name=nearest isoclinic vertices are {{radic|3}} away in third surrounding shell}} The opposite vertex is 180° = &lt;small&gt;{{pi}}&lt;/small&gt; away along a diameter of length 2. Finally, as the 24-cell is radially equilateral, its center is 1 edge length away from all vertices.

To visualize how the interior polytopes of the 24-cell fit together (as described [[#Constructions|below]]), keep in mind that the four chord lengths ({{sqrt|1}}, {{sqrt|2}}, {{sqrt|3}}, {{sqrt|4}}) are the long diameters of the [[W:Hypercube|hypercube]]s of dimensions 1 through 4: the long diameter of the square is {{sqrt|2}}; the long diameter of the cube is {{sqrt|3}}; and the long diameter of the tesseract is {{sqrt|4}}.{{Efn|Thus ({{sqrt|1}}, {{sqrt|2}}, {{sqrt|3}}, {{sqrt|4}}) are the vertex chord lengths of the tesseract as well as of the 24-cell. They are also the diameters of the tesseract (from short to long), though not of the 24-cell.}} Moreover, the long diameter of the octahedron is {{sqrt|2}} like the square; and the long diameter of the 24-cell itself is {{sqrt|4}} like the tesseract.

==== Geodesics ====
[[Image:stereographic polytope 24cell faces.png|thumb|[[W:Stereographic projection|Stereographic projection]] of the 24-cell's 16 central hexagons onto their great circles. Each great circle is divided into 6 arc-edges at the intersections where 4 great circles cross.]]
The vertex chords of the 24-cell are arranged in [[W:Geodesic|geodesic]] [[W:great circle|great circle]] polygons.{{Efn|A geodesic great circle lies in a 2-dimensional plane which passes through the center of the polytope. Notice that in 4 dimensions this central plane does ''not'' bisect the polytope into two equal-sized parts, as it would in 3 dimensions, just as a diameter (a central line) bisects a circle but does not bisect a sphere. Another difference is that in 4 dimensions not all pairs of great circles intersect at two points, as they do in 3 dimensions; some pairs do, but some pairs of great circles are non-intersecting Clifford parallels.{{Efn|name=Clifford parallels}}}} The [[W:Geodesic distance|geodesic distance]] between two 24-cell vertices along a path of {{sqrt|1}} edges is always 1, 2, or 3, and it is 3 only for opposite vertices.{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

The {{sqrt|1}} edges occur in 16 [[#Great hexagons|hexagonal great circles]] (in planes inclined at 60 degrees to each other), 4 of which cross{{Efn|name=cuboctahedral hexagons}} at each vertex.{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:Vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:Cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The cube is not radially equilateral in Euclidean 3-space &lt;math&gt;\mathbb{R}^3&lt;/math&gt;, but a cubic pyramid is radially equilateral in the curved 3-space of the 24-cell's surface, the [[W:3-sphere|3-sphere]] &lt;math&gt;\mathbb{S}^3&lt;/math&gt;. In 4-space the 8 edges radiating from its apex are not actually its radii: the apex of the [[W:Cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices. But in curved 3-space the edges radiating symmetrically from the apex ''are'' radii, so the cube is radially equilateral ''in that curved 3-space'' &lt;math&gt;\mathbb{S}^3&lt;/math&gt;. In Euclidean 4-space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; 24 edges radiating symmetrically from a central point make the radially equilateral 24-cell,{{Efn|name=radially equilateral}} and a symmetrical subset of 16 of those edges make the [[W:Tesseract#Radial equilateral symmetry|radially equilateral tesseract]].}}|name=24-cell vertex figure}} The 96 distinct {{sqrt|1}} edges divide the surface into 96 triangular faces and 24 octahedral cells: a 24-cell. The 16 hexagonal great circles can be divided into 4 sets of 4 non-intersecting [[W:Clifford parallel|Clifford parallel]] geodesics, such that only one hexagonal great circle in each set passes through each vertex, and the 4 hexagons in each set reach all 24 vertices.{{Efn|name=hexagonal fibrations}}

{| class=&quot;wikitable floatright&quot;
|+ [[W:Orthographic projection|Orthogonal projection]]s of the 24-cell
|- style=&quot;text-align:center;&quot;
![[W:Coxeter plane|Coxeter plane]]
!colspan=2|F&lt;sub&gt;4&lt;/sub&gt;
|- style=&quot;text-align:center;&quot;
!Graph
|colspan=2|[[File:24-cell t0_F4.svg|100px]]
|- style=&quot;text-align:center;&quot;
![[W:Dihedral symmetry|Dihedral symmetry]]
|colspan=2|[12]
|- style=&quot;text-align:center;&quot;
!Coxeter plane
!B&lt;sub&gt;3&lt;/sub&gt; / A&lt;sub&gt;2&lt;/sub&gt; (a)
!B&lt;sub&gt;3&lt;/sub&gt; / A&lt;sub&gt;2&lt;/sub&gt; (b)
|- style=&quot;text-align:center;&quot;
!Graph
|[[File:24-cell t0_B3.svg|100px]]
|[[File:24-cell t3_B3.svg|100px]]
|- style=&quot;text-align:center;&quot;
!Dihedral symmetry
|[6]
|[6]
|- style=&quot;text-align:center;&quot;
!Coxeter plane
!B&lt;sub&gt;4&lt;/sub&gt;
!B&lt;sub&gt;2&lt;/sub&gt; / A&lt;sub&gt;3&lt;/sub&gt;
|- style=&quot;text-align:center;&quot;
!Graph
|[[File:24-cell t0_B4.svg|100px]]
|[[File:24-cell t0_B2.svg|100px]]
|- style=&quot;text-align:center;&quot;
!Dihedral symmetry
|[8]
|[4]
|}
The {{sqrt|2}} chords occur in 18 [[#Great squares|square great circles]] (3 sets of 6 orthogonal planes{{Efn|name=Six orthogonal planes of the Cartesian basis}}), 3 of which cross at each vertex.{{Efn|Six {{sqrt|2}} chords converge in 3-space from the face centers of the 24-cell's cubical vertex figure{{Efn|name=full size vertex figure}} and meet at its center (the vertex), where they form 3 straight lines which cross there perpendicularly. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell, and eight {{sqrt|1}} edges converge from there, but let us ignore them now, since 7 straight lines crossing at the center is confusing to visualize all at once. Each of the six {{sqrt|2}} chords runs from this cube's center (the vertex) through a face center to the center of an adjacent (face-bonded) cube, which is another vertex of the 24-cell: not a nearest vertex (at the cube corners), but one located 90° away in a second concentric shell of six {{sqrt|2}}-distant vertices that surrounds the first shell of eight {{sqrt|1}}-distant vertices. The face-center through which the {{sqrt|2}} chord passes is the mid-point of the {{sqrt|2}} chord, so it lies inside the 24-cell.|name=|group=}} The 72 distinct {{sqrt|2}} chords do not run in the same planes as the hexagonal great circles; they do not follow the 24-cell's edges, they pass through its octagonal cell centers.{{Efn|One can cut the 24-cell through 6 vertices (in any hexagonal great circle plane), or through 4 vertices (in any square great circle plane). One can see this in the [[W:Cuboctahedron|cuboctahedron]] (the central [[W:hyperplane|hyperplane]] of the 24-cell), where there are four hexagonal great circles (along the edges) and six square great circles (across the square faces diagonally).}} The 72 {{sqrt|2}} chords are the 3 orthogonal axes of the 24 octahedral cells, joining vertices which are 2 {{radic|1}} edges apart. The 18 square great circles can be divided into 3 sets of 6 non-intersecting Clifford parallel geodesics,{{Efn|[[File:Hopf band wikipedia.png|thumb|Two [[W:Clifford parallel|Clifford parallel]] [[W:Great circle|great circle]]s on the [[W:3-sphere|3-sphere]] spanned by a twisted [[W:Annulus (mathematics)|annulus]]. They have a common center point in [[W:Rotations in 4-dimensional Euclidean space|4-dimensional Euclidean space]], and could lie in [[W:Completely orthogonal|completely orthogonal]] rotation planes.]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point.{{Sfn|Tyrrell|Semple|1971|loc=§3. Clifford's original definition of parallelism|pp=5-6}} A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the 2-sphere will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect; various sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. Perhaps the simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles.{{Efn|name=Six orthogonal planes of the Cartesian basis}} Each completely orthogonal pair is Clifford parallel. The two circles cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 3-sphere.{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but [[W:Completely orthogonal|completely orthogonal]] to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} Because they are perpendicular and share a common center,{{Efn|In 4-space, two great circles can be perpendicular and share a common center ''which is their only point of intersection'', because there is more than one great [[W:2-sphere|2-sphere]] on the [[W:3-sphere|3-sphere]]. The dimensionally analogous structure to a [[W:Great circle|great circle]] (a great 1-sphere) is a great 2-sphere,{{Sfn|Stillwell|2001|p=24}} which is an ordinary sphere that constitutes an ''equator'' boundary dividing the 3-sphere into two equal halves, just as a great circle divides the 2-sphere. Although two Clifford parallel great circles{{Efn|name=Clifford parallels}} occupy the same 3-sphere, they lie on different great 2-spheres. The great 2-spheres are [[#Clifford parallel polytopes|Clifford parallel 3-dimensional objects]], displaced relative to each other by a fixed distance ''d'' in the fourth dimension. Their corresponding points (on their two surfaces) are ''d'' apart. The 2-spheres (by which we mean their surfaces) do not intersect at all, although they have a common center point in 4-space. The displacement ''d'' between a pair of their corresponding points is the [[#Geodesics|chord of a great circle]] which intersects both 2-spheres, so ''d'' can be represented equivalently as a linear chordal distance, or as an angular distance.|name=great 2-spheres}} the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]].|name=Clifford parallels}} such that only one square great circle in each set passes through each vertex, and the 6 squares in each set reach all 24 vertices.{{Efn|name=square fibrations}}

The {{sqrt|3}} chords occur in 32 [[#Great triangles|triangular great circles]] in 16 planes, 4 of which cross at each vertex.{{Efn|Eight {{sqrt|3}} chords converge from the corners of the 24-cell's cubical vertex figure{{Efn|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. Each of the eight {{sqrt|3}} chords runs from this cube's center to the center of a diagonally adjacent (vertex-bonded) cube,{{Efn|name=missing the nearest vertices}} which is another vertex of the 24-cell: one located 120° away in a third concentric shell of eight {{sqrt|3}}-distant vertices surrounding the second shell of six {{sqrt|2}}-distant vertices that surrounds the first shell of eight {{sqrt|1}}-distant vertices.|name=nearest isoclinic vertices are {{radic|3}} away in third surrounding shell}} The 96 distinct {{sqrt|3}} chords{{Efn|name=cube diagonals}} run vertex-to-every-other-vertex in the same planes as the hexagonal great circles.{{Efn|name=central triangles}} They are the 3 edges of the 32 great triangles inscribed in the 16 great hexagons, joining vertices which are 2 {{sqrt|1}} edges apart on a great circle.{{Efn|name=three 8-cells}}

The {{sqrt|4}} chords occur as 12 vertex-to-vertex diameters (3 sets of 4 orthogonal axes), the 24 radii around the 25th central vertex.

The sum of the squared lengths{{Efn|The sum of 1・96 + 2・72 + 3・96 + 4・12 is 576.}} of all these distinct chords of the 24-cell is 576 = 24&lt;sup&gt;2&lt;/sup&gt;.{{Efn|The sum of the squared lengths of all the distinct chords of any regular convex n-polytope of unit radius is the square of the number of vertices.{{Sfn|Copher|2019|loc=§3.2 Theorem 3.4|p=6}}}} These are all the central polygons through vertices, but in 4-space there are geodesics on the 3-sphere which do not lie in central planes at all. There are geodesic shortest paths between two 24-cell vertices that are helical rather than simply circular; they correspond to diagonal [[#Isoclinic rotations|isoclinic rotations]] rather than [[#Simple rotations|simple rotations]].{{Efn|name=isoclinic geodesic}}

The {{sqrt|1}} edges occur in 48 parallel pairs, {{sqrt|3}} apart. The {{sqrt|2}} chords occur in 36 parallel pairs, {{sqrt|2}} apart. The {{sqrt|3}} chords occur in 48 parallel pairs, {{sqrt|1}} apart.{{Efn|Each pair of parallel {{sqrt|1}} edges joins a pair of parallel {{sqrt|3}} chords to form one of 48 rectangles (inscribed in the 16 central hexagons), and each pair of parallel {{sqrt|2}} chords joins another pair of parallel {{sqrt|2}} chords to form one of the 18 central squares.|name=|group=}}

The central planes of the 24-cell can be divided into 4 orthogonal central hyperplanes (3-spaces) each forming a [[W:Cuboctahedron|cuboctahedron]]. The great hexagons are 60 degrees apart; the great squares are 90 degrees or 60 degrees apart; a great square and a great hexagon are 90 degrees ''and'' 60 degrees apart.{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;.}} Since all planes in the same hyperplane{{Efn|name=hyperplanes}} are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles ([[W:Completely orthogonal|completely orthogonal]]) or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes ''may'' be isoclinic, but often they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} Each set of similar central polygons (squares or hexagons) can be divided into 4 sets of non-intersecting Clifford parallel polygons (of 6 squares or 4 hexagons).{{Efn|Each pair of Clifford parallel polygons lies in two different hyperplanes (cuboctahedrons). The 4 Clifford parallel hexagons lie in 4 different cuboctahedrons.}} Each set of Clifford parallel great circles is a parallel [[W:Hopf fibration|fiber bundle]] which visits all 24 vertices just once.

Each great circle intersects{{Efn|name=how planes intersect}} with the other great circles to which it is not Clifford parallel at one {{sqrt|4}} diameter of the 24-cell.{{Efn|Two intersecting great squares or great hexagons share two opposing vertices, but squares or hexagons on Clifford parallel great circles share no vertices. Two intersecting great triangles share only one vertex, since they lack opposing vertices.|name=how great circle planes intersect|group=}} Great circles which are [[W:Completely orthogonal|completely orthogonal]] or otherwise Clifford parallel{{Efn|name=Clifford parallels}} do not intersect at all: they pass through disjoint sets of vertices.{{Efn|name=pairs of completely orthogonal planes}}

=== Constructions ===
Triangles and squares come together uniquely in the 24-cell to generate, as interior features,{{Efn|Interior features are not considered elements of the polytope. For example, the center of a 24-cell is a noteworthy feature (as are its long radii), but these interior features do not count as elements in [[#As a configuration|its configuration matrix]], which counts only elementary features (which are not interior to any other feature including the polytope itself). Interior features are not rendered in most of the diagrams and illustrations in this article (they are normally invisible). In illustrations showing interior features, we always draw interior edges as dashed lines, to distinguish them from elementary edges.|name=interior features|group=}} all of the triangle-faced and square-faced regular convex polytopes in the first four dimensions (with caveats for the [[5-cell]] and the [[600-cell]]).{{Efn|The 600-cell is larger than the 24-cell, and contains the 24-cell as an interior feature.{{Sfn|Coxeter|1973|p=153|loc=8.5. Gosset's construction for {3,3,5}|ps=: &quot;In fact, the vertices of {3,3,5}, each taken 5 times, are the vertices of 25 {3,4,3}'s.&quot;}} The regular 5-cell is not found in the interior of any convex regular 4-polytope except the [[120-cell]],{{Sfn|Coxeter|1973|p=304|loc=Table VI(iv) II={5,3,3}|ps=: Faceting {5,3,3}[120𝛼&lt;sub&gt;4&lt;/sub&gt;]{3,3,5} of the 120-cell reveals 120 regular 5-cells.}} though every convex 4-polytope can be [[#Characteristic orthoscheme|deconstructed into irregular 5-cells.]]|name=|group=}} Consequently, there are numerous ways to construct or deconstruct the 24-cell.

==== Reciprocal constructions from 8-cell and 16-cell ====
The 8 integer vertices (±1, 0, 0, 0) are the vertices of a regular [[16-cell]], and the 16 half-integer vertices (±{{sfrac|1|2}}, ±{{sfrac|1|2}}, ±{{sfrac|1|2}}, ±{{sfrac|1|2}}) are the vertices of its dual, the [[W:Tesseract|tesseract]] (8-cell).{{Sfn|Egan|2021|loc=animation of a rotating 24-cell|ps=: {{color|red}} half-integer vertices (tesseract), {{Font color|fg=yellow|bg=black|text=yellow}} and {{color|black}} integer vertices (16-cell).}} The tesseract gives Gosset's construction{{Sfn|Coxeter|1973|p=150|loc=Gosset}} of the 24-cell, equivalent to cutting a tesseract into 8 [[W:Cubic pyramid|cubic pyramid]]s, and then attaching them to the facets of a second tesseract. The analogous construction in 3-space gives the [[W:Rhombic dodecahedron|rhombic dodecahedron]] which, however, is not regular.{{Efn|[[File:R1-cube.gif|thumb|150px|Construction of a [[W:Rhombic dodecahedron|rhombic dodecahedron]] from a cube.]]This animation shows the construction of a [[W:Rhombic dodecahedron|rhombic dodecahedron]] from a cube, by inverting the center-to-face pyramids of a cube. Gosset's construction of a 24-cell from a tesseract is the 4-dimensional analogue of this process, inverting the center-to-cell pyramids of an 8-cell (tesseract).{{Sfn|Coxeter|1973|p=150|loc=Gosset}}|name=rhombic dodecahedron from a cube}} The 16-cell gives the reciprocal construction of the 24-cell, Cesaro's construction,{{Sfn|Coxeter|1973|p=148|loc=§8.2. Cesaro's construction for {3, 4, 3}.}} equivalent to rectifying a 16-cell (truncating its corners at the mid-edges, as described [[#Great squares|above]]). The analogous construction in 3-space gives the [[W:Cuboctahedron|cuboctahedron]] (dual of the rhombic dodecahedron) which, however, is not regular. The tesseract and the 16-cell are the only regular 4-polytopes in the 24-cell.{{Sfn|Coxeter|1973|p=302|loc=Table VI(ii) II={3,4,3}, Result column}}

We can further divide the 16 half-integer vertices into two groups: those whose coordinates contain an even number of minus (−) signs and those with an odd number. Each of these groups of 8 vertices also define a regular 16-cell. This shows that the vertices of the 24-cell can be grouped into three disjoint sets of eight with each set defining a regular 16-cell, and with the complement defining the dual tesseract.{{Sfn|Coxeter|1973|pp=149-150|loc=§8.22. see illustrations Fig. 8.2&lt;small&gt;A&lt;/small&gt; and Fig 8.2&lt;small&gt;B&lt;/small&gt;|p=|ps=}} This also shows that the symmetries of the 16-cell form a subgroup of index 3 of the symmetry group of the 24-cell.{{Efn|name=three 16-cells form three tesseracts}}

==== Diminishings ====
We can [[W:Faceting|facet]] the 24-cell by cutting{{Efn|We can cut a vertex off a polygon with a 0-dimensional cutting instrument (like the point of a knife, or the head of a zipper) by sweeping it along a 1-dimensional line, exposing a new edge. We can cut a vertex off a polyhedron with a 1-dimensional cutting edge (like a knife) by sweeping it through a 2-dimensional face plane, exposing a new face. We can cut a vertex off a polychoron (a 4-polytope) with a 2-dimensional cutting plane (like a snowplow), by sweeping it through a 3-dimensional cell volume, exposing a new cell. Notice that as within the new edge length of the polygon or the new face area of the polyhedron, every point within the new cell volume is now exposed on the surface of the polychoron.}} through interior cells bounded by vertex chords to remove vertices, exposing the [[W:Facet (geometry)|facets]] of interior 4-polytopes [[W:Inscribed figure|inscribed]] in the 24-cell. One can cut a 24-cell through any planar hexagon of 6 vertices, any planar rectangle of 4 vertices, or any triangle of 3 vertices. The great circle central planes ([[#Geodesics|above]]) are only some of those planes. Here we shall expose some of the others: the face planes{{Efn|Each cell face plane intersects with the other face planes of its kind to which it is not completely orthogonal or parallel at their characteristic vertex chord edge. Adjacent face planes of orthogonally-faced cells (such as cubes) intersect at an edge since they are not completely orthogonal.{{Efn|name=how planes intersect}} Although their dihedral angle is 90 degrees in the boundary 3-space, they lie in the same hyperplane{{Efn|name=hyperplanes}} (they are coincident rather than perpendicular in the fourth dimension); thus they intersect in a line, as non-parallel planes do in any 3-space.|name=how face planes intersect}} of interior polytopes.{{Efn|The only planes through exactly 6 vertices of the 24-cell (not counting the central vertex) are the '''16 hexagonal great circles'''. There are no planes through exactly 5 vertices. There are several kinds of planes through exactly 4 vertices: the 18 {{sqrt|2}} square great circles, the '''72 {{sqrt|1}} square (tesseract) faces''', and 144 {{sqrt|1}} by {{sqrt|2}} rectangles. The planes through exactly 3 vertices are the 96 {{sqrt|2}} equilateral triangle (16-cell) faces, and the '''96 {{sqrt|1}} equilateral triangle (24-cell) faces'''. There are an infinite number of central planes through exactly two vertices (great circle [[W:Digon|digon]]s); 16 are distinguished, as each is [[W:Completely orthogonal|completely orthogonal]] to one of the 16 hexagonal great circles. '''Only the polygons composed of 24-cell {{radic|1}} edges are visible''' in the projections and rotating animations illustrating this article; the others contain invisible interior chords.{{Efn|name=interior features}}|name=planes through vertices|group=}}

===== 8-cell =====
Starting with a complete 24-cell, remove 8 orthogonal vertices (4 opposite pairs on 4 perpendicular axes), and the 8 edges which radiate from each, by cutting through 8 cubic cells bounded by {{sqrt|1}} edges to remove 8 [[W:Cubic pyramid|cubic pyramid]]s whose [[W:Apex (geometry)|apexes]] are the vertices to be removed. This removes 4 edges from each hexagonal great circle (retaining just one opposite pair of edges), so no continuous hexagonal great circles remain. Now 3 perpendicular edges meet and form the corner of a cube at each of the 16 remaining vertices,{{Efn|The 24-cell's cubical vertex figure{{Efn|name=full size vertex figure}} has been truncated to a tetrahedral vertex figure (see [[#Relationships among interior polytopes|Kepler's drawing]]). The vertex cube has vanished, and now there are only 4 corners of the vertex figure where before there were 8. Four tesseract edges converge from the tetrahedron vertices and meet at its center, where they do not cross (since the tetrahedron does not have opposing vertices).|name=|group=}} and the 32 remaining edges divide the surface into 24 square faces and 8 cubic cells: a [[W:Tesseract|tesseract]]. There are three ways you can do this (choose a set of 8 orthogonal vertices out of 24), so there are three such tesseracts inscribed in the 24-cell.{{Efn|name=three 8-cells}} They overlap with each other, but most of their element sets are disjoint: they share some vertex count, but no edge length, face area, or cell volume.{{Efn|name=vertex-bonded octahedra}} They do share 4-content, their common core.{{Efn||name=common core|group=}}

===== 16-cell =====
Starting with a complete 24-cell, remove the 16 vertices of a tesseract (retaining the 8 vertices you removed above), by cutting through 16 tetrahedral cells bounded by {{sqrt|2}} chords to remove 16 [[W:Tetrahedral pyramid|tetrahedral pyramid]]s whose apexes are the vertices to be removed. This removes 12 great squares (retaining just one orthogonal set) and all the {{sqrt|1}} edges, exposing {{sqrt|2}} chords as the new edges. Now the remaining 6 great squares cross perpendicularly, 3 at each of 8 remaining vertices,{{Efn|The 24-cell's cubical vertex figure{{Efn|name=full size vertex figure}} has been truncated to an octahedral vertex figure. The vertex cube has vanished, and now there are only 6 corners of the vertex figure where before there were 8. The 6 {{sqrt|2}} chords which formerly converged from cube face centers now converge from octahedron vertices; but just as before, they meet at the center where 3 straight lines cross perpendicularly. The octahedron vertices are located 90° away outside the vanished cube, at the new nearest vertices; before truncation those were 24-cell vertices in the second shell of surrounding vertices.|name=|group=}} and their 24 edges divide the surface into 32 triangular faces and 16 tetrahedral cells: a [[16-cell]]. There are three ways you can do this (remove 1 of 3 sets of tesseract vertices), so there are three such 16-cells inscribed in the 24-cell.{{Efn|name=three isoclinic 16-cells}} They overlap with each other, but all of their element sets are disjoint:{{Efn|name=completely disjoint}} they do not share any vertex count, edge length,{{Efn|name=root 2 chords}} or face area, but they do share cell volume. They also share 4-content, their common core.{{Efn||name=common core|group=}}

==== Tetrahedral constructions ====
The 24-cell can be constructed radially from 96 equilateral triangles of edge length {{sqrt|1}} which meet at the center of the polytope, each contributing two radii and an edge.{{Efn|name=radially equilateral|group=}} They form 96 {{sqrt|1}} tetrahedra (each contributing one 24-cell face), all sharing the 25th central apex vertex. These form 24 octahedral pyramids (half-16-cells) with their apexes at the center.

The 24-cell can be constructed from 96 equilateral triangles of edge length {{sqrt|2}}, where the three vertices of each triangle are  located 90° = &lt;small&gt;{{sfrac|{{pi}}|2}}&lt;/small&gt; away from each other on the 3-sphere. They form 48 {{sqrt|2}}-edge tetrahedra (the cells of the [[#16-cell|three 16-cells]]), centered at the 24 mid-edge-radii of the 24-cell.{{Efn|Each of the 72 {{sqrt|2}} chords in the 24-cell is a face diagonal in two distinct cubical cells (of different 8-cells) and an edge of four tetrahedral cells (in just one 16-cell).|name=root 2 chords}}

The 24-cell can be constructed directly from its [[#Characteristic orthoscheme|characteristic simplex]] {{Coxeter–Dynkin diagram|node|3|node|4|node|3|node}}, the [[5-cell#Irregular 5-cells|irregular 5-cell]] which is the [[W:Fundamental region|fundamental region]] of its [[W:Coxeter group|symmetry group]] [[W:F4 polytope|F&lt;sub&gt;4&lt;/sub&gt;]], by reflection of that 4-[[W:Orthoscheme|orthoscheme]] in its own cells (which are 3-orthoschemes).{{Efn|An [[W:Orthoscheme|orthoscheme]] is a [[W:chiral|chiral]] irregular [[W:Simplex|simplex]] with [[W:Right triangle|right triangle]] faces that is characteristic of some polytope if it will exactly fill that polytope with the reflections of itself in its own [[W:Facet (geometry)|facet]]s (its ''mirror walls''). Every regular polytope can be dissected radially into instances of its [[W:Orthoscheme#Characteristic simplex of the general regular polytope|characteristic orthoscheme]] surrounding its center. The characteristic orthoscheme has the shape described by the same [[W:Coxeter-Dynkin diagram|Coxeter-Dynkin diagram]] as the regular polytope without the ''generating point'' ring.|name=characteristic orthoscheme}}

==== Cubic constructions ====
The 24-cell is not only the 24-octahedral-cell, it is also the 24-cubical-cell, although the cubes are cells of the three 8-cells, not cells of the 24-cell, in which they are not volumetrically disjoint.

The 24-cell can be constructed from 24 cubes of its own edge length (three 8-cells).{{Efn|name=three 8-cells}} Each of the cubes is shared by 2 8-cells, each of the cubes' square faces is shared by 4 cubes (in 2 8-cells), each of the 96 edges is shared by 8 square faces (in 4 cubes in 2 8-cells), and each of the 96 vertices is shared by 16 edges (in 8 square faces in 4 cubes in 2 8-cells).

==== Relationships among interior polytopes ====
The 24-cell, three tesseracts, and three 16-cells are deeply entwined around their common center, and intersect in a common core.{{Efn|A simple way of stating this relationship is that the common core of the {{radic|2}}-radius 4-polytopes is the unit-radius 24-cell. The common core of the 24-cell and its inscribed 8-cells and 16-cells is the unit-radius 24-cell's insphere-inscribed dual 24-cell of edge length and radius {{radic|1/2}}.{{Sfn|Coxeter|1995|p=29|loc=(Paper 3) ''Two aspects of the regular 24-cell in four dimensions''|ps=; &quot;The common content of the 4-cube and the 16-cell is a smaller {3,4,3} whose vertices are the permutations of [(±{{sfrac|1|2}}, ±{{sfrac|1|2}}, 0, 0)]&quot;.}} Rectifying any of the three 16-cells reveals this smaller 24-cell, which has a 4-content of only 1/2 (1/4 that of the unit-radius 24-cell). Its vertices lie at the centers of the 24-cell's octahedral cells, which are also the centers of the tesseracts' square faces, and are also the centers of the 16-cells' edges. {{Sfn|Coxeter|1973|p=147|loc=§8.1 The simple truncations of the general regular polytope|ps=; &quot;At a point of contact, [elements of a regular polytope and elements of its dual in which it is inscribed in some manner] lie in [[W:completely orthogonal|completely orthogonal]] subspaces of the tangent hyperplane to the sphere [of reciprocation], so their only common point is the point of contact itself....{{Efn|name=how planes intersect}} In fact, the [various] radii &lt;sub&gt;0&lt;/sub&gt;𝑹, &lt;sub&gt;1&lt;/sub&gt;𝑹, &lt;sub&gt;2&lt;/sub&gt;𝑹, ... determine the polytopes ... whose vertices are the centers of elements 𝐈𝐈&lt;sub&gt;0&lt;/sub&gt;, 𝐈𝐈&lt;sub&gt;1&lt;/sub&gt;, 𝐈𝐈&lt;sub&gt;2&lt;/sub&gt;, ... of the original polytope.&quot;}}|name=common core|group=}} The tesseracts and the 16-cells are rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other. This means that the corresponding vertices of two tesseracts or two 16-cells are {{radic|3}} (120°) apart.{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diameters). The 8-cells are not completely disjoint (they share vertices),{{Efn|name=completely disjoint}} but each {{radic|3}} chord occurs as a cube long diameter in just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell as cube diameters.{{Efn|name=nearest isoclinic vertices are {{radic|3}} away in third surrounding shell}}|name=three 8-cells}}

The tesseracts are inscribed in the 24-cell{{Efn|The 24 vertices of the 24-cell, each used twice, are the vertices of three 16-vertex tesseracts.|name=|group=}} such that their vertices and edges are exterior elements of the 24-cell, but their square faces and cubical cells lie inside the 24-cell (they are not elements of the 24-cell). The 16-cells are inscribed in the 24-cell{{Efn|The 24 vertices of the 24-cell, each used once, are the vertices of three 8-vertex 16-cells.{{Efn|name=three basis 16-cells}}|name=|group=}} such that only their vertices are exterior elements of the 24-cell: their edges, triangular faces, and tetrahedral cells lie inside the 24-cell. The interior{{Efn|The edges of the 16-cells are not shown in any of the renderings in this article; if we wanted to show interior edges, they could be drawn as dashed lines. The edges of the inscribed tesseracts are always visible, because they are also edges of the 24-cell.}} 16-cell edges have length {{sqrt|2}}.{{Efn|name=great linking triangles}}[[File:Kepler's tetrahedron in cube.png|thumb|Kepler's drawing of tetrahedra in the cube.{{Sfn|Kepler|1619|p=181}}]]

The 16-cells are also inscribed in the tesseracts: their {{sqrt|2}} edges are the face diagonals of the tesseract, and their 8 vertices occupy every other vertex of the tesseract. Each tesseract has two 16-cells inscribed in it (occupying the opposite vertices and face diagonals), so each 16-cell is inscribed in two of the three 8-cells.{{Sfn|van Ittersum|2020|loc=§4.2|pp=73-79}}{{Efn|name=three 16-cells form three tesseracts}} This is reminiscent of the way, in 3 dimensions, two opposing regular tetrahedra can be inscribed in a cube, as discovered by Kepler.{{Sfn|Kepler|1619|p=181}} In fact it is the exact dimensional analogy (the [[W:Demihypercube|demihypercube]]s), and the 48 tetrahedral cells are inscribed in the 24 cubical cells in just that way.{{Sfn|Coxeter|1973|p=269|loc=§14.32|ps=. &quot;For instance, in the case of &lt;math&gt;\gamma_4[2\beta_4]&lt;/math&gt;....&quot;}}{{Efn|name=root 2 chords}}

The 24-cell encloses the three tesseracts within its envelope of octahedral facets, leaving 4-dimensional space in some places between its envelope and each tesseract's envelope of cubes. Each tesseract encloses two of the three 16-cells, leaving 4-dimensional space in some places between its envelope and each 16-cell's envelope of tetrahedra. Thus there are measurable{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii): The sixteen regular polytopes {''p,q,r''} in four dimensions|ps=; An invaluable table providing all 20 metrics of each 4-polytope in edge length units. They must be algebraically converted to compare polytopes of unit radius.}} 4-dimensional interstices{{Efn|The 4-dimensional content of the unit edge length tesseract is 1 (by definition). The content of the unit edge length 24-cell is 2, so half its content is inside each tesseract, and half is between their envelopes. Each 16-cell (edge length {{sqrt|2}}) encloses a content of 2/3, leaving 1/3 of an enclosing tesseract between their envelopes.|name=|group=}} between the 24-cell, 8-cell and 16-cell envelopes. The shapes filling these gaps are [[W:Hyperpyramid|4-pyramids]], alluded to above.{{Efn|Between the 24-cell envelope and the 8-cell envelope, we have the 8 cubic pyramids of Gosset's construction. Between the 8-cell envelope and the 16-cell envelope, we have 16 right [[5-cell#Irregular 5-cell|tetrahedral pyramids]], with their apexes filling the corners of the tesseract.}}

==== Boundary cells ====
Despite the 4-dimensional interstices between 24-cell, 8-cell and 16-cell envelopes, their 3-dimensional volumes overlap. The different envelopes are separated in some places, and in contact in other places (where no 4-pyramid lies between them). Where they are in contact, they merge and share cell volume: they are the same 3-membrane in those places, not two separate but adjacent 3-dimensional layers.{{Efn|Because there are three overlapping tesseracts inscribed in the 24-cell,{{Efn|name=three 8-cells}} each octahedral cell lies ''on'' a cubic cell of one tesseract (in the cubic pyramid based on the cube, but not in the cube's volume), and ''in'' two cubic cells of each of the other two tesseracts (cubic cells which it spans, sharing their volume).{{Efn|name=octahedral diameters}}|name=octahedra both on and in cubes}} Because there are a total of 7 envelopes, there are places where several envelopes come together and merge volume, and also places where envelopes interpenetrate (cross from inside to outside each other).

Some interior features lie within the 3-space of the (outer) boundary envelope of the 24-cell itself: each octahedral cell is bisected by three perpendicular squares (one from each of the tesseracts), and the diagonals of those squares (which cross each other perpendicularly at the center of the octahedron) are 16-cell edges (one from each 16-cell). Each square bisects an octahedron into two square pyramids, and also bonds two adjacent cubic cells of a tesseract together as their common face.{{Efn|Consider the three perpendicular {{sqrt|2}} long diameters of the octahedral cell.{{Sfn|van Ittersum|2020|p=79}} Each of them is an edge of a different 16-cell. Two of them are the face diagonals of the square face between two cubes; each is a {{sqrt|2}} chord that connects two vertices of those 8-cell cubes across a square face, connects two vertices of two 16-cell tetrahedra (inscribed in the cubes), and connects two opposite vertices of a 24-cell octahedron (diagonally across two of the three orthogonal square central sections).{{Efn|name=root 2 chords}} The third perpendicular long diameter of the octahedron does exactly the same (by symmetry); so it also connects two vertices of a pair of cubes across their common square face: but a different pair of cubes, from one of the other tesseracts in the 24-cell.{{Efn|name=vertex-bonded octahedra}}|name=octahedral diameters}}

As we saw [[#Relationships among interior polytopes|above]], 16-cell {{sqrt|2}} tetrahedral cells are inscribed in tesseract {{sqrt|1}} cubic cells, sharing the same volume. 24-cell {{sqrt|1}} octahedral cells overlap their volume with {{sqrt|1}} cubic cells: they are bisected by a square face into two square pyramids,{{sfn|Coxeter|1973|page=150|postscript=: &quot;Thus the 24 cells of the {3, 4, 3} are dipyramids based on the 24 squares of the &lt;math&gt;\gamma_4&lt;/math&gt;. (Their centres are the mid-points of the 24 edges of the &lt;math&gt;\beta_4&lt;/math&gt;.)&quot;}} the apexes of which also lie at a vertex of a cube.{{Efn|This might appear at first to be angularly impossible, and indeed it would be in a flat space of only three dimensions. If two cubes rest face-to-face in an ordinary 3-dimensional space (e.g. on the surface of a table in an ordinary 3-dimensional room), an octahedron will fit inside them such that four of its six vertices are at the four corners of the square face between the two cubes; but then the other two octahedral vertices will not lie at a cube corner (they will fall within the volume of the two cubes, but not at a cube vertex). In four dimensions, this is no less true! The other two octahedral vertices do ''not'' lie at a corner of the adjacent face-bonded cube in the same tesseract. However, in the 24-cell there is not just one inscribed tesseract (of 8 cubes), there are three overlapping tesseracts (of 8 cubes each). The other two octahedral vertices ''do'' lie at the corner of a cube: but a cube in another (overlapping) tesseract.{{Efn|name=octahedra both on and in cubes}}}} The octahedra share volume not only with the cubes, but with the tetrahedra inscribed in them; thus the 24-cell, tesseracts, and 16-cells all share some boundary volume.{{Efn|name=octahedra both on and in cubes}}

=== As a configuration ===
This [[W:Regular 4-polytope#As configurations|configuration matrix]]{{Sfn|Coxeter|1973|p=12|loc=§1.8. Configurations}} represents the 24-cell. The rows and columns correspond to vertices, edges, faces, and cells. The diagonal numbers say how many of each element occur in the whole 24-cell. The non-diagonal numbers say how many of the column's element occur in or at the row's element.

&lt;math display=&quot;block&quot;&gt;\begin{bmatrix}\begin{matrix}24 &amp; 8 &amp; 12 &amp; 6 \\ 2 &amp; 96 &amp; 3 &amp; 3 \\ 3 &amp; 3 &amp; 96 &amp; 2 \\ 6 &amp; 12 &amp; 8 &amp; 24 \end{matrix}\end{bmatrix}&lt;/math&gt;

Since the 24-cell is self-dual, its matrix is identical to its 180 degree rotation.

==Symmetries, root systems, and tessellations==
[[File:F4 roots by 24-cell duals.svg|thumb|upright|The compound of the 24 vertices of the 24-cell (red nodes), and its unscaled dual (yellow nodes), represent the 48 root vectors of the [[W:F4 (mathematics)|F&lt;sub&gt;4&lt;/sub&gt;]] group, as shown in this F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane projection]]

The 24 root vectors of the [[W:D4 (root system)|D&lt;sub&gt;4&lt;/sub&gt; root system]] of the [[W:Simple Lie group|simple Lie group]] [[W:SO(8)|SO(8)]] form the vertices of a 24-cell. The vertices can be seen in 3 [[W:Hyperplane|hyperplane]]s,{{Efn|One way to visualize the ''n''-dimensional [[W:Hyperplane|hyperplane]]s is as the ''n''-spaces which can be defined by ''n + 1'' points. A point is the 0-space which is defined by 1 point. A line is the 1-space which is defined by 2 points which are not coincident. A plane is the 2-space which is defined by 3 points which are not colinear (any triangle). In 4-space, a 3-dimensional hyperplane is the 3-space which is defined by 4 points which are not coplanar (any tetrahedron). In 5-space, a 4-dimensional hyperplane is the 4-space which is defined by 5 points which are not cocellular (any 5-cell). These [[W:Simplex|simplex]] figures divide the hyperplane into two parts (inside and outside the figure), but in addition they divide the enclosing space into two parts (above and below the hyperplane). The ''n'' points ''bound'' a finite simplex figure (from the outside), and they ''define'' an infinite hyperplane (from the inside).{{Sfn|Coxeter|1973|loc=§7.2.|p=120|ps=: &quot;... any ''n''+1 points which do not lie in an (''n''-1)-space are the vertices of an ''n''-dimensional ''simplex''.... Thus the general simplex may alternatively be defined as a finite region of ''n''-space enclosed by ''n''+1 ''hyperplanes'' or (''n''-1)-spaces.&quot;}} These two divisions are orthogonal, so the defining simplex divides space into six regions: inside the simplex and in the hyperplane, inside the simplex but above or below the hyperplane, outside the simplex but in the hyperplane, and outside the simplex above or below the hyperplane.|name=hyperplanes|group=}} with the 6 vertices of an [[W:Octahedron|octahedron]] cell on each of the outer hyperplanes and 12 vertices of a [[W:Cuboctahedron|cuboctahedron]] on a central hyperplane. These vertices, combined with the 8 vertices of the [[16-cell]], represent the 32 root vectors of the B&lt;sub&gt;4&lt;/sub&gt; and C&lt;sub&gt;4&lt;/sub&gt; simple Lie groups.

The 48 vertices (or strictly speaking their radius vectors) of the union of the 24-cell and its dual form the [[W:Root system|root system]] of type [[W:F4 (mathematics)|F&lt;sub&gt;4&lt;/sub&gt;]].{{Sfn|van Ittersum|2020|loc=§4.2.5|p=78}} The 24 vertices of the original 24-cell form a root system of type D&lt;sub&gt;4&lt;/sub&gt;; its size has the ratio {{sqrt|2}}:1. This is likewise true for the 24 vertices of its dual. The full [[W:Symmetry group|symmetry group]] of the 24-cell is the [[W:Weyl group|Weyl group]] of F&lt;sub&gt;4&lt;/sub&gt;, which is generated by [[W:Reflection (mathematics)|reflections]] through the hyperplanes orthogonal to the F&lt;sub&gt;4&lt;/sub&gt; roots. This is a [[W:Solvable group|solvable group]] of order 1152. The rotational symmetry group of the 24-cell is of order 576.

===Quaternionic interpretation===
[[File:Binary tetrahedral group elements.png|thumb|The 24 quaternion{{Efn|name=quaternions}} elements of the [[W:Binary tetrahedral group|binary tetrahedral group]] match the vertices of the 24-cell. Seen in 4-fold symmetry projection:
* 1 order-1: 1
* 1 order-2: -1
* 6 order-4: ±i, ±j, ±k
* 8 order-6: (+1±i±j±k)/2
* 8 order-3: (-1±i±j±k)/2.]]When interpreted as the [[W:Quaternion|quaternion]]s,{{Efn|In [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]], a [[W:Quaternion|quaternion]] is simply a (w, x, y, z) Cartesian coordinate. [[W:William Rowan Hamilton|Hamilton]] did not see them as such when he [[W:History of quaternions|discovered the quaternions]]. [[W:Ludwig Schläfli|Schläfli]] would be the first to consider [[W:4-dimensional space|four-dimensional Euclidean space]], publishing his discovery of the regular [[W:Polyscheme|polyscheme]]s in 1852, but Hamilton would never be influenced by that work, which remained obscure into the 20th century. Hamilton found the quaternions when he realized that a fourth dimension, in some sense, would be necessary in order to model rotations in three-dimensional space.{{Sfn|Stillwell|2001|p=18-21}} Although he described a quaternion as an ''ordered four-element multiple of real numbers'', the quaternions were for him an extension of the complex numbers, not a Euclidean space of four dimensions.|name=quaternions}} the F&lt;sub&gt;4&lt;/sub&gt; [[W:root lattice|root lattice]] (which is the integral span of the vertices of the 24-cell) is closed under multiplication and is therefore a [[W:ring (mathematics)|ring]]. This is the ring of [[W:Hurwitz integral quaternion|Hurwitz integral quaternion]]s. The vertices of the 24-cell form the [[W:Group of units|group of units]] (i.e. the group of invertible elements) in the Hurwitz quaternion ring (this group is also known as the [[W:Binary tetrahedral group|binary tetrahedral group]]). The vertices of the 24-cell are precisely the 24 Hurwitz quaternions with norm squared 1, and the vertices of the dual 24-cell are those with norm squared 2. The D&lt;sub&gt;4&lt;/sub&gt; root lattice is the [[W:Dual lattice|dual]] of the F&lt;sub&gt;4&lt;/sub&gt; and is given by the subring of Hurwitz quaternions with even norm squared.{{Sfn|Egan|2021|ps=; quaternions, the binary tetrahedral group and the binary octahedral group, with rotating illustrations.}}

Viewed as the 24 unit [[W:Hurwitz quaternion|Hurwitz quaternion]]s, the [[#Great hexagons|unit radius coordinates]] of the 24-cell represent (in antipodal pairs) the 12 rotations of a regular tetrahedron.{{Sfn|Stillwell|2001|p=22}}

Vertices of other [[W:Convex regular 4-polytope|convex regular 4-polytope]]s also form multiplicative groups of quaternions, but few of them generate a root lattice.{{Sfn|Koca|Al-Ajmi|Koc|2007}}

===Voronoi cells===
The [[W:Voronoi cell|Voronoi cell]]s of the [[W:D4 (root system)|D&lt;sub&gt;4&lt;/sub&gt;]] root lattice are regular 24-cells. The corresponding Voronoi tessellation gives the [[W:Tessellation|tessellation]] of 4-dimensional [[W:Euclidean space|Euclidean space]] by regular 24-cells, the [[W:24-cell honeycomb|24-cell honeycomb]]. The 24-cells are centered at the D&lt;sub&gt;4&lt;/sub&gt; lattice points (Hurwitz quaternions with even norm squared) while the vertices are at the F&lt;sub&gt;4&lt;/sub&gt; lattice points with odd norm squared. Each 24-cell of this tessellation has 24 neighbors. With each of these it shares an octahedron. It also has 24 other neighbors with which it shares only a single vertex. Eight 24-cells meet at any given vertex in this tessellation. The [[W:Schläfli symbol|Schläfli symbol]] for this tessellation is {3,4,3,3}. It is one of only three regular tessellations of '''R'''&lt;sup&gt;4&lt;/sup&gt;.

The unit [[W:Ball (mathematics)|balls]] inscribed in the 24-cells of this tessellation give rise to the densest known [[W:lattice packing|lattice packing]] of [[W:Hypersphere|hypersphere]]s in 4 dimensions. The vertex configuration of the 24-cell has also been shown to give the [[W:24-cell honeycomb#Kissing number|highest possible kissing number in 4 dimensions]].

===Radially equilateral honeycomb===
The dual tessellation of the [[W:24-cell honeycomb|24-cell honeycomb {3,4,3,3}]] is the [[W:16-cell honeycomb|16-cell honeycomb {3,3,4,3}]]. The third regular tessellation of four dimensional space is the [[W:Tesseractic honeycomb|tesseractic honeycomb {4,3,3,4}]], whose vertices can be described by 4-integer Cartesian coordinates.{{Efn|name=quaternions}} The congruent relationships among these three tessellations can be helpful in visualizing the 24-cell, in particular the radial equilateral symmetry which it shares with the tesseract.{{Efn||name=radially equilateral}}

A honeycomb of unit edge length 24-cells may be overlaid on a honeycomb of unit edge length tesseracts such that every vertex of a tesseract (every 4-integer coordinate) is also the vertex of a 24-cell (and tesseract edges are also 24-cell edges), and every center of a 24-cell is also the center of a tesseract.{{Sfn|Coxeter|1973|p=163|ps=: Coxeter notes that [[W:Thorold Gosset|Thorold Gosset]] was apparently the first to see that the cells of the 24-cell honeycomb {3,4,3,3} are concentric with alternate cells of the tesseractic honeycomb {4,3,3,4}, and that this observation enabled Gosset's method of construction of the complete set of regular polytopes and honeycombs.}} The 24-cells are twice as large as the tesseracts by 4-dimensional content (hypervolume), so overall there are two tesseracts for every 24-cell, only half of which are inscribed in a 24-cell. If those tesseracts are colored black, and their adjacent tesseracts (with which they share a cubical facet) are colored red, a 4-dimensional checkerboard results.{{Sfn|Coxeter|1973|p=156|loc=|ps=: &quot;...the chess-board has an n-dimensional analogue.&quot;}} Of the 24 center-to-vertex radii{{Efn|It is important to visualize the radii only as invisible interior features of the 24-cell (dashed lines), since they are not edges of the honeycomb. Similarly, the center of the 24-cell is empty (not a vertex of the honeycomb).}} of each 24-cell, 16 are also the radii of a black tesseract inscribed in the 24-cell. The other 8 radii extend outside the black tesseract (through the centers of its cubical facets) to the centers of the 8 adjacent red tesseracts. Thus the 24-cell honeycomb and the tesseractic honeycomb coincide in a special way: 8 of the 24 vertices of each 24-cell do not occur at a vertex of a tesseract (they occur at the center of a tesseract instead). Each black tesseract is cut from a 24-cell by truncating it at these 8 vertices, slicing off 8 cubic pyramids (as in reversing Gosset's construction,{{Sfn|Coxeter|1973|p=150|loc=Gosset}} but instead of being removed the pyramids are simply colored red and left in place). Eight 24-cells meet at the center of each red tesseract: each one meets its opposite at that shared vertex, and the six others at a shared octahedral cell. &lt;!-- illustration needed: the red/black checkerboard of the combined 24-cell honeycomb and tesseractic honeycomb; use a vertex-first projection of the 24-cells, and outline the edges of the rhombic dodecahedra as blue lines --&gt;

The red tesseracts are filled cells (they contain a central vertex and radii); the black tesseracts are empty cells. The vertex set of this union of two honeycombs includes the vertices of all the 24-cells and tesseracts, plus the centers of the red tesseracts. Adding the 24-cell centers (which are also the black tesseract centers) to this honeycomb yields a 16-cell honeycomb, the vertex set of which includes all the vertices and centers of all the 24-cells and tesseracts. The formerly empty centers of adjacent 24-cells become the opposite vertices of a unit edge length 16-cell. 24 half-16-cells (octahedral pyramids) meet at each formerly empty center to fill each 24-cell, and their octahedral bases are the 6-vertex octahedral facets of the 24-cell (shared with an adjacent 24-cell).{{Efn|Unlike the 24-cell and the tesseract, the 16-cell is not radially equilateral; therefore 16-cells of two different sizes (unit edge length versus unit radius) occur in the unit edge length honeycomb. The twenty-four 16-cells that meet at the center of each 24-cell have unit edge length, and radius {{sfrac|{{radic|2}}|2}}. The three 16-cells inscribed in each 24-cell have edge length {{radic|2}}, and unit radius.}}

Notice the complete absence of pentagons anywhere in this union of three honeycombs. Like the 24-cell, 4-dimensional Euclidean space itself is entirely filled by a complex of all the polytopes that can be built out of regular triangles and squares (except the 5-cell), but that complex does not require (or permit) any of the pentagonal polytopes.{{Efn|name=pentagonal polytopes}}

== Rotations ==
[[File:24-cell-3CP.gif|thumb|The 24-point 24-cell contains three 8-point 16-cells (red, green, and blue), double-rotated by 60 degrees with respect to each other.{{Efn|name=three isoclinic 16-cells}} Each 8-point 16-cell is a coordinate system basis frame of four perpendicular (w,x,y,z) axes.{{Efn|name=three basis 16-cells}} One octahedral cell of the 24 cells is emphasized. Each octahedral cell has two vertices of each color, delimiting an invisible perpendicular axis of the octahedron, which is a {{radic|2}} edge of the red, green, or blue 16-cell.{{Efn|name=octahedral diameters}}]]
The [[#Geometry|regular convex 4-polytopes]] are an [[W:Group action|expression]] of their underlying [[W:Symmetry (geometry)|symmetry]] which is known as [[W:SO(4)|SO(4)]],{{Sfn|Goucher|2019|loc=Spin Groups}} the [[W:Orthogonal group|group]] of rotations{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}} about a fixed point in 4-dimensional Euclidean space.{{Efn|[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] may occur around a plane, as when adjacent cells are folded around their plane of intersection (by analogy to the way adjacent faces are folded around their line of intersection).{{Efn|Three dimensional [[W:Rotation (mathematics)#In Euclidean geometry|rotations]] occur around an axis line. [[W:Rotations in 4-dimensional Euclidean space|Four dimensional rotations]] may occur around a plane. So in three dimensions we may fold planes around a common line (as when folding a flat net of 6 squares up into a cube), and in four dimensions we may fold cells around a common plane (as when [[W:Tesseract#Geometry|folding a flat net of 8 cubes up into a tesseract]]). Folding around a square face is just folding around ''two'' of its orthogonal edges ''at the same time''; there is not enough space in three dimensions to do this, just as there is not enough space in two dimensions to fold around a line (only enough to fold around a point).|name=simple rotations|group=}} But in four dimensions there is yet another way in which rotations can occur, called a '''[[W:Rotations in 4-dimensional Euclidean space#Geometry of 4D rotations|double rotation]]'''. Double rotations are an emergent phenomenon in the fourth dimension and have no analogy in three dimensions: folding up square faces and folding up cubical cells are both examples of '''simple rotations''', the only kind that occur in fewer than four dimensions. In 3-dimensional rotations, the points in a line remain fixed during the rotation, while every other point moves. In 4-dimensional simple rotations, the points in a plane remain fixed during the rotation, while every other point moves. ''In 4-dimensional double rotations, a point remains fixed during rotation, and every other point moves'' (as in a 2-dimensional rotation!).{{Efn|There are (at least) two kinds of correct [[W:Four-dimensional space#Dimensional analogy|dimensional analogies]]: the usual kind between dimension ''n'' and dimension ''n'' + 1, and the much rarer and less obvious kind between dimension ''n'' and dimension ''n'' + 2. An example of the latter is that rotations in 4-space may take place around a single point, as do rotations in 2-space. Another is the [[W:n-sphere#Other relations|''n''-sphere rule]] that the ''surface area'' of the sphere embedded in ''n''+2 dimensions is exactly 2''π r'' times the ''volume'' enclosed by the sphere embedded in ''n'' dimensions, the most well-known examples being that the circumference of a circle is 2''π r'' times 1, and the surface area of the ordinary sphere is 2''π r'' times 2''r''. Coxeter cites{{Sfn|Coxeter|1973|p=119|loc=§7.1. Dimensional Analogy|ps=: &quot;For instance, seeing that the circumference of a circle is 2''π r'', while the surface of a sphere is 4''π r ''&lt;sup&gt;2&lt;/sup&gt;, ... it is unlikely that the use of analogy, unaided by computation, would ever lead us to the correct expression [for the hyper-surface of a hyper-sphere], 2''π'' &lt;sup&gt;2&lt;/sup&gt;''r'' &lt;sup&gt;3&lt;/sup&gt;.&quot;}} this as an instance in which dimensional analogy can fail us as a method, but it is really our failure to recognize whether a one- or two-dimensional analogy is the appropriate method.|name=two-dimensional analogy}}|name=double rotations}}

=== The 3 Cartesian bases of the 24-cell ===
There are three distinct orientations of the tesseractic honeycomb which could be made to coincide with the 24-cell [[#Radially equilateral honeycomb|honeycomb]], depending on which of the 24-cell's three disjoint sets of 8 orthogonal vertices (which set of 4 perpendicular axes, or equivalently, which inscribed basis 16-cell){{Efn|name=three basis 16-cells}} was chosen to align it, just as three tesseracts can be inscribed in the 24-cell, rotated with respect to each other.{{Efn|name=three 8-cells}} The distance from one of these orientations to another is an [[#Isoclinic rotations|isoclinic rotation]] through 60 degrees (a [[W:Rotations in 4-dimensional Euclidean space#Double rotations|double rotation]] of 60 degrees in each pair of orthogonal invariant planes, around a single fixed point).{{Efn|name=Clifford displacement}} This rotation can be seen most clearly in the hexagonal central planes, where every hexagon rotates to change which of its three diameters is aligned with a coordinate system axis.{{Efn|name=non-orthogonal hexagons|group=}}

=== Planes of rotation ===
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes.{{Sfn|Kim|Rote|2016|p=6|loc=§5. Four-Dimensional Rotations}} Thus the general rotation in 4-space is a ''double rotation''.{{Sfn|Perez-Gracia|Thomas|2017|loc=§7. Conclusions|ps=; &quot;Rotations in three dimensions are determined by a rotation axis and the rotation angle about it, where the rotation axis is perpendicular to the plane in which points are being rotated. The situation in four dimensions is more complicated. In this case, rotations are determined by two orthogonal planes
and two angles, one for each plane. Cayley proved that a general 4D rotation can always be decomposed into two 4D rotations, each of them being determined by two equal rotation angles up to a sign change.&quot;}} There are two important special cases, called a ''simple rotation'' and an ''isoclinic rotation''.{{Efn|A [[W:Rotations in 4-dimensional Euclidean space|rotation in 4-space]] is completely characterized by choosing an invariant plane and an angle and direction (left or right) through which it rotates, and another angle and direction through which its one completely orthogonal invariant plane rotates. Two rotational displacements are identical if they have the same pair of invariant planes of rotation, through the same angles in the same directions (and hence also the same chiral pairing of directions). Thus the general rotation in 4-space is a '''double rotation''', characterized by ''two'' angles. A '''simple rotation''' is a special case in which one rotational angle is 0.{{Efn|Any double rotation (including an isoclinic rotation) can be seen as the composition of two simple rotations ''a'' and ''b'': the ''left'' double rotation as ''a'' then ''b'', and the ''right'' double rotation as ''b'' then ''a''. Simple rotations are not commutative; left and right rotations (in general) reach different destinations. The difference between a double rotation and its two composing simple rotations is that the double rotation is 4-dimensionally diagonal: each moving vertex reaches its destination ''directly'' without passing through the intermediate point touched by ''a'' then ''b'', or the other intermediate point touched by ''b'' then ''a'', by rotating on a single helical geodesic (so it is the shortest path).{{Efn|name=helical geodesic}} Conversely, any simple rotation can be seen as the composition of two ''equal-angled'' double rotations (a left isoclinic rotation and a right isoclinic rotation),{{Efn|name=one true circle}} as discovered by [[W:Arthur Cayley|Cayley]]; perhaps surprisingly, this composition ''is'' commutative, and is possible for any double rotation as well.{{Sfn|Perez-Gracia|Thomas|2017}}|name=double rotation}} An '''isoclinic rotation''' is a different special case,{{Efn|name=Clifford displacement}} similar but not identical to two simple rotations through the ''same'' angle.{{Efn|name=plane movement in rotations}}|name=identical rotations}}

==== Simple rotations ====
[[Image:24-cell.gif|thumb|A 3D projection of a 24-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Efn|name=planes through vertices}}]]In 3 dimensions a spinning polyhedron has a single invariant central ''plane of rotation''. The plane is an [[W:Invariant set|invariant set]] because each point in the plane moves in a circle but stays within the plane. Only ''one'' of a polyhedron's central planes can be invariant during a particular rotation; the choice of invariant central plane, and the angular distance and direction it is rotated, completely specifies the rotation. Points outside the invariant plane also move in circles (unless they are on the fixed ''axis of rotation'' perpendicular to the invariant plane), but the circles do not lie within a [[#Geodesics|''central'' plane]].

When a 4-polytope is rotating with only one invariant central plane, the same kind of [[W:Rotations in 4-dimensional Euclidean space#Simple rotations|simple rotation]] is happening that occurs in 3 dimensions. One difference is that instead of a fixed axis of rotation, there is an entire fixed central plane in which the points do not move. The fixed plane is the one central plane that is [[W:Completely orthogonal|completely orthogonal]] to the invariant plane of rotation. In the 24-cell, there is a simple rotation which will take any vertex ''directly'' to any other vertex, also moving most of the other vertices but leaving at least 2 and at most 6 other vertices fixed (the vertices that the fixed central plane intersects). The vertex moves along a great circle in the invariant plane of rotation between adjacent vertices of a great hexagon, a great square or a great [[W:Digon|digon]], and the completely orthogonal fixed plane is a digon, a square or a hexagon, respectively.{{Efn|In the 24-cell each great square plane is [[W:Completely orthogonal|completely orthogonal]] to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two antipodal vertices: a great [[W:Digon|digon]] plane.|name=pairs of completely orthogonal planes}}

==== Double rotations ====
[[Image:24-cell-orig.gif|thumb|A 3D projection of a 24-cell performing a [[W:SO(4)#Geometry of 4D rotations|double rotation]].]]The points in the completely orthogonal central plane are not ''constrained'' to be fixed. It is also possible for them to be rotating in circles, as a second invariant plane, at a rate independent of the first invariant plane's rotation: a [[W:Rotations in 4-dimensional Euclidean space#Double rotations|double rotation]] in two perpendicular non-intersecting planes{{Efn|name=how planes intersect at a single point}} of rotation at once.{{Efn|name=double rotation}} In a double rotation there is no fixed plane or axis: every point moves except the center point. The angular distance rotated may be different in the two completely orthogonal central planes, but they are always both invariant: their circularly moving points remain within the plane ''as the whole plane tilts sideways'' in the completely orthogonal rotation. A rotation in 4-space always has (at least) ''two'' completely orthogonal invariant planes of rotation, although in a simple rotation the angle of rotation in one of them is 0.

Double rotations come in two [[W:Chiral|chiral]] forms: ''left'' and ''right'' rotations.{{Efn|The adjectives ''left'' and ''right'' are commonly used in two different senses, to distinguish two distinct kinds of pairing. They can refer to alternate directions: the hand on the left side of the body, versus the hand on the right side. Or they can refer to a [[W:Chiral|chiral]] pair of enantiomorphous objects: a left hand is the mirror image of a right hand (like an inside-out glove). In the case of hands the sense intended is rarely ambiguous, because of course the hand on your left side ''is'' the mirror image of the hand on your right side: a hand is either left ''or'' right in both senses. But in the case of double-rotating 4-dimensional objects, only one sense of left versus right properly applies: the enantiomorphous sense, in which the left and right rotation are inside-out mirror images of each other. There ''are'' two directions, which we may call positive and negative, in which moving vertices may be circling on their isoclines, but it would be ambiguous to label those circular directions &quot;right&quot; and &quot;left&quot;, since a rotation's direction and its chirality are independent properties: a right (or left) rotation may be circling in either the positive or negative direction. The left rotation is not rotating &quot;to the left&quot;, the right rotation is not rotating &quot;to the right&quot;, and unlike your left and right hands, double rotations do not lie on the left or right side of the 4-polytope. If double rotations must be analogized to left and right hands, they are better thought of as a pair of clasped hands, centered on the body, because of course they have a common center.|name=clasped hands}} In a double rotation each vertex moves in a spiral along two orthogonal great circles at once.{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in their places in the plane ''as the plane moves'', rotating ''and'' tilting sideways by the angle that the ''other'' plane rotates.|name=helical geodesic}} Either the path is right-hand [[W:Screw thread#Handedness|threaded]] (like most screws and bolts), moving along the circles in the &quot;same&quot; directions, or it is left-hand threaded (like a reverse-threaded bolt), moving along the circles in what we conventionally say are &quot;opposite&quot; directions (according to the [[W:Right hand rule|right hand rule]] by which we conventionally say which way is &quot;up&quot; on each of the 4 coordinate axes).{{Sfn|Perez-Gracia|Thomas|2017|loc=§5. A useful mapping|pp=12−13}}

In double rotations of the 24-cell that take vertices to vertices, one invariant plane of rotation contains either a great hexagon, a great square, or only an axis (two vertices, a great digon). The completely orthogonal invariant plane of rotation will necessarily contain a great digon, a great square, or a great hexagon, respectively. The selection of an invariant plane of rotation, a rotational direction and angle through which to rotate it, and a rotational direction and angle through which to rotate its completely orthogonal plane, completely determines the nature of the rotational displacement. In the 24-cell there are several noteworthy kinds of double rotation permitted by these parameters.{{Sfn|Coxeter|1995|loc=(Paper 3) ''Two aspects of the regular 24-cell in four dimensions''|pp=30-32|ps=; §3. The Dodecagonal Aspect;{{Efn|name=Petrie dodecagram and Clifford hexagram}} Coxeter considers the 150°/30° double rotation of period 12 which locates 12 of the 225 distinct 24-cells inscribed in the [[120-cell]], a regular 4-polytope with 120 dodecahedral cells that is the convex hull of the compound of 25 disjoint 24-cells.}}

==== Isoclinic rotations ====
When the angles of rotation in the two completely orthogonal invariant planes are exactly the same, a [[W:Rotations in 4-dimensional Euclidean space#Special property of SO(4) among rotation groups in general|remarkably symmetric]] [[W:Geometric transformation|transformation]] occurs:{{Sfn|Perez-Gracia|Thomas|2017|loc=§2. Isoclinic rotations|pp=2−3}} all the great circle planes Clifford parallel{{Efn|name=Clifford parallels}} to the pair of invariant planes become pairs of invariant planes of rotation themselves, through that same angle, and the 4-polytope rotates [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] in many directions at once.{{Sfn|Kim|Rote|2016|loc=§6. Angles between two Planes in 4-Space|pp=7-10}} Each vertex moves an equal distance in four orthogonal directions at the same time.{{Efn|In an [[#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance|Pythagorean distance]] equal to the square root of four times the square of that distance. All vertices are displaced to a vertex at least two edge lengths away.{{Efn|name=missing the nearest vertices}} For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} ≈ 0.866 (half the {{radic|3}} chord length) in four orthogonal directions.{{Efn|{{radic|3/4}} ≈ 0.866 is the long radius of the {{radic|2}}-edge regular tetrahedron (the unit-radius 16-cell's cell). Those four tetrahedron radii are not orthogonal, and they radiate symmetrically compressed into 3 dimensions (not 4). The four orthogonal {{radic|3/4}} ≈ 0.866 displacements summing to a 120° degree displacement in the 24-cell's characteristic isoclinic rotation{{Efn|name=isoclinic 4-dimensional diagonal}} are not as easy to visualize as radii, but they can be imagined as successive orthogonal steps in a path extending in all 4 dimensions, along the orthogonal edges of a [[5-cell#Orthoschemes|4-orthoscheme]]. In an actual left (or right) isoclinic rotation the four orthogonal {{radic|3/4}} ≈ 0.866 steps of each 120° displacement are concurrent, not successive, so they ''are'' actually symmetrical radii in 4 dimensions. In fact they are four orthogonal [[#Characteristic orthoscheme|mid-edge radii of a unit-radius 24-cell]] centered at the rotating vertex. Finally, in 2 dimensional units, {{radic|3/4}} ≈ 0.866 is the area of the equilateral triangle face of the unit-edge, unit-radius 24-cell. The area of the radial equilateral triangles in a unit-radius radially equilateral polytope{{Efn|name=radially equilateral}} is {{radic|3/4}} ≈ 0.866.|name=root 3/4}}|name=isoclinic 4-dimensional diagonal}} In the 24-cell any isoclinic rotation through 60 degrees in a hexagonal plane takes each vertex to a vertex two edge lengths away, rotates ''all 16'' hexagons by 60 degrees, and takes ''every'' great circle polygon (square,{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} hexagon or triangle) to a Clifford parallel great circle polygon of the same kind 120 degrees away. An isoclinic rotation is also called a ''Clifford displacement'', after its [[W:William Kingdon Clifford|discoverer]].{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle in the completely orthogonal rotation.{{Efn|name=one true circle}} A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways.{{Efn|name=plane movement in rotations}} All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon 120 degrees away. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 120 degrees away.|name=Clifford displacement}}

The 24-cell in the ''double'' rotation animation appears to turn itself inside out.{{Efn|That a double rotation can turn a 4-polytope inside out is even more noticeable in the [[W:Rotations in 4-dimensional Euclidean space#Double rotations|tesseract double rotation]].}} It appears to, because it actually does, reversing the [[W:Chirality|chirality]] of the whole 4-polytope just the way your bathroom mirror reverses the chirality of your image by a 180 degree reflection. Each 360 degree isoclinic rotation is as if the 24-cell surface had been stripped off like a glove and turned inside out, making a right-hand glove into a left-hand glove (or vice versa).{{Sfn|Coxeter|1973|p=141|loc=§7.x. Historical remarks|ps=; &quot;[[W:August Ferdinand Möbius|Möbius]] realized, as early as 1827, that a four-dimensional rotation would be required to bring two enantiomorphous solids into coincidence. This idea was neatly deployed by [[W:H. G. Wells|H. G. Wells]] in ''The Plattner Story''.&quot;}}

In a simple rotation of the 24-cell in a hexagonal plane, each vertex in the plane rotates first along an edge to an adjacent vertex 60 degrees away. But in an isoclinic rotation in ''two'' completely orthogonal planes one of which is a great hexagon,{{Efn|name=pairs of completely orthogonal planes}} each vertex rotates first to a vertex ''two'' edge lengths away ({{radic|3}} and 120° distant). The double 60-degree rotation's helical geodesics pass through every other vertex, missing the vertices in between.{{Efn|In an isoclinic rotation vertices move diagonally, like the [[W:bishop (chess)|bishop]]s in [[W:Chess|chess]]. Vertices in an isoclinic rotation ''cannot'' reach their orthogonally nearest neighbor vertices{{Efn|name=8 nearest vertices}} by double-rotating directly toward them (and also orthogonally to that direction), because that double rotation takes them diagonally between their nearest vertices, missing them, to a vertex farther away in a larger-radius surrounding shell of vertices,{{Efn|name=nearest isoclinic vertices are {{radic|3}} away in third surrounding shell}} the way bishops are confined to the white or black squares of the [[W:Chessboard|chessboard]] and cannot reach squares of the opposite color, even those immediately adjacent.{{Efn|Isoclinic rotations{{Efn|name=isoclinic geodesic}} partition the 24 cells (and the 24 vertices) of the 24-cell into two disjoint subsets of 12 cells (and 12 vertices), even and odd (or black and white), which shift places among themselves, in a manner dimensionally analogous to the way the [[W:Bishop (chess)|bishops]]' diagonal moves{{Efn|name=missing the nearest vertices}} restrict them to the black or white squares of the [[W:Chessboard|chessboard]].{{Efn|Left and right isoclinic rotations partition the 24 cells (and 24 vertices) into black and white in the same way.{{Sfn|Coxeter|1973|p=156|loc=|ps=: &quot;...the chess-board has an n-dimensional analogue.&quot;}} The rotations of all fibrations of the same kind of great polygon use the same chessboard, which is a convention of the coordinate system based on even and odd coordinates. ''Left and right are not colors:'' in either a left (or right) rotation half the moving vertices are black, running along black isoclines through black vertices, and the other half are white vertices, also rotating among themselves.{{Efn|Chirality and even/odd parity are distinct flavors. Things which have even/odd coordinate parity are '''''black or white:''''' the squares of the [[W:Chessboard|chessboard]],{{Efn|Since it is difficult to color points and lines white, we sometimes use black and red instead of black and white. In particular, isocline chords are sometimes shown as black or red ''dashed'' lines.{{Efn|name=interior features}}|name=black and red}} '''cells''', '''vertices''' and the '''isoclines''' which connect them by isoclinic rotation.{{Efn|name=isoclinic geodesic}} Everything else is '''''black and white:''''' e.g. adjacent '''face-bonded cell pairs''', or '''edges''' and '''chords''' which are black at one end and white at the other. Things which have [[W:Chirality|chirality]] come in '''''right or left''''' enantiomorphous forms: '''[[#Isoclinic rotations|isoclinic rotations]]''' and '''chiral objects''' which include '''[[#Characteristic orthoscheme|characteristic orthoscheme]]s''', '''[[#Chiral symmetry operations|sets of Clifford parallel great polygon planes]]''',{{Efn|name=completely orthogonal Clifford parallels are special}} '''[[W:Fiber bundle|fiber bundle]]s''' of Clifford parallel circles (whether or not the circles themselves are chiral), and the chiral cell rings of tetrahedra found in the [[16-cell#Helical construction|16-cell]] and [[600-cell#Boerdijk–Coxeter helix rings|600-cell]]. Things which have '''''neither''''' an even/odd parity nor a chirality include all '''edges''' and '''faces''' (shared by black and white cells), '''[[#Geodesics|great circle polygons]]''' and their '''[[W:Hopf fibration|fibration]]s''', and non-chiral cell rings such as the 24-cell's [[#Cell rings|cell rings of octahedra]]. Some things are associated with '''''both''''' an even/odd parity and a chirality: '''isoclines''' are black or white because they connect vertices which are all of the same color, and they ''act'' as left or right chiral objects when they are vertex paths in a left or right rotation, although they have no inherent chirality themselves. Each left (or right) rotation traverses an equal number of black and white isoclines.{{Efn|name=Clifford polygon}}|name=left-right versus black-white}}|name=isoclinic chessboard}}|name=black and white}} Things moving diagonally move farther than 1 unit of distance in each movement step ({{radic|2}} on the chessboard, {{radic|3}} in the 24-cell), but at the cost of ''missing'' half the destinations.{{Efn|name=one true circle}} However, in an isoclinic rotation of a rigid body all the vertices rotate at once, so every destination ''will'' be reached by some vertex. Moreover, there is another isoclinic rotation in hexagon invariant planes which does take each vertex to an adjacent (nearest) vertex. A 24-cell can displace each vertex to a vertex 60° away (a nearest vertex) by rotating isoclinically by 30° in two completely orthogonal invariant planes (one of them a hexagon), ''not'' by double-rotating directly toward the nearest vertex (and also orthogonally to that direction), but instead by double-rotating directly toward a more distant vertex (and also orthogonally to that direction). This helical 30° isoclinic rotation takes the vertex 60° to its nearest-neighbor vertex by a ''different path'' than a simple 60° rotation would. The path along the helical isocline and the path along the simple great circle have the same 60° arc-length, but they consist of disjoint sets of points (except for their endpoints, the two vertices). They are both geodesic (shortest) arcs, but on two alternate kinds of geodesic circle. One is doubly curved (through all four dimensions), and one is simply curved (lying in a two-dimensional plane).|name=missing the nearest vertices}} Each {{radic|3}} chord of the helical geodesic{{Efn|Although adjacent vertices on the isoclinic geodesic are a {{radic|3}} chord apart, a point on a rigid body under rotation does not travel along a chord: it moves along an arc between the two endpoints of the chord (a longer distance). In a ''simple'' rotation between two vertices {{radic|3}} apart, the vertex moves along the arc of a hexagonal great circle to a vertex two great hexagon edges away, and passes through the intervening hexagon vertex midway. But in an ''isoclinic'' rotation between two vertices {{radic|3}} apart the vertex moves along a helical arc called an isocline (not a planar great circle),{{Efn|name=isoclinic geodesic}} which does ''not'' pass through an intervening vertex: it misses the vertex nearest to its midpoint.{{Efn|name=missing the nearest vertices}}|name=isocline misses vertex}} crosses between two Clifford parallel hexagon central planes, and lies in another hexagon central plane that intersects them both.{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart,{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline, and just {{radic|1}} apart on some great hexagon. Between V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt;, the isoclinic rotation has gone the long way around the 24-cell over two {{radic|3}} chords to reach a vertex that was only {{radic|1}} away. More generally, isoclines are geodesics because the distance between their successive vertices is the shortest distance between those two vertices in some rotation connecting them, but on the 3-sphere there may be another rotation which is shorter. A path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}} P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;3&lt;/sub&gt; are adjacent vertices, {{radic|1}} apart.{{Efn|name=skew hexagram}} The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation, and one half of the 24-cell's double-loop hexagram&lt;sub&gt;2&lt;/sub&gt; Clifford polygon.{{Efn|name=Clifford polygon}}|name=360 degree geodesic path visiting 3 hexagonal planes}} The {{radic|3}} chords meet at a 60° angle, but since they lie in different planes they form a [[W:Helix|helix]] not a [[#Great triangles|triangle]]. Three {{radic|3}} chords and 360° of rotation takes the vertex to an adjacent vertex, not back to itself. The helix of {{radic|3}} chords closes into a loop only after six {{radic|3}} chords: a 720° rotation twice around the 24-cell{{Efn|An isoclinic rotation by 60° is two simple rotations by 60° at the same time.{{Efn|The composition of two simple 60° rotations in a pair of completely orthogonal invariant planes is a 60° isoclinic rotation in ''four'' pairs of completely orthogonal invariant planes.{{Efn|name=double rotation}} Thus the isoclinic rotation is the compound of four simple rotations, and all 24 vertices rotate in invariant hexagon planes, versus just 6 vertices in a simple rotation.}} It moves all the vertices 120° at the same time, in various different directions. Six successive diagonal rotational increments, of 60°x60° each, move each vertex through 720° on a Möbius double loop called an ''isocline'', ''twice'' around the 24-cell and back to its point of origin, in the ''same time'' (six rotational units) that it would take a simple rotation to take the vertex ''once'' around the 24-cell on an ordinary great circle.{{Efn|name=double threaded}} The helical double loop 4𝝅 isocline is just another kind of ''single'' full circle, of the same time interval and period (6 chords) as the simple great circle. The isocline is ''one'' true circle,{{Efn|name=4-dimensional great circles}} as perfectly round and geodesic as the simple great circle, even through its chords are {{radic|3}} longer, its circumference is 4𝝅 instead of 2𝝅,{{Efn|All 3-sphere isoclines of the same circumference are directly congruent circles.{{Efn|name=not all isoclines are circles}} An ordinary great circle is an isocline of circumference &lt;math&gt;2\pi r&lt;/math&gt;; simple rotations of unit-radius polytopes take place on 2𝝅 isoclines. Double rotations may have isoclines of other than &lt;math&gt;2\pi r&lt;/math&gt; circumference. The ''characteristic rotation'' of a regular 4-polytope is the isoclinic rotation in which the central planes containing its edges are invariant planes of rotation. The 16-cell and 24-cell edge-rotate on isoclines of 4𝝅 circumference. The 600-cell edge-rotates on isoclines of 5𝝅 circumference.|name=isocline circumference}} it circles through four dimensions instead of two,{{Efn|name=Villarceau circles}} and it acts in two chiral forms (left and right) even though all such circles of the same circumference are directly congruent.{{Efn|name=Clifford polygon}} Nevertheless, to avoid confusion we always refer to it as an ''isocline'' and reserve the term ''great circle'' for an ordinary great circle in the plane.{{Efn|name=isocline}}|name=one true circle}} on a [[W:Skew polygon#Regular skew polygons in four dimensions|skew]] [[W:Hexagram|hexagram]] with {{radic|3}} edges.{{Efn|name=skew hexagram}} Even though all 24 vertices and all the hexagons rotate at once, a 360 degree isoclinic rotation moves each vertex only halfway around its circuit. After 360 degrees each helix has departed from 3 vertices and reached a fourth vertex adjacent to the original vertex, but has ''not'' arrived back exactly at the vertex it departed from. Each central plane (every hexagon or square in the 24-cell) has rotated 360 degrees ''and'' been tilted sideways all the way around 360 degrees back to its original position (like a coin flipping twice), but the 24-cell's [[W:Orientation entanglement|orientation]] in the 4-space in which it is embedded is now different.{{Sfn|Mebius|2015|loc=Motivation|pp=2-3|ps=; &quot;This research originated from ... the desire to construct a computer implementation of a specific motion of the human arm, known among folk dance experts as the ''Philippine wine dance'' or ''Binasuan'' and performed by physicist [[W:Richard P. Feynman|Richard P. Feynman]] during his [[W:Dirac|Dirac]] memorial lecture 1986{{Sfn|Feynman|Weinberg|1987|loc=The reason for antiparticles}} to show that a single rotation (2𝝅) is not equivalent in all respects to no rotation at all, whereas a double rotation (4𝝅) is.&quot;}} Because the 24-cell is now inside-out, if the isoclinic rotation is continued in the ''same'' direction through another 360 degrees, the 24 moving vertices will pass through the other half of the vertices that were missed on the first revolution (the 12 antipodal vertices of the 12 that were hit the first time around), and each isoclinic geodesic ''will'' arrive back at the vertex it departed from, forming a closed six-chord helical loop. It takes a 720 degree isoclinic rotation for each [[#Helical hexagrams and their isoclines|hexagram&lt;sub&gt;2&lt;/sub&gt; geodesic]] to complete a circuit through every ''second'' vertex of its six vertices by [[W:Winding number|winding]] around the 24-cell twice, returning the 24-cell to its original chiral orientation.{{Efn|In a 720° isoclinic rotation of a ''rigid'' 24-cell the 24 vertices rotate along four separate Clifford parallel hexagram&lt;sub&gt;2&lt;/sub&gt; geodesic loops (six vertices circling in each loop) and return to their original positions.{{Efn|name=Villarceau circles}}}}

The hexagonal winding path that each vertex takes as it loops twice around the 24-cell forms a double helix bent into a [[W:Möbius strip|Möbius ring]], so that the two strands of the double helix form a continuous single strand in a closed loop.{{Efn|Because the 24-cell's helical hexagram&lt;sub&gt;2&lt;/sub&gt; geodesic is bent into a twisted ring in the fourth dimension like a [[W:Möbius strip|Möbius strip]], its [[W:Screw thread|screw thread]] doubles back across itself in each revolution, reversing its chirality{{Efn|name=Clifford polygon}} but without ever changing its even/odd parity of rotation (black or white).{{Efn|name=black and white}} The 6-vertex isoclinic path forms a Möbius double loop, like a 3-dimensional double helix with the ends of its two parallel 3-vertex helices cross-connected to each other. This 60° isocline{{Efn|A strip of paper can form a [[W:Möbius strip#Polyhedral surfaces and flat foldings|flattened Möbius strip]] in the plane by folding it at &lt;math&gt;60^\circ&lt;/math&gt; angles so that its center line lies along an equilateral triangle, and attaching the ends. The shortest strip for which this is possible consists of three equilateral paper triangles, folded at the edges where two triangles meet. Since the loop traverses both sides of each paper triangle, it is a hexagonal loop over six equilateral triangles. Its [[W:Aspect ratio|aspect ratio]]{{snd}}the ratio of the strip's length{{efn|The length of a strip can be measured at its centerline, or by cutting the resulting Möbius strip perpendicularly to its boundary so that it forms a rectangle.}} to its width{{snd}}is {{nowrap|&lt;math&gt;\sqrt 3\approx 1.73&lt;/math&gt;.}}}} is a [[W:Skew polygon|skewed]] instance of the [[W:Polygram (geometry)#Regular compound polygons|regular compound polygon]] denoted {6/2}{{=}}2{3} or hexagram&lt;sub&gt;2&lt;/sub&gt;.{{Efn|name=skew hexagram}} Successive {{radic|3}} edges belong to different [[#8-cell|8-cells]], as the 720° isoclinic rotation takes each hexagon through all six hexagons in the [[#6-cell rings|6-cell ring]], and each 8-cell through all three 8-cells twice.{{Efn|name=three 8-cells}}|name=double threaded}} In the first revolution the vertex traverses one 3-chord strand of the double helix; in the second revolution it traverses the second 3-chord strand, moving in the same rotational direction with the same handedness (bending either left or right) throughout. Although this isoclinic Möbius [[#6-cell rings|ring]] is a circular spiral through all 4 dimensions, not a 2-dimensional circle, like a great circle it is a geodesic because it is the shortest path from vertex to vertex.{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''.{{Efn||name=double rotation}} A '''[[W:Geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:Helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:Screw threads|screw threads]] either, because they form a closed loop like any circle.{{Efn|name=double threaded}} Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in ''two'' orthogonal great circles at once.{{Efn|Isoclinic geodesics or ''isoclines'' are 4-dimensional great circles in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two orthogonal great circles at once.{{Efn|name=not all isoclines are circles}} They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of great circles (great 1-spheres).{{Efn|name=great 2-spheres}} Discrete isoclines are polygons;{{Efn|name=Clifford polygon}} discrete great 2-spheres are polyhedra.|name=4-dimensional great circles}} They are true circles,{{Efn|name=one true circle}} and even form [[W:Hopf fibration|fibrations]] like ordinary 2-dimensional great circles.{{Efn|name=hexagonal fibrations}}{{Efn|name=square fibrations}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are [[W:Geodesics|geodesics]], and isoclines on the [[W:3-sphere|3-sphere]] are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.|name=not all isoclines are circles}} they always occur in pairs{{Efn|Isoclines on the 3-sphere occur in non-intersecting pairs of even/odd coordinate parity.{{Efn|name=black and white}} A single black or white isocline forms a [[W:Möbius loop|Möbius loop]] called the {1,1} torus knot or Villarceau circle{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot rather than as a planar cut.&quot;}} in which each of two &quot;circles&quot; linked in a Möbius &quot;figure eight&quot; loop traverses through all four dimensions.{{Efn|name=Clifford polygon}} The double loop is a true circle in four dimensions.{{Efn|name=one true circle}} Even and odd isoclines are also linked, not in a Möbius loop but as a [[W:Hopf link|Hopf link]] of two non-intersecting circles,{{Efn|name=Clifford parallels}} as are all the Clifford parallel isoclines of a [[W:Hopf fibration|Hopf fiber bundle]].|name=Villarceau circles}} as [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]], the geodesic paths traversed by vertices in an [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] around the 3-sphere through the non-adjacent vertices{{Efn|name=missing the nearest vertices}} of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew]] '''Clifford polygon'''.{{Efn|name=Clifford polygon}}|name=isoclinic geodesic}}

=== Clifford parallel polytopes ===
Two planes are also called ''isoclinic'' if an isoclinic rotation will bring them together.{{Efn|name=two angles between central planes}} The isoclinic planes are precisely those central planes with Clifford parallel geodesic great circles.{{Sfn|Kim|Rote|2016|loc=Relations to Clifford parallelism|pp=8-9}} Clifford parallel great circles do not intersect,{{Efn|name=Clifford parallels}} so isoclinic great circle polygons have disjoint vertices. In the 24-cell every hexagonal central plane is isoclinic to three others, and every square central plane is isoclinic to five others. We can pick out 4 mutually isoclinic (Clifford parallel) great hexagons (four different ways) covering all 24 vertices of the 24-cell just once (a hexagonal fibration).{{Efn|The 24-cell has four sets of 4 non-intersecting [[W:Clifford parallel|Clifford parallel]]{{Efn|name=Clifford parallels}} great circles each passing through 6 vertices (a great hexagon), with only one great hexagon in each set passing through each vertex, and the 4 hexagons in each set reaching all 24 vertices.{{Efn|name=four hexagonal fibrations}} Each set constitutes a discrete [[W:Hopf fibration|Hopf fibration]] of non-intersecting linked great circles. The 24-cell can also be divided (eight different ways) into 4 disjoint subsets of 6 vertices (hexagrams) that do ''not'' lie in a hexagonal central plane, each skew [[#Helical hexagrams and their  isoclines|hexagram forming an isoclinic geodesic or ''isocline'']] that is the rotational circle traversed by those 6 vertices in one particular left or right [[#Isoclinic rotations|isoclinic rotation]]. Each of these sets of four Clifford parallel isoclines belongs to one of the four discrete Hopf fibrations of hexagonal great circles.{{Efn|Each set of [[W:Clifford parallel|Clifford parallel]] [[#Geodesics|great circle]] polygons is a different bundle of fibers than the corresponding set of Clifford parallel isocline{{Efn|name=isoclinic geodesic}} polygrams, but the two [[W:Fiber bundles|fiber bundles]] together constitute the ''same'' discrete [[W:Hopf fibration|Hopf fibration]], because they enumerate the 24 vertices together by their intersection in the same distinct (left or right) isoclinic rotation. They are the [[W:Warp and woof|warp and woof]] of the same woven fabric that is the fibration.|name=great circles and isoclines are same fibration}}|name=hexagonal fibrations}} We can pick out 6 mutually isoclinic (Clifford parallel) great squares{{Efn|Each great square plane is isoclinic (Clifford parallel) to five other square planes but [[W:Completely orthogonal|completely orthogonal]] to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal). There is also another way in which completely orthogonal planes are in a distinguished category of Clifford parallel planes: they are not [[W:Chiral|chiral]], or strictly speaking they possess both chiralities. A pair of isoclinic (Clifford parallel) planes is either a ''left pair'' or a ''right pair'', unless they are separated by two angles of 90° (completely orthogonal planes) or 0° (coincident planes).{{Sfn|Kim|Rote|2016|p=8|loc=Left and Right Pairs of Isoclinic Planes}} Most isoclinic planes are brought together only by a left isoclinic rotation or a right isoclinic rotation, respectively. Completely orthogonal planes are special: the pair of planes is both a left and a right pair, so either a left or a right isoclinic rotation will bring them together. This occurs because isoclinic square planes are 180° apart at all vertex pairs: not just Clifford parallel but completely orthogonal. The isoclines (chiral vertex paths){{Efn|name=isoclinic geodesic}} of 90° isoclinic rotations are special for the same reason. Left and right isoclines loop through the same set of antipodal vertices (hitting both ends of each [[16-cell#Helical construction|16-cell axis]]), instead of looping through disjoint left and right subsets of black or white antipodal vertices (hitting just one end of each axis), as the left and right isoclines of all other fibrations do.|name=completely orthogonal Clifford parallels are special}} (three different ways) covering all 24 vertices of the 24-cell just once (a square fibration).{{Efn|The 24-cell has three sets of 6 non-intersecting Clifford parallel great circles each passing through 4 vertices (a great square), with only one great square in each set passing through each vertex, and the 6 squares in each set reaching all 24 vertices.{{Efn|name=three square fibrations}} Each set constitutes a discrete [[W:Hopf fibration|Hopf fibration]] of 6 non-intersecting linked great squares, which is simply the compound of the three inscribed 16-cell's discrete Hopf fibrations of 2 great squares. The 24-cell can also be divided (six different ways) into 3 disjoint subsets of 8 vertices (octagrams) that do ''not'' lie in a square central plane, but comprise a 16-cell and lie on a skew [[#Helical octagrams and thei isoclines|octagram&lt;sub&gt;3&lt;/sub&gt; forming an isoclinic geodesic or ''isocline'']] that is the rotational cirle traversed by those 8 vertices in one particular left or right [[16-cell#Rotations|isoclinic rotation]] as they rotate positions within the 16-cell.|name=square fibrations}} Every isoclinic rotation taking vertices to vertices corresponds to a discrete fibration.{{Efn|name=fibrations are distinguished only by rotations}}

Two dimensional great circle polygons are not the only polytopes in the 24-cell which are parallel in the Clifford sense.{{Sfn|Tyrrell|Semple|1971|pp=1-9|loc=§1. Introduction}} Congruent polytopes of 2, 3 or 4 dimensions can be said to be Clifford parallel in 4 dimensions if their corresponding vertices are all the same distance apart. The three 16-cells inscribed in the 24-cell are Clifford parallels. Clifford parallel polytopes are ''completely disjoint'' polytopes.{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or linage.|name=completely disjoint}} A 60 degree isoclinic rotation in hexagonal planes takes each 16-cell to a disjoint 16-cell. Like all [[#Double rotations|double rotations]], isoclinic rotations come in two [[W:Chiral|chiral]] forms: there is a disjoint 16-cell to the ''left'' of each 16-cell, and another to its ''right''.{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=Six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[#Great hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[#Great squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:Tesseract|hypercube (a tesseract or 8-cell)]], in [[#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells (as in [[#Reciprocal constructions from 8-cell and 16-cell|Gosset's construction of the 24-cell]]). The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[W:3-sphere|3-sphere]] symmetric: four [[#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' orthogonal great circles at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:Chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell (whose vertices are one {{radic|1}} edge away) by rotating toward it;{{Efn|name=missing the nearest vertices}} it can only reach the 16-cell ''beyond'' it (120° away). But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only [[#Double rotations|sense in which the two 16-cells are left or right]] of each other.){{Efn|name=clasped hands}}|name=three isoclinic 16-cells}}

All Clifford parallel 4-polytopes are related by an isoclinic rotation,{{Efn|name=Clifford displacement}} but not all isoclinic polytopes are Clifford parallels (completely disjoint).{{Efn|All isoclinic ''planes'' are Clifford parallels (completely disjoint).{{Efn|name=completely disjoint}} Three and four dimensional cocentric objects may intersect (sharing elements) but still be related by an isoclinic rotation. Polyhedra and 4-polytopes may be isoclinic and ''not'' disjoint, if all of their corresponding planes are either Clifford parallel, or cocellular (in the same hyperplane) or coincident (the same plane).}} The three 8-cells in the 24-cell are isoclinic but not Clifford parallel. Like the 16-cells, they are rotated 60 degrees isoclinically with respect to each other, but their vertices are not all disjoint (and therefore not all equidistant). Each vertex occurs in two of the three 8-cells (as each 16-cell occurs in two of the three 8-cells).{{Efn|name=three 8-cells}}

Isoclinic rotations relate the convex regular 4-polytopes to each other. An isoclinic rotation of a single 16-cell will generate{{Efn|By ''generate'' we mean simply that some vertex of the first polytope will visit each vertex of the generated polytope in the course of the rotation.}} a 24-cell. A simple rotation of a single 16-cell will not, because its vertices will not reach either of the other two 16-cells' vertices in the course of the rotation. An isoclinic rotation of the 24-cell will generate the 600-cell, and an isoclinic rotation of the 600-cell will generate the 120-cell. (Or they can all be generated directly by an isoclinic rotation of the 16-cell, generating isoclinic copies of itself.) The different convex regular 4-polytopes nest inside each other, and multiple instances of the same 4-polytope hide next to each other in the Clifford parallel spaces that comprise the 3-sphere.{{Sfn|Tyrrell|Semple|1971|loc=Clifford Parallel Spaces and Clifford Reguli|pp=20-33}} For an object of more than one dimension, the only way to reach these parallel subspaces directly is by isoclinic rotation. Like a key operating a four-dimensional lock, an object must twist in two completely perpendicular tumbler cylinders at once in order to move the short distance between Clifford parallel subspaces.

=== Rings ===
In the 24-cell there are sets of rings of six different kinds, described separately in detail in other sections of this article. This section describes how the different kinds of rings are [[#Relationships among interior polytopes|intertwined]].

The 24-cell contains four kinds of [[#Geodesics|geodesic fibers]] (polygonal rings running through vertices): [[#Great squares|great circle squares]] and their [[16-cell#Helical construction|isoclinic helix octagrams]],{{Efn|name=square fibrations}} and [[#Great hexagons|great circle hexagons]] and their [[#Isoclinic rotations|isoclinic helix hexagrams]].{{Efn|name=hexagonal fibrations}} It also contains two kinds of [[#Cell rings|cell rings]] (chains of octahedra bent into a ring in the fourth dimension): four octahedra connected vertex-to-vertex and bent into a square, and six octahedra connected face-to-face and bent into a hexagon.

==== 4-cell rings ====
Four unit-edge-length octahedra can be connected vertex-to-vertex along a common axis of length 4{{radic|2}}. The axis can then be bent into a square of edge length {{radic|2}}. Although it is possible to do this in a space of only three dimensions, that is not how it occurs in the 24-cell. Although the {{radic|2}} axes of the four octahedra occupy the same plane, forming one of the 18 {{radic|2}} great squares of the 24-cell, each octahedron occupies a different 3-dimensional hyperplane,{{Efn|Just as each face of a [[W:Polyhedron|polyhedron]] occupies a different (2-dimensional) face plane, each cell of a [[W:Polychoron|polychoron]] occupies a different (3-dimensional) cell [[W:Hyperplane|hyperplane]].{{Efn|name=hyperplanes}}}} and all four dimensions are utilized. The 24-cell can be partitioned into 6 such 4-cell rings (three different ways), mutually interlinked like adjacent links in a chain (but these [[W:Link (knot theory)|links]] all have a common center). An [[#Isoclinic rotations|isoclinic rotation]] in a great square plane by a multiple of 90° takes each octahedron in the ring to an octahedron in the ring.

==== 6-cell rings ====
[[File:Six face-bonded octahedra.jpg|thumb|400px|A 4-dimensional ring of 6 face-bonded octahedra, bounded by two intersecting sets of three Clifford parallel great hexagons of different colors, cut and laid out flat in 3 dimensional space.{{Efn|name=6-cell ring}}]]Six regular octahedra can be connected face-to-face along a common axis that passes through their centers of volume, forming a stack or column with only triangular faces. In a space of four dimensions, the axis can then be bent 60° in the fourth dimension at each of the six octahedron centers, in a plane orthogonal to all three orthogonal central planes of each octahedron, such that the top and bottom triangular faces of the column become coincident. The column becomes a ring around a hexagonal axis. The 24-cell can be partitioned into 4 such rings (four different ways), mutually interlinked. Because the hexagonal axis joins cell centers (not vertices), it is not a great hexagon of the 24-cell.{{Efn|The axial hexagon of the 6-octahedron ring does not intersect any vertices or edges of the 24-cell, but it does hit faces. In a unit-edge-length 24-cell, it has edges of length 1/2.{{Efn|When unit-edge octahedra are placed face-to-face the distance between their centers of volume is {{radic|2/3}} ≈ 0.816.{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(i): Octahedron}} When 24 face-bonded octahedra are bent into a 24-cell lying on the 3-sphere, the centers of the octahedra are closer together in 4-space. Within the curved 3-dimensional surface space filled by the 24 cells, the cell centers are still {{radic|2/3}} apart along the curved geodesics that join them. But on the straight chords that join them, which dip inside the 3-sphere, they are only 1/2 edge length apart.}} Because it joins six cell centers, the axial hexagon is a great hexagon of the smaller dual 24-cell that is formed by joining the 24 cell centers.{{Efn|name=common core}}}} However, six great hexagons can be found in the ring of six octahedra, running along the edges of the octahedra. In the column of six octahedra (before it is bent into a ring) there are six spiral paths along edges running up the column: three parallel helices spiraling clockwise, and three parallel helices spiraling counterclockwise. Each clockwise helix intersects each counterclockwise helix at two vertices three edge lengths apart. Bending the column into a ring changes these helices into great circle hexagons.{{Efn|There is a choice of planes in which to fold the column into a ring, but they are equivalent in that they produce congruent rings. Whichever folding planes are chosen, each of the six helices joins its own two ends and forms a simple great circle hexagon. These hexagons are ''not'' helices: they lie on ordinary flat great circles. Three of them are Clifford parallel{{Efn|name=Clifford parallels}} and belong to one [[#Great hexagons|hexagonal]] fibration. They intersect the other three, which belong to another hexagonal fibration. The three parallel great circles of each fibration spiral around each other in the sense that they form a [[W:Link (knot theory)|link]] of three ordinary circles, but they are not twisted: the 6-cell ring has no [[W:Torsion of a curve|torsion]], either clockwise or counterclockwise.{{Efn|name=6-cell ring is not chiral}}|name=6-cell ring}} The ring has two sets of three great hexagons, each on three Clifford parallel great circles.{{Efn|The three great hexagons are Clifford parallel, which is different than ordinary parallelism.{{Efn|name=Clifford parallels}} Clifford parallel great hexagons pass through each other like adjacent links of a chain, forming a [[W:Hopf link|Hopf link]]. Unlike links in a 3-dimensional chain, they share the same center point. In the 24-cell, Clifford parallel great hexagons occur in sets of four, not three. The fourth parallel hexagon lies completely outside the 6-cell ring; its 6 vertices are completely disjoint from the ring's 18 vertices.}} The great hexagons in each parallel set of three do not intersect, but each intersects the other three great hexagons (to which it is not Clifford parallel) at two antipodal vertices.

A [[#Simple rotations|simple rotation]] in any of the great hexagon planes by a multiple of 60° rotates only that hexagon invariantly, taking each vertex in that hexagon to a vertex in the same hexagon. An [[#Isoclinic rotations|isoclinic rotation]] by 60° in any of the six great hexagon planes rotates all three Clifford parallel great hexagons invariantly, and takes each octahedron in the ring to a ''non-adjacent'' octahedron in the ring.{{Efn|An isoclinic rotation by a multiple of 60° takes even-numbered octahedra in the ring to even-numbered octahedra, and odd-numbered octahedra to odd-numbered octahedra.{{Efn|In the column of 6 octahedral cells, we number the cells 0-5 going up the column. We also label each vertex with an integer 0-5 based on how many edge lengths it is up the column.}} It is impossible for an even-numbered octahedron to reach an odd-numbered octahedron, or vice versa, by a left or a right isoclinic rotation alone.{{Efn|name=black and white}}|name=black and white octahedra}}

Each isoclinically displaced octahedron is also rotated itself. After a 360° isoclinic rotation each octahedron is back in the same position, but in a different orientation. In a 720° isoclinic rotation, its vertices are returned to their original [[W:Orientation entanglement|orientation]].

Four Clifford parallel great hexagons comprise a discrete fiber bundle covering all 24 vertices in a [[W:Hopf fibration|Hopf fibration]]. The 24-cell has four such [[#Great hexagons|discrete hexagonal fibrations]] &lt;math&gt;F_a, F_b, F_c, F_d&lt;/math&gt;. Each great hexagon belongs to just one fibration, and the four fibrations are defined by disjoint sets of four great hexagons each.{{Sfn|Kim|Rote|2016|loc=§8.3 Properties of the Hopf Fibration|pp=14-16|ps=; Corollary 9. Every great circle belongs to a unique right [(and left)] Hopf bundle.}} Each fibration is the domain (container) of a unique left-right pair of isoclinic rotations (left and right Hopf fiber bundles).{{Efn|The choice of a partitioning of a regular 4-polytope into cell rings (a fibration) is arbitrary, because all of its cells are identical. No particular fibration is distinguished, ''unless'' the 4-polytope is rotating. Each fibration corresponds to a left-right pair of isoclinic rotations in a particular set of Clifford parallel invariant central planes of rotation. In the 24-cell, distinguishing a hexagonal fibration{{Efn|name=hexagonal fibrations}} means choosing a cell-disjoint set of four 6-cell rings that is the unique container of a left-right pair of isoclinic rotations in four Clifford parallel hexagonal invariant planes. The left and right rotations take place in chiral subspaces of that container,{{Sfn|Kim|Rote|2016|p=12|loc=§8 The Construction of Hopf Fibrations; 3}} but the fibration and the octahedral cell rings themselves are not chiral objects.{{Efn|name=6-cell ring is not chiral}}|name=fibrations are distinguished only by rotations}}

Four cell-disjoint 6-cell rings also comprise each discrete fibration defined by four Clifford parallel great hexagons. Each 6-cell ring contains only 18 of the 24 vertices, and only 6 of the 16 great hexagons, which we see illustrated above running along the cell ring's edges: 3 spiraling clockwise and 3 counterclockwise. Those 6 hexagons running along the cell ring's edges are not among the set of four parallel hexagons which define the fibration. For example, one of the four 6-cell rings in fibration &lt;math&gt;F_a&lt;/math&gt; contains 3 parallel hexagons running clockwise along the cell ring's edges from fibration &lt;math&gt;F_b&lt;/math&gt;, and 3 parallel hexagons running counterclockwise along the cell ring's edges from fibration &lt;math&gt;F_c&lt;/math&gt;, but that cell ring contains no great hexagons from fibration &lt;math&gt;F_a&lt;/math&gt; or fibration &lt;math&gt;F_d&lt;/math&gt;.

The 24-cell contains 16 great hexagons, divided into four disjoint sets of four hexagons, each disjoint set uniquely defining a fibration. Each fibration is also a distinct set of four cell-disjoint 6-cell rings. The 24-cell has exactly 16 distinct 6-cell rings. Each 6-cell ring belongs to just one of the four fibrations.{{Efn|The dual polytope of the 24-cell is another 24-cell. It can be constructed by placing vertices at the 24 cell centers. Each 6-cell ring corresponds to a great hexagon in the dual 24-cell, so there are 16 distinct 6-cell rings, as there are 16 distinct great hexagons, each belonging to just one fibration.}}

==== Helical hexagrams and their isoclines ====
Another kind of geodesic fiber, the [[#Isoclinic rotations|helical hexagram isoclines]], can be found within a 6-cell ring of octahedra. Each of these geodesics runs through every ''second'' vertex of a skew [[W:Hexagram|hexagram]]&lt;sub&gt;2&lt;/sub&gt;, which in the unit-radius, unit-edge-length 24-cell has six {{radic|3}} edges. The hexagram does not lie in a single central plane, but is composed of six linked {{radic|3}} chords from the six different hexagon great circles in the 6-cell ring. The isocline geodesic fiber is the path of an isoclinic rotation,{{Efn|name=isoclinic geodesic}} a helical rather than simply circular path around the 24-cell which links vertices two edge lengths apart and consequently must wrap twice around the 24-cell before completing its six-vertex loop.{{Efn|The chord-path of an isocline (the geodesic along which a vertex moves under isoclinic rotation) may be called the 4-polytope's '''Clifford polygon''', as it is the skew polygonal shape of the rotational circles traversed by the 4-polytope's vertices in its characteristic [[W:Clifford displacement|Clifford displacement]].{{Sfn|Tyrrell|Semple|1971|loc=Linear Systems of Clifford Parallels|pp=34-57}} The isocline is a helical Möbius double loop which reverses its chirality twice in the course of a full double circuit. The double loop is entirely contained within a single [[#Cell rings|cell ring]], where it follows chords connecting even (odd) vertices: typically opposite vertices of adjacent cells, two edge lengths apart.{{Efn|name=black and white}} Both &quot;halves&quot; of the double loop pass through each cell in the cell ring, but intersect only two even (odd) vertices in each even (odd) cell. Each pair of intersected vertices in an even (odd) cell lie opposite each other on the [[W:Möbius strip|Möbius strip]], exactly one edge length apart. Thus each cell has both helices passing through it, which are Clifford parallels{{Efn|name=Clifford parallels}} of opposite chirality at each pair of parallel points. Globally these two helices are a single connected circle of ''both'' chiralities, with no net [[W:Torsion of a curve|torsion]]. An isocline acts as a left (or right) isocline when traversed by a left (or right) rotation (of different fibrations).{{Efn|name=one true circle}}|name=Clifford polygon}} Rather than a flat hexagon, it forms a [[W:Skew polygon|skew]] hexagram out of two three-sided 360 degree half-loops: open triangles joined end-to-end to each other in a six-sided Möbius loop.{{Efn|name=double threaded}}

Each 6-cell ring contains six such hexagram isoclines, three black and three white, that connect even and odd vertices respectively.{{Efn|Only one kind of 6-cell ring exists, not two different chiral kinds (right-handed and left-handed), because octahedra have opposing faces and form untwisted cell rings. In addition to two sets of three Clifford parallel{{Efn|name=Clifford parallels}} [[#Great hexagons|great hexagons]], three black and three white [[#Isoclinic rotations|isoclinic hexagram geodesics]] run through the [[#6-cell rings|6-cell ring]].{{Efn|name=hexagonal fibrations}} Each of these chiral skew [[W:Hexagram|hexagram]]s lies on a different kind of circle called an ''isocline'',{{Efn|name=not all isoclines are circles}} a helical circle [[W:Winding number|winding]] through all four dimensions instead of lying in a single plane.{{Efn|name=isoclinic geodesic}} These helical great circles occur in Clifford parallel [[W:Hopf fibration|fiber bundles]] just as ordinary planar great circles do. In the 6-cell ring, black and white hexagrams pass through even and odd vertices respectively, and miss the vertices in between, so the isoclines are disjoint.{{Efn|name=black and white}}|name=6-cell ring is not chiral}} Each of the three black-white pairs of isoclines belongs to one of the three fibrations in which the 6-cell ring occurs. Each fibration's right (or left) rotation traverses two black isoclines and two white isoclines in parallel, rotating all 24 vertices.{{Efn|name=missing the nearest vertices}}

Beginning at any vertex at one end of the column of six octahedra, we can follow an isoclinic path of {{radic|3}} chords of an isocline from octahedron to octahedron. In the 24-cell the {{radic|1}} edges are [[#Great hexagons|great hexagon]] edges (and octahedron edges); in the column of six octahedra we see six great hexagons running along the octahedra's edges. The {{radic|3}} chords are great hexagon diagonals, joining great hexagon vertices two {{radic|1}} edges apart. We find them in the ring of six octahedra running from a vertex in one octahedron to a vertex in the next octahedron, passing through the face shared by the two octahedra (but not touching any of the face's 3 vertices). Each {{radic|3}} chord is a chord of just one great hexagon (an edge of a [[#Great triangles|great triangle]] inscribed in that great hexagon), but successive {{radic|3}} chords belong to different great hexagons.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} At each vertex the isoclinic path of {{radic|3}} chords bends 60 degrees in two central planes{{Efn|Two central planes in which the path bends 60° at the vertex are (a) the great hexagon plane that the chord ''before'' the vertex belongs to, and (b) the great hexagon plane that the chord ''after'' the vertex belongs to. Plane (b) contains the 120° isocline chord joining the original vertex to a vertex in great hexagon plane (c), Clifford parallel to (a); the vertex moves over this chord to this next vertex. The angle of inclination between the Clifford parallel (isoclinic) great hexagon planes (a) and (c) is also 60°. In this 60° interval of the isoclinic rotation, great hexagon plane (a) rotates 60° within itself ''and'' tilts 60° in an orthogonal plane (not plane (b)) to become great hexagon plane (c). The three great hexagon planes (a), (b) and (c) are not orthogonal (they are inclined at 60° to each other), but (a) and (b) are two central hexagons in the same cuboctahedron, and (b) and (c) likewise in an orthogonal cuboctahedron.{{Efn|name=cuboctahedral hexagons}}}} at once: 60 degrees around the great hexagon that the chord before the vertex belongs to, and 60 degrees into the plane of a different great hexagon entirely, that the chord after the vertex belongs to.{{Efn|At each vertex there is only one adjacent great hexagon plane that the isocline can bend 60 degrees into: the isoclinic path is ''deterministic'' in the sense that it is linear, not branching, because each vertex in the cell ring is a place where just two of the six great hexagons contained in the cell ring cross. If each great hexagon is given edges and chords of a particular color (as in the 6-cell ring illustration), we can name each great hexagon by its color, and each kind of vertex by a hyphenated two-color name. The cell ring contains 18 vertices named by the 9 unique two-color combinations; each vertex and its antipodal vertex have the same two colors in their name, since when two great hexagons intersect they do so at antipodal vertices. Each isoclinic skew hexagram{{Efn|Each half of a skew hexagram is an open triangle of three {{radic|3}} chords, the two open ends of which are one {{radic|1}} edge length apart. The two halves, like the whole isocline, have no inherent chirality but the same parity-color (black or white). The halves are the two opposite &quot;edges&quot; of a [[W:Möbius strip|Möbius strip]] that is {{radic|1}} wide; it actually has only one edge, which is a single continuous circle with 6 chords.|name=skew hexagram}} contains one {{radic|3}} chord of each color, and visits 6 of the 9 different color-pairs of vertex.{{Efn|Each vertex of the 6-cell ring is intersected by two skew hexagrams of the same parity (black or white) belonging to different fibrations.{{Efn|name=6-cell ring is not chiral}}|name=hexagrams hitting vertex of 6-cell ring}} Each 6-cell ring contains six such isoclinic skew hexagrams, three black and three white.{{Efn|name=hexagrams missing vertex of 6-cell ring}}|name=Möbius double loop hexagram}} Thus the path follows one great hexagon from each octahedron to the next, but switches to another of the six great hexagons in the next link of the hexagram&lt;sub&gt;2&lt;/sub&gt; path. Followed along the column of six octahedra (and &quot;around the end&quot; where the column is bent into a ring) the path may at first appear to be zig-zagging between three adjacent parallel hexagonal central planes (like a [[W:Petrie polygon|Petrie polygon]]), but it is not: any isoclinic path we can pick out always zig-zags between ''two sets'' of three adjacent parallel hexagonal central planes, intersecting only every even (or odd) vertex and never changing its inherent even/odd parity, as it visits all six of the great hexagons in the 6-cell ring in rotation.{{Efn|The 24-cell's [[W:Petrie polygon#The Petrie polygon of regular polychora (4-polytopes)|Petrie polygon]] is a skew [[W:Skew polygon#Regular skew polygons in four dimensions|dodecagon]] {12} and also (orthogonally) a skew [[W:Dodecagram|dodecagram]] {12/5} which zig-zags 90° left and right like the edges dividing the black and white squares on the [[W:Chessboard|chessboard]].{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii); 24-cell ''h&lt;sub&gt;1&lt;/sub&gt; is {12}, h&lt;sub&gt;2&lt;/sub&gt; is {12/5}''}} In contrast, the skew hexagram&lt;sub&gt;2&lt;/sub&gt; isocline does not zig-zag, and stays on one side or the other of the dividing line between black and white, like the [[W:Bishop (chess)|bishop]]s' paths along the diagonals of either the black or white squares of the chessboard.{{Efn|name=missing the nearest vertices}} The Petrie dodecagon is a circular helix of {{radic|1}} edges that zig-zag 90° left and right along 12 edges of 6 different octahedra (with 3 consecutive edges in each octahedron) in a 360° rotation. In contrast, the isoclinic hexagram&lt;sub&gt;2&lt;/sub&gt; has {{radic|3}} edges which all bend either left or right at every ''second'' vertex along a geodesic spiral of ''both'' chiralities (left and right){{Efn|name=Clifford polygon}} but only one color (black or white),{{Efn|name=black and white}} visiting one vertex of each of those same 6 octahedra in a 720° rotation.|name=Petrie dodecagram and Clifford hexagram}} When it has traversed one chord from each of the six great hexagons, after 720 degrees of isoclinic rotation (either left or right), it closes its skew hexagram and begins to repeat itself, circling again through the black (or white) vertices and cells.

At each vertex, there are four great hexagons{{Efn|Each pair of adjacent edges of a great hexagon has just one isocline curving alongside it,{{Efn|Each vertex of a 6-cell ring is missed by the two halves of the same Möbius double loop hexagram,{{Efn|name=Möbius double loop hexagram}} which curve past it on either side.|name=hexagrams missing vertex of 6-cell ring}} missing the vertex between the two edges (but not the way the {{radic|3}} edge of the great triangle inscribed in the great hexagon misses the vertex,{{Efn|The {{radic|3}} chord passes through the mid-edge of one of the 24-cell's {{radic|1}} radii. Since the 24-cell can be constructed, with its long radii, from {{radic|1}} triangles which meet at its center,{{Efn|name=radially equilateral}} this is a mid-edge of one of the six {{radic|1}} triangles in a great hexagon, as seen in the [[#Hypercubic chords|chord diagram]].|name=root 3 chord hits a mid-radius}} because the isocline is an arc on the surface not a chord). If we number the vertices around the hexagon 0-5, the hexagon has three pairs of adjacent edges connecting even vertices (one inscribed great triangle), and three pairs connecting odd vertices (the other inscribed great triangle). Even and odd pairs of edges have the arc of a black and a white isocline respectively curving alongside.{{Efn|name=black and white}} The three black and three white isoclines belong to the same 6-cell ring of the same fibration.{{Efn|name=Möbius double loop hexagram}}|name=isoclines at hexagons}} and four hexagram isoclines (all black or all white) that cross at the vertex.{{Efn|Each hexagram isocline hits only one end of an axis, unlike a great circle which hits both ends. Clifford parallel pairs of black and white isoclines from the same left-right pair of isoclinic rotations (the same fibration) do not intersect, but they hit opposite (antipodal) vertices of ''one'' of the 24-cell's 12 axes.|name=hexagram isoclines at an axis}} Four hexagram isoclines (two black and two white) comprise a unique (left or right) fiber bundle of isoclines covering all 24 vertices in each distinct (left or right) isoclinic rotation. Each fibration has a unique left and right isoclinic rotation, and corresponding unique left and right fiber bundles of isoclines.{{Efn|The isoclines themselves are not left or right, only the bundles are. Each isocline is left ''and'' right.{{Efn|name=Clifford polygon}}}} There are 16 distinct hexagram isoclines in the 24-cell (8 black and 8 white).{{Efn|The 12 black-white pairs of hexagram isoclines in each fibration{{Efn|name=hexagram isoclines at an axis}} and the 16 distinct hexagram isoclines in the 24-cell form a [[W:Reye configuration|Reye configuration]] 12&lt;sub&gt;4&lt;/sub&gt;16&lt;sub&gt;3&lt;/sub&gt;, just the way the 24-cell's 12 axes and [[#Great hexagons|16 hexagons]] do. Each of the 12 black-white pairs occurs in one cell ring of each fibration of 4 hexagram isoclines, and each cell ring contains 3 black-white pairs of the 16 hexagram isoclines.|name=a right (left) isoclinic rotation is a Reye configuration}} Each isocline is a skew ''Clifford polygon'' of no inherent chirality, but acts as a left (or right) isocline when traversed by a left (or right) rotation in different fibrations.{{Efn|name=Clifford polygon}}

==== Helical octagrams and their isoclines ====
The 24-cell contains 18 helical [[W:Octagram|octagram]] isoclines (9 black and 9 white). Three pairs of octagram edge-helices are found in each of the three inscribed 16-cells, described elsewhere as the [[16-cell#Helical construction|helical construction of the 16-cell]]. In summary, each 16-cell can be decomposed (three different ways) into a left-right pair of 8-cell rings of {{radic|2}}-edged tetrahedral cells. Each 8-cell ring twists either left or right around an axial octagram helix of eight chords. In each 16-cell there are exactly 6 distinct helices, identical octagrams which each circle through all eight vertices. Each acts as either a left helix or a right helix or a Petrie polygon in each of the six distinct isoclinic rotations (three left and three right), and has no inherent chirality except in respect to a particular rotation. Adjacent vertices on the octagram isoclines are {{radic|2}} = 90° apart, so the circumference of the isocline is 4𝝅. An ''isoclinic'' rotation by 90° in great square invariant planes takes each vertex to its antipodal vertex, four vertices away in either direction along the isocline, and {{radic|4}} = 180° distant across the diameter of the isocline.

Each of the 3 fibrations of the 24-cell's 18 great squares corresponds to a distinct left (and right) isoclinic rotation in great square invariant planes. Each 60° step of the rotation takes 6 disjoint great squares (2 from each 16-cell) to great squares in a neighboring 16-cell, on [[16-cell#Helical construction|8-chord helical isoclines characteristic of the 16-cell]].{{Efn|As [[16-cell#Helical construction|in the 16-cell, the isocline is an octagram]] which intersects only 8 vertices, even though the 24-cell has more vertices closer together than the 16-cell. The isocline curve misses the additional vertices in between. As in the 16-cell, the first vertex it intersects is {{radic|2}} away. The 24-cell employs more octagram isoclines (3 in parallel in each rotation) than the 16-cell does (1 in each rotation). The 3 helical isoclines are Clifford parallel;{{Efn|name=Clifford parallels}} they spiral around each other in a triple helix, with the disjoint helices' corresponding vertex pairs joined by {{radic|1}} {{=}} 60° chords. The triple helix of 3 isoclines contains 24 disjoint {{radic|2}} edges (6 disjoint great squares) and 24 vertices, and constitutes a discrete fibration of the 24-cell, just as the 4-cell ring does.|name=octagram isoclines}}

In the 24-cell, these 18 helical octagram isoclines can be found within the six orthogonal [[#4-cell rings|4-cell rings]] of octahedra. Each 4-cell ring has cells bonded vertex-to-vertex around a great square axis, and we find antipodal vertices at opposite vertices of the great square. A {{radic|4}} chord (the diameter of the great square and of the isocline) connects them. [[#Boundary cells|Boundary cells]] describes how the {{radic|2}} axes of the 24-cell's octahedral cells are the edges of the 16-cell's tetrahedral cells, each tetrahedron is inscribed in a (tesseract) cube, and each octahedron is inscribed in a pair of cubes (from different tesseracts), bridging them.{{Efn|name=octahedral diameters}} The vertex-bonded octahedra of the 4-cell ring also lie in different tesseracts.{{Efn|Two tesseracts share only vertices, not any edges, faces, cubes (with inscribed tetrahedra), or octahedra (whose central square planes are square faces of cubes). An octahedron that touches another octahedron at a vertex (but not at an edge or a face) is touching an octahedron in another tesseract, and a pair of adjacent cubes in the other tesseract whose common square face the octahedron spans, and a tetrahedron inscribed in each of those cubes.|name=vertex-bonded octahedra}} The isocline's four {{radic|4}} diameter chords form an [[W:Octagram#Star polygon compounds|octagram&lt;sub&gt;8{4}=4{2}&lt;/sub&gt;]] with {{radic|4}} edges that each run from the vertex of one cube and octahedron and tetrahedron, to the vertex of another cube and octahedron and tetrahedron (in a different tesseract), straight through the center of the 24-cell on one of the 12 {{radic|4}} axes.

The octahedra in the 4-cell rings are vertex-bonded to more than two other octahedra, because three 4-cell rings (and their three axial great squares, which belong to different 16-cells) cross at 90° at each bonding vertex. At that vertex the octagram makes two right-angled turns at once: 90° around the great square, and 90° orthogonally into a different 4-cell ring entirely. The 180° four-edge arc joining two ends of each {{radic|4}} diameter chord of the octagram runs through the volumes and opposite vertices of two face-bonded {{radic|2}} tetrahedra (in the same 16-cell), which are also the opposite vertices of two vertex-bonded octahedra in different 4-cell rings (and different tesseracts). The [[W:Octagram|720° octagram]] isocline runs through 8 vertices of the four-cell ring and through the volumes of 16 tetrahedra. At each vertex, there are three great squares and six octagram isoclines (three black-white pairs) that cross at the vertex.{{Efn|name=completely orthogonal Clifford parallels are special}}

This is the characteristic rotation of the 16-cell, ''not'' the 24-cell's characteristic rotation, and it does not take whole 16-cells ''of the 24-cell'' to each other the way the [[#Helical hexagrams and their isoclines|24-cell's rotation in great hexagon planes]] does.{{Efn|The [[600-cell#Squares and 4𝝅 octagrams|600-cell's isoclinic rotation in great square planes]] takes whole 16-cells to other 16-cells in different 24-cells.}}

{| class=&quot;wikitable&quot; width=610
!colspan=5|Five ways of looking at a [[W:Skew polygon|skew]] [[W:24-gon#Related polygons|24-gram]]
|-
![[16-cell#Rotations|Edge path]]
![[W:Petrie polygon|Petrie polygon]]s
![[600-cell#Squares and 4𝝅 octagrams|In a 600-cell]]
![[#Great squares|Discrete fibration]]
![[16-cell#Helical construction|Diameter chords]]
|-
![[16-cell#Helical construction|16-cells]]&lt;sub&gt;3{3/8}&lt;/sub&gt;
![[W:Petrie polygon#The Petrie polygon of regular polychora (4-polytopes)|Dodecagons]]&lt;sub&gt;2{12}&lt;/sub&gt;
![[W:24-gon#Related polygons|24-gram]]&lt;sub&gt;{24/5}&lt;/sub&gt;
![[#Great squares|Squares]]&lt;sub&gt;6{4}&lt;/sub&gt;
![[W:24-gon#Related polygons|&lt;sub&gt;{24/12}={12/2}&lt;/sub&gt;]]
|-
|align=center|[[File:Regular_star_figure_3(8,3).svg|120px]]
|align=center|[[File:Regular_star_figure_2(12,1).svg|120px]]
|align=center|[[File:Regular_star_polygon_24-5.svg|120px]]
|align=center|[[File:Regular_star_figure_6(4,1).svg|120px]]
|align=center|[[File:Regular_star_figure_12(2,1).svg|120px]]
|-
|The 24-cell's three inscribed Clifford parallel 16-cells revealed as disjoint 8-point 4-polytopes with {{radic|2}} edges.{{Efn|name=octagram isoclines}}
|2 [[W:Skew polygon|skew polygon]]s of 12 {{radic|1}} edges each. The 24-cell can be decomposed into 2 disjoint zig-zag [[W:Dodecagon|dodecagon]]s (4 different ways).{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii); 24-cell Petrie polygon ''h&lt;sub&gt;1&lt;/sub&gt;'' is {12} }}
|In [[600-cell#Hexagons|compounds of 5 24-cells]], isoclines with [[600-cell#Golden chords|golden chords]] of length &lt;big&gt;φ&lt;/big&gt; {{=}} {{radic|2.𝚽}} connect all 24-cells in [[600-cell#Squares and 4𝝅 octagrams|24-chord circuits]].{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii); 24-cell Petrie polygon orthogonal ''h&lt;sub&gt;2&lt;/sub&gt;'' is [[W:Dodecagon#Related figures|{12/5}]], half of [[W:24-gon#Related polygons|{24/5}]] as each Petrie polygon is half the 24-cell}}
|Their isoclinic rotation takes 6 Clifford parallel (disjoint) great squares with {{radic|2}} edges to each other.
|Two vertices four {{radic|2}} chords apart on the circular isocline are antipodal vertices joined by a {{radic|4}} axis.
|}

===Characteristic orthoscheme===
{| class=&quot;wikitable floatright&quot;
!colspan=6|Characteristics of the 24-cell{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii); &quot;24-cell&quot;}}
|-
!align=right|
!align=center|edge{{Sfn|Coxeter|1973|p=139|loc=§7.9 The characteristic simplex}}
!colspan=2 align=center|arc
!colspan=2 align=center|dihedral{{Sfn|Coxeter|1973|p=290|loc=Table I(ii); &quot;dihedral angles&quot;}}
|-
!align=right|𝒍
|align=center|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;60°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{3}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;120°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{2\pi}{3}&lt;/math&gt;&lt;/small&gt;
|-
|
|
|
|
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|-
!align=right|𝟀
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{3}} \approx 0.577&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;45°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{4}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;45°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{4}&lt;/math&gt;&lt;/small&gt;
|-
!align=right|𝝉{{Efn|{{Harv|Coxeter|1973}} uses the greek letter 𝝓 (phi) to represent one of the three ''characteristic angles'' 𝟀, 𝝓, 𝟁 of a regular polytope. Because 𝝓 is commonly used to represent the [[W:Golden ratio|golden ratio]] constant ≈ 1.618, for which Coxeter uses 𝝉 (tau), we reverse Coxeter's conventions, and use 𝝉 to represent the characteristic angle.|name=reversed greek symbols}}
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{4}} = 0.5&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;30°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{6}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;60°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{3}&lt;/math&gt;&lt;/small&gt;
|-
!align=right|𝟁
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{12}} \approx 0.289&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;30°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{6}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;60°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{3}&lt;/math&gt;&lt;/small&gt;
|-
|
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|
|
|
|-
!align=right|&lt;small&gt;&lt;math&gt;_0R^3/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{2}} \approx 0.707&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;45°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{4}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;90°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{2}&lt;/math&gt;&lt;/small&gt;
|-
!align=right|&lt;small&gt;&lt;math&gt;_1R^3/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{4}} = 0.5&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;30°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{6}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;90°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{2}&lt;/math&gt;&lt;/small&gt;
|-
!align=right|&lt;small&gt;&lt;math&gt;_2R^3/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{6}} \approx 0.408&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;30°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{6}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;90°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{2}&lt;/math&gt;&lt;/small&gt;
|-
|
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|
|-
!align=right|&lt;small&gt;&lt;math&gt;_0R^4/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|align=center|
|align=center|
|align=center|
|align=center|
|-
!align=right|&lt;small&gt;&lt;math&gt;_1R^4/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{3}{4}} \approx 0.866&lt;/math&gt;&lt;/small&gt;{{Efn|name=root 3/4}}
|align=center|
|align=center|
|align=center|
|align=center|
|-
!align=right|&lt;small&gt;&lt;math&gt;_2R^4/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{2}{3}} \approx 0.816&lt;/math&gt;&lt;/small&gt;
|align=center|
|align=center|
|align=center|
|align=center|
|-
!align=right|&lt;small&gt;&lt;math&gt;_3R^4/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{2}} \approx 0.707&lt;/math&gt;&lt;/small&gt;
|align=center|
|align=center|
|align=center|
|align=center|
|}
Every regular 4-polytope has its [[W:Orthoscheme#Characteristic simplex of the general regular polytope|characteristic 4-orthoscheme]], an [[5-cell#Irregular 5-cells|irregular 5-cell]].{{Efn|name=characteristic orthoscheme}} The '''characteristic 5-cell of the regular 24-cell''' is represented by the [[W:Coxeter-Dynkin diagram|Coxeter-Dynkin diagram]] {{Coxeter–Dynkin diagram|node|3|node|4|node|3|node}}, which can be read as a list of the dihedral angles between its mirror facets.{{Efn|For a regular ''k''-polytope, the [[W:Coxeter-Dynkin diagram|Coxeter-Dynkin diagram]] of the characteristic ''k-''orthoscheme is the ''k''-polytope's diagram without the [[W:Coxeter-Dynkin diagram#Application with uniform polytopes|generating point ring]]. The regular ''k-''polytope is subdivided by its symmetry (''k''-1)-elements into ''g'' instances of its characteristic ''k''-orthoscheme that surround its center, where ''g'' is the ''order'' of the ''k''-polytope's [[W:Coxeter group|symmetry group]].{{Sfn|Coxeter|1973|pp=130-133|loc=§7.6 The symmetry group of the general regular polytope}}}} It is an irregular [[W:Hyperpyramid|tetrahedral pyramid]] based on the [[W:Octahedron#Characteristic orthoscheme|characteristic tetrahedron of the regular octahedron]]. The regular 24-cell is subdivided by its symmetry hyperplanes into 1152 instances of its characteristic 5-cell that all meet at its center.{{Sfn|Kim|Rote|2016|pp=17-20|loc=§10 The Coxeter Classification of Four-Dimensional Point Groups}}

The characteristic 5-cell (4-orthoscheme) has four more edges than its base characteristic tetrahedron (3-orthoscheme), joining the four vertices of the base to its apex (the fifth vertex of the 4-orthoscheme, at the center of the regular 24-cell).{{Efn|The four edges of each 4-orthoscheme which meet at the center of the regular 4-polytope are of unequal length, because they are the four characteristic radii of the regular 4-polytope: a vertex radius, an edge center radius, a face center radius, and a cell center radius. The five vertices of the 4-orthoscheme always include one regular 4-polytope vertex, one regular 4-polytope edge center, one regular 4-polytope face center, one regular 4-polytope cell center, and the regular 4-polytope center. Those five vertices (in that order) comprise a path along four mutually perpendicular edges (that makes three right angle turns), the characteristic feature of a 4-orthoscheme. The 4-orthoscheme has five dissimilar 3-orthoscheme facets.|name=characteristic radii}} If the regular 24-cell has radius and edge length 𝒍 = 1, its characteristic 5-cell's ten edges have lengths &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{3}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{4}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{12}}&lt;/math&gt;&lt;/small&gt; around its exterior right-triangle face (the edges opposite the ''characteristic angles'' 𝟀, 𝝉, 𝟁),{{Efn|name=reversed greek symbols}} plus &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{2}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{4}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{6}}&lt;/math&gt;&lt;/small&gt; (the other three edges of the exterior 3-orthoscheme facet the characteristic tetrahedron, which are the ''characteristic radii'' of the octahedron), plus &lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{3}{4}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{2}{3}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{2}}&lt;/math&gt;&lt;/small&gt; (edges which are the characteristic radii of the 24-cell). The 4-edge path along orthogonal edges of the orthoscheme is &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{4}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{12}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{6}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{2}}&lt;/math&gt;&lt;/small&gt;, first from a 24-cell vertex to a 24-cell edge center, then turning 90° to a 24-cell face center, then turning 90° to a 24-cell octahedral cell center, then turning 90° to the 24-cell center.

=== Reflections ===
The 24-cell can be [[#Tetrahedral constructions|constructed by the reflections of its characteristic 5-cell]] in its own facets (its tetrahedral mirror walls).{{Efn|The reflecting surface of a (3-dimensional) polyhedron consists of 2-dimensional faces; the reflecting surface of a (4-dimensional) [[W:Polychoron|polychoron]] consists of 3-dimensional cells.}} Reflections and rotations are related: a reflection in an ''even'' number of ''intersecting'' mirrors is a rotation.{{Sfn|Coxeter|1973|pp=33-38|loc=§3.1 Congruent transformations}} Consequently, regular polytopes can be generated by reflections or by rotations. For example, any [[#Isoclinic rotations|720° isoclinic rotation]] of the 24-cell in a hexagonal invariant plane takes ''each'' of the 24 vertices to and through 5 other vertices and back to itself, on a skew [[#Helical hexagrams and their isoclines|hexagram&lt;sub&gt;2&lt;/sub&gt; geodesic isocline]] that winds twice around the 3-sphere on every ''second'' vertex of the hexagram. Any set of [[#The 3 Cartesian bases of the 24-cell|four orthogonal pairs of antipodal vertices]] (the 8 vertices of one of the [[#Relationships among interior polytopes|three inscribed 16-cells]]) performing ''half'' such an orbit visits 3 * 8 = 24 distinct vertices and [[#Clifford parallel polytopes|generates the 24-cell]] sequentially in 3 steps of a single 360° isoclinic rotation, just as any single characteristic 5-cell reflecting itself in its own mirror walls generates the 24 vertices simultaneously by reflection.

Tracing the orbit of ''one'' such 16-cell vertex during the 360° isoclinic rotation reveals more about the relationship between reflections and rotations as generative operations.{{Efn|&lt;blockquote&gt;Let Q denote a rotation, R a reflection, T a translation, and let Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T denote a product of several such transformations, all commutative with one another. Then RT is a glide-reflection (in two or three dimensions), QR is a rotary-reflection, QT is a screw-displacement, and Q&lt;sup&gt;2&lt;/sup&gt; is a double rotation (in four dimensions).&lt;br&gt;&lt;br&gt;Every orthogonal transformation is expressible as
{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt;&lt;br&gt;where 2''q'' + ''r'' ≤ ''n'', the number of dimensions. Transformations involving a translation are expressible as {{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T&lt;br&gt;where 2''q'' + ''r'' + 1 ≤ ''n''.&lt;br&gt;&lt;br&gt;For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q&lt;sup&gt;2&lt;/sup&gt;, or a screw-displacement QT (where the rotation component Q is a simple rotation). Every enantiomorphous transformation in 4-space (reversing chirality) is a QRT.{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}&lt;/blockquote&gt;|name=transformations}} The vertex follows an [[#Helical hexagrams and their isoclines|isocline]] (a doubly curved geodesic circle) rather than an ordinary great circle.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} The isocline connects vertices two edge lengths apart, but curves away from the great circle path over the two edges connecting those vertices, missing the vertex in between.{{Efn|name=isocline misses vertex}} Although the isocline does not follow any one great circle, it is contained within a ring of another kind: in the 24-cell it stays within a [[#6-cell rings|6-cell ring]] of spherical{{Sfn|Coxeter|1973|p=138|ps=; &quot;We allow the Schläfli symbol {p,..., v} to have three different meanings: a Euclidean polytope, a spherical polytope, and a spherical honeycomb. This need not cause any confusion, so long as the situation is frankly recognized. The differences are clearly seen in the concept of dihedral angle.&quot;}} octahedral cells, intersecting one vertex in each cell, and passing through the volume of two adjacent cells near the missed vertex.

=== Chiral symmetry operations ===

A [[W:Symmetry operation|symmetry operation]] is a rotation or reflection which leaves the object indistinguishable from itself before the transformation. The 24-cell has 1152 distinct symmetry operations (576 rotations and 576 reflections). Each rotation is equivalent to two [[#Reflections|reflections]], in a distinct pair of non-parallel mirror planes.{{Efn|name=transformations}}

Pictured are sets of disjoint [[#Geodesics|great circle polygons]], each in a distinct central plane of the 24-cell. For example, {24/4}=4{6} is an orthogonal projection of the 24-cell picturing 4 of its [16] great hexagon planes.{{Efn|name=four hexagonal fibrations}} The 4 planes lie Clifford parallel to the projection plane and to each other, and their great polygons collectively constitute a discrete [[W:Hopf fibration|Hopf fibration]] of 4 non-intersecting great circles which visit all 24 vertices just once.

Each row of the table describes a class of distinct rotations. Each '''rotation class''' takes the '''left planes''' pictured to the corresponding '''right planes''' pictured.{{Efn|The left planes are Clifford parallel, and the right planes are Clifford parallel; each set of planes is a fibration. Each left plane is Clifford parallel to its corresponding right plane in an isoclinic rotation,{{Efn|In an ''isoclinic'' rotation each invariant plane is Clifford parallel to the plane it moves to, and they do not intersect at any time (except at the central point). In a ''simple'' rotation the invariant plane intersects the plane it moves to in a line, and moves to it by rotating around that line.|name=plane movement in rotations}} but the two sets of planes are not all mutually Clifford parallel; they are different fibrations, except in table rows where the left and right planes are the same set.}} The vertices of the moving planes move in parallel along the polygonal '''isocline''' paths pictured. For example, the &lt;math&gt;[32]R_{q7,q8}&lt;/math&gt; rotation class consists of [32] distinct rotational displacements by an arc-distance of {{sfrac|2𝝅|3}} = 120° between 16 great hexagon planes represented by quaternion group &lt;math&gt;q7&lt;/math&gt; and a corresponding set of 16 great hexagon planes represented by quaternion group &lt;math&gt;q8&lt;/math&gt;.{{Efn|A quaternion group &lt;math&gt;\pm{q_n}&lt;/math&gt; corresponds to a distinct set of Clifford parallel great circle polygons, e.g. &lt;math&gt;q7&lt;/math&gt; corresponds to a set of four disjoint great hexagons.{{Efn|[[File:Regular_star_figure_4(6,1).svg|thumb|200px|The 24-cell as a compound of four non-intersecting great hexagons {24/4}=4{6}.]]There are 4 sets of 4 disjoint great hexagons in the 24-cell (of a total of [16] distinct great hexagons), designated &lt;math&gt;q7&lt;/math&gt;, &lt;math&gt;-q7&lt;/math&gt;, &lt;math&gt;q8&lt;/math&gt; and &lt;math&gt;-q8&lt;/math&gt;.{{Efn|name=union of q7 and q8}} Each named set of 4 Clifford parallel{{Efn|name=Clifford parallels}} hexagons comprises a [[#Chiral symmetry operations|discrete fibration]] covering all 24 vertices.|name=four hexagonal fibrations}} Note that &lt;math&gt;q_n&lt;/math&gt; and &lt;math&gt;-{q_n}&lt;/math&gt; generally are distinct sets. The corresponding vertices of the &lt;math&gt;q_n&lt;/math&gt; planes and the &lt;math&gt;-{q_n}&lt;/math&gt; planes are 180° apart.{{Efn|name=two angles between central planes}}|name=quaternion group}} One of the [32] distinct rotations of this class moves the representative [[#Great hexagons|vertex coordinate]] &lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt; to the vertex coordinate &lt;math&gt;(\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2})&lt;/math&gt;.{{Efn|A quaternion Cartesian coordinate designates a vertex joined to a ''top vertex'' by one instance of a [[#Hypercubic chords|distinct chord]]. The conventional top vertex of a [[#Great hexagons|unit radius 4-polytope]] in standard (vertex-up) orientation is &lt;math&gt;(0,0,1,0)&lt;/math&gt;, the Cartesian &quot;north pole&quot;. Thus e.g. &lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt; designates a {{radic|1}} chord of 60° arc-length. Each such distinct chord is an edge of a distinct [[#Geodesics|great circle polygon]], in this example a [[#Great hexagons|great hexagon]], intersecting the north and south poles. Great circle polygons occur in sets of Clifford parallel central planes, each set of disjoint great circles comprising a discrete [[W:Hopf fibration|Hopf fibration]] that intersects every vertex just once. One great circle polygon in each set intersects the north and south poles. This quaternion coordinate &lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt; is thus representative of the 4 disjoint great hexagons pictured, a quaternion group{{Efn|name=quaternion group}} which comprise one distinct fibration of the [16] great hexagons (four fibrations of great hexagons) that occur in the 24-cell.{{Efn|name=four hexagonal fibrations}}|name=north pole relative coordinate}}

{| class=wikitable style=&quot;white-space:nowrap;text-align:center&quot;
!colspan=15|Proper [[W:SO(4)|rotations]] of the 24-cell [[W:F4 (mathematics)|symmetry group ''F&lt;sub&gt;4&lt;/sub&gt;'']]{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes, Table 2, Symmetry operations|pp=1438-1439}}
|-
!Isocline{{Efn|An ''isocline'' is the circular geodesic path taken by a vertex that lies in an invariant plane of rotation, during a complete revolution. In an [[#Isoclinic rotations|isoclinic rotation]] every vertex lies in an invariant plane of rotation, and the isocline it rotates on is a helical geodesic circle that winds through all four dimensions, not a simple geodesic great circle in the plane. In a [[#Simple rotations|simple rotation]] there is only one invariant plane of rotation, and each vertex that lies in it rotates on a simple geodesic great circle in the plane. Both the helical geodesic isocline of an isoclinic rotation and the simple geodesic isocline of a simple rotation are great circles, but to avoid confusion between them we generally reserve the term ''isocline'' for the former, and reserve the term ''great circle'' for the latter, an ordinary great circle in the plane. Strictly, however, the latter is an isocline of circumference &lt;math&gt;2\pi r&lt;/math&gt;, and the former is an isocline of circumference greater than &lt;math&gt;2\pi r&lt;/math&gt;.{{Efn|name=isoclinic geodesic}}|name=isocline}}
!colspan=4|Rotation class{{Efn|Each class of rotational displacements (each table row) corresponds to a distinct rigid left (and right) [[#Isoclinic rotations|isoclinic rotation]] in multiple invariant planes concurrently.{{Efn|name=invariant planes of an isoclinic rotation}} The '''Isocline''' is the path followed by a vertex,{{Efn|name=isocline}} which is a helical geodesic circle that does not lie in any one central plane. Each rotational displacement takes one invariant '''Left plane''' to the corresponding invariant '''Right plane''', with all the left (or right) displacements taking place concurrently.{{Efn|name=plane movement in rotations}} Each left plane is separated from the corresponding right plane by two equal angles,{{Efn|name=two angles between central planes}} each equal to one half of the arc-angle by which each vertex is displaced (the angle and distance that appears in the '''Rotation class''' column).|name=isoclinic rotation}}
!colspan=5|Left planes &lt;math&gt;ql&lt;/math&gt;{{Efn|In an [[#Isoclinic rotations|isoclinic rotation]], all the '''Left planes''' move together, remain Clifford parallel while moving, and carry all their points with them to the '''Right planes''' as they move: they are invariant planes.{{Efn|name=plane movement in rotations}} Because the left (and right) set of central polygons are a fibration covering all the vertices, every vertex is a point carried along in an invariant plane.|name=invariant planes of an isoclinic rotation}}
!colspan=5|Right planes &lt;math&gt;qr&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/8}=4{6/2}]]{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/4}=4{3} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|3}} chords. Each disjoint triangle can be seen as a skew {6/2} [[W:Hexagram|hexagram]] with {{radic|3}} edges: two open skew triangles with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅. The hexagram projects to a single triangle in two dimensions because it skews through all four dimensions. Those 4 disjoint skew [[#Helical hexagrams and their isoclines|hexagram isoclines]] are the Clifford parallel circular vertex paths of the fibration's characteristic left (and right) [[#Isoclinic rotations|isoclinic rotation]].{{Efn|name=isoclinic geodesic}} The 4 Clifford parallel great hexagons of the fibration are invariant planes of this rotation. The great hexagons rotate in incremental displacements of 60° like wheels ''and'' 60° orthogonally like coins flipping, displacing each vertex by 120°, as their vertices move along parallel helical isocline paths through successive Clifford parallel hexagon planes.{{Efn|Each hexagon rides on only three skew hexagram isoclines, not six, because opposite vertices of each hexagon ride on opposing rails of the same Clifford hexagram, in the same (not opposite) rotational direction.{{Efn|name=Clifford polygon}}}} Alternatively, the 4 triangles can be seen as 8 disjoint triangles: 4 pairs of Clifford parallel [[#Great triangles|great triangles]], where two opposing great triangles lie in the same [[#Great hexagons|great hexagon central plane]], so a fibration of 4 Clifford parallel great hexagon planes is represented.{{Efn|name=four hexagonal fibrations}} This illustrates that the 4 hexagram isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 4 great hexagons.|name=hexagram}}&lt;br&gt;[[File:Regular_star_figure_4(3,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,q8}&lt;/math&gt;&lt;br&gt;[16] 4𝝅 {6/2}
|colspan=4|&lt;math&gt;[32]R_{q7,q8}&lt;/math&gt;{{Efn|The &lt;math&gt;[32]R_{q7,q8}&lt;/math&gt; isoclinic rotation in great hexagon invariant planes takes each vertex to a vertex two vertices away (120° {{=}} {{radic|3}} away), without passing through any intervening vertices. Each left hexagon rotates 60° (like a wheel) at the same time that it tilts sideways by 60° (in an orthogonal central plane) into its corresponding right hexagon plane. Repeated 6 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,q8}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]{{Efn|name=four hexagonal fibrations}}&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;{{Efn|name=north pole relative coordinate}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/8}=4{6/2}]]{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/4}=4{3} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|3}} chords. The 4 triangles can be seen as 8 disjoint triangles: 4 pairs of Clifford parallel [[#Great triangles|great triangles]], where two opposing great triangles lie in the same [[#Great hexagons|great hexagon central plane]], so a fibration of 4 Clifford parallel great hexagon planes is represented, as in the 4 left planes of this rotation class (table row).{{Efn|name=four hexagonal fibrations}}|name=great triangles}}&lt;br&gt;[[File:Regular_star_figure_4(3,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q8}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|{{sfrac|2𝝅|3}}
|120°
|{{radic|3}}
|1.732~
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|2𝝅|3}}
|120°
|{{radic|3}}
|1.732~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/2}=2{12}]]{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/2}=2{6} dodecagram]], each point represents two vertices, and each line represents multiple 24-cell edges. Each disjoint hexagon can be seen as a skew {12} [[W:Dodecagon|dodecagon]], a Petrie polygon of the 24-cell, by viewing it as two open skew hexagons with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅. The dodecagon projects to a single hexagon in two dimensions because it skews through all four dimensions. Those 2 disjoint skew dodecagons are the Clifford parallel circular vertex paths of the fibration's characteristic left (and right) [[#Isoclinic rotations|isoclinic rotation]].{{Efn|name=isoclinic geodesic}} The 4 Clifford parallel great hexagons of the fibration are invariant planes of this rotation. The great hexagons rotate in incremental displacements of 30° like wheels ''and'' 30° orthogonally like coins flipping, displacing each vertex by 60°, as their vertices move along parallel helical isocline paths through successive Clifford parallel hexagon planes.{{Efn|Each hexagon rides on only two parallel dodecagon isoclines, not six, because only alternate vertices of each hexagon ride on different dodecagon rails; the three vertices of each great triangle inscribed in the great hexagon occupy the same dodecagon Petrie polygon, four vertices apart, and they circulate on that isocline.{{Efn|name=Clifford polygon}}}} Alternatively, the 2 hexagons can be seen as 4 disjoint hexagons: 2 pairs of Clifford parallel great hexagons, so a fibration of 4 Clifford parallel great hexagon planes is represented.{{Efn|name=four hexagonal fibrations}} This illustrates that the 2 dodecagon isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 4 great hexagons.|name=dodecagon}}&lt;br&gt;[[File:Regular_star_figure_2(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,-q8}&lt;/math&gt;&lt;br&gt;[16] 4𝝅 {12}
|colspan=4|&lt;math&gt;[32]R_{q7,-q8}&lt;/math&gt;{{Efn|The &lt;math&gt;[32]R_{q7,-q8}&lt;/math&gt; isoclinic rotation in great hexagon invariant planes takes each vertex to a vertex one vertex away (60° {{=}} {{radic|1}} away), without passing through any intervening vertices.{{Efn|At the mid-point of the isocline arc (30° away) it passes directly over the mid-point of a 24-cell edge.}} Each left hexagon rotates 30° (like a wheel) at the same time that it tilts sideways by 30° (in an orthogonal central plane) into its corresponding right hexagon plane. Repeated 12 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,-q8}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q8}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(-\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/1}={24}]]&lt;br&gt;[[File:Regular_polygon_24.svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,q7}&lt;/math&gt;&lt;br&gt;[16] 4𝝅 {1}
|colspan=4|&lt;math&gt;[32]R_{q7,q7}&lt;/math&gt;{{Efn|The &lt;math&gt;[32]R_{q7,q7}&lt;/math&gt; isoclinic rotation in great hexagon invariant planes takes each vertex through a 360° rotation and back to itself (360° {{=}} {{radic|0}} away), without passing through any intervening vertices. Each left hexagon rotates 180° (like a wheel) at the same time that it tilts sideways by 180° (in an orthogonal central plane) into its corresponding right hexagon plane. Repeated 2 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,q7}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|2𝝅
|360°
|{{radic|0}}
|0
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,-q7}&lt;/math&gt;&lt;br&gt;[16] 4𝝅 {2}
|colspan=4|&lt;math&gt;[32]R_{q7,-q7}&lt;/math&gt;{{Efn|The &lt;math&gt;[32]R_{q7,-q7}&lt;/math&gt; isoclinic rotation in hexagon invariant planes takes each vertex to a vertex three vertices away (180° {{=}} {{radic|4}} away),{{Efn|name=quaternion group}} without passing through any intervening vertices. Each left hexagon rotates 90° (like a wheel) at the same time that it tilts sideways by 90° (in an orthogonal central plane) into its corresponding right hexagon plane. Repeated 4 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,-q7}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/8}=4{6/2}]]{{Efn|name=great triangles}}&lt;br&gt;[[File:Regular_star_figure_4(3,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(-\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|𝝅
|180°
|{{radic|4}}
|2
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|2𝝅|3}}
|120°
|{{radic|3}}
|1.732~
|- style=&quot;background: #E6FFEE;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/2}=2{12}]]{{Efn|name=dodecagon}}&lt;br&gt;[[File:Regular_star_figure_2(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,q1}&lt;/math&gt;&lt;br&gt;[8] 4𝝅 {12}
|colspan=4|&lt;math&gt;[16]R_{q7,q1}&lt;/math&gt;{{Efn|The &lt;math&gt;[16]R_{q7,q1}&lt;/math&gt; isoclinic rotation in great hexagon invariant planes takes each vertex to a vertex one vertex away (60° {{=}} {{radic|1}} away), without passing through any intervening vertices. Each left hexagon rotates 30° (like a wheel) at the same time that it tilts sideways by 30° (in an orthogonal central plane) into its corresponding right square plane.{{Efn|This ''hybrid isoclinic rotation'' carries the two kinds of [[#Geodesics|central planes]] to each other: great square planes [[16-cell#Coordinates|characteristic of the 16-cell]] and great hexagon (great triangle) planes [[#Great hexagons|characteristic of the 24-cell]].{{Efn|The edges and 4𝝅 characteristic [[16-cell#Rotations|rotations of the 16-cell]] lie in the great square central planes. Rotations of this type are an expression of the [[W:Hyperoctahedral group|&lt;math&gt;B_4&lt;/math&gt; symmetry group]]. The edges and 4𝝅 characteristic [[#Rotations|rotations of the 24-cell]] lie in the great hexagon (great triangle) central planes. Rotations of this type are an expression of the [[W:F4 (mathematics)|&lt;math&gt;F_4&lt;/math&gt; symmetry group]].|name=edge rotation planes}} This is possible because some great hexagon planes lie Clifford parallel to some great square planes.{{Efn|Two great circle polygons either intersect in a common axis, or they are Clifford parallel (isoclinic) and share no vertices.{{Efn||name=two angles between central planes}} Three great squares and four great hexagons intersect at each 24-cell vertex. Each great hexagon intersects 9 distinct great squares, 3 in each of its 3 axes, and lies Clifford parallel to the other 9 great squares. Each great square intersects 8 distinct great hexagons, 4 in each of its 2 axes, and lies Clifford parallel to the other 8 great hexagons.|name=hybrid isoclinic planes}}|name=hybrid isoclinic rotation}} Repeated 12 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,q1}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[8] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]{{Efn|[[File:Regular_star_figure_6(4,1).svg|thumb|200px|The 24-cell as a compound of six non-intersecting great squares {24/6}=6{4}.]]There are 3 sets of 6 disjoint great squares in the 24-cell (of a total of [18] distinct great squares),{{Efn|The 24-cell has 18 great squares, in 3 disjoint sets of 6 mutually orthogonal great squares comprising a 16-cell.{{Efn|name=Six orthogonal planes of the Cartesian basis}} Within each 16-cell are 3 sets of 2 completely orthogonal great squares, so each great square is disjoint not only from all the great squares in the other two 16-cells, but also from one other great square in the same 16-cell. Each great square is disjoint from 13 others, and shares two vertices (an axis) with 4 others (in the same 16-cell).|name=unions of q1 q2 q3}} designated &lt;math&gt;\pm q1&lt;/math&gt;, &lt;math&gt;\pm q2&lt;/math&gt;, and &lt;math&gt;\pm q3&lt;/math&gt;. Each named set{{Efn|Because in the 24-cell each great square is completely orthogonal to another great square, the quaternion groups &lt;math&gt;q1&lt;/math&gt; and &lt;math&gt;-{q1}&lt;/math&gt; (for example) correspond to the same set of great square planes. That distinct set of 6 disjoint great squares &lt;math&gt;\pm q1&lt;/math&gt; has two names, used in the left (or right) rotational context, because it constitutes both a left and a right fibration of great squares.|name=two quaternion group names for square fibrations}} of 6 Clifford parallel{{Efn|name=Clifford parallels}} squares comprises a [[#Chiral symmetry operations|discrete fibration]] covering all 24 vertices.|name=three square fibrations}}&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1}&lt;/math&gt;&lt;br&gt;[8] 2𝝅 {4}
|colspan=4|&lt;math&gt;(1,0,0,0)&lt;/math&gt;
|- style=&quot;background: #E6FFEE;&quot;|
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: #E6FFEE;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/8}=4{6/2}]]{{Efn|name=hexagram}}&lt;br&gt;[[File:Regular_star_figure_4(3,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,-q1}&lt;/math&gt;&lt;br&gt;[8] 4𝝅 {6/2}
|colspan=4|&lt;math&gt;[16]R_{q7,-q1}&lt;/math&gt;{{Efn|The &lt;math&gt;[16]R_{q7,-q1}&lt;/math&gt; isoclinic rotation in hexagon invariant planes takes each vertex to a vertex two vertices away (120° {{=}} {{radic|3}} away), without passing through any intervening vertices. Each left hexagon rotates 60° (like a wheel) at the same time that it tilts sideways by 60° (in an orthogonal central plane) into its corresponding right square plane.{{Efn|name=hybrid isoclinic rotation}} Repeated 6 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,-q1}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[8] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q1}&lt;/math&gt;&lt;br&gt;[8] 2𝝅 {4}
|colspan=4|&lt;math&gt;(-1,0,0,0)&lt;/math&gt;
|- style=&quot;background: #E6FFEE;&quot;|
|{{sfrac|2𝝅|3}}
|120°
|{{radic|3}}
|1.732~
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/1}={24}]]&lt;br&gt;[[File:Regular_polygon_24.svg|100px]]&lt;br&gt;&lt;math&gt;^{q6,q6}&lt;/math&gt;&lt;br&gt;[18] 4𝝅 {1}
|colspan=4|&lt;math&gt;[36]R_{q6,q6}&lt;/math&gt;{{Efn|The &lt;math&gt;[36]R_{q6,q6}&lt;/math&gt; isoclinic rotation in great square invariant planes takes each vertex through a 360° rotation and back to itself (360° {{=}} {{radic|0}} away), without passing through any intervening vertices. Each left square rotates 180° (like a wheel) at the same time that it tilts sideways by 180° (in an orthogonal central plane) into its corresponding right square plane. Repeated 2 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq6,q6}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6}&lt;/math&gt;&lt;br&gt;[18] 2𝝅 {4}
|colspan=4|&lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt;{{Efn|The representative coordinate &lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt; is not a vertex of the unit-radius 24-cell in standard (vertex-up) orientation, it is the center of an octahedral cell. Some of the 24-cell's lines of symmetry (Coxeter's &quot;reflecting circles&quot;) run through cell centers rather than through vertices, and quaternion group &lt;math&gt;q6&lt;/math&gt; corresponds to a set of those. However, &lt;math&gt;q6&lt;/math&gt; also corresponds to the set of great squares pictured, which lie orthogonal to those cells (completely disjoint from the cell).{{Efn|A quaternion Cartesian coordinate designates a vertex joined to a ''top vertex'' by one instance of a [[#Hypercubic chords|distinct chord]]. The conventional top vertex of a [[#Great hexagons|unit radius 4-polytope]] in ''cell-first'' orientation is &lt;math&gt;(0,0,\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2})&lt;/math&gt;. Thus e.g. &lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt; designates a {{radic|2}} chord of 90° arc-length. Each such distinct chord is an edge of a distinct [[#Geodesics|great circle polygon]], in this example a [[#Great squares|great square]], intersecting the top vertex. Great circle polygons occur in sets of Clifford parallel central planes, each set of disjoint great circles comprising a discrete [[W:Hopf fibration|Hopf fibration]] that intersects every vertex just once. One great circle polygon in each set intersects the top vertex. This quaternion coordinate &lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt; is thus representative of the 6 disjoint great squares pictured, a quaternion group{{Efn|name=quaternion group}} which comprise one distinct fibration of the [18] great squares (three fibrations of great squares) that occur in the 24-cell.{{Efn|name=three square fibrations}}|name=north cell relative coordinate}}|name=lines of symmetry}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6}&lt;/math&gt;&lt;br&gt;[18] 2𝝅 {4}
|colspan=4|&lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|2𝝅
|360°
|{{radic|0}}
|0
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6,-q6}&lt;/math&gt;&lt;br&gt;[18] 4𝝅 {2}
|colspan=4|&lt;math&gt;[36]R_{q6,-q6}&lt;/math&gt;{{Efn|The &lt;math&gt;[36]R_{q6,-q6}&lt;/math&gt; isoclinic rotation in great square invariant planes takes each vertex to a vertex 180° {{=}} {{radic|4}} away,{{Efn|name=quaternion group}} without passing through any intervening vertices. Each left square rotates 90° (like a wheel) at the same time that it tilts sideways by 90° (in an orthogonal central plane) into its corresponding right square, ''which in this rotation is the completely orthogonal plane''. Repeated 4 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq6,-q6}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6}&lt;/math&gt;&lt;br&gt;[18] 2𝝅 {4}
|colspan=4|&lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q6}&lt;/math&gt;&lt;br&gt;[18] 2𝝅 {4}
|colspan=4|&lt;math&gt;(-\tfrac{\sqrt{2}}{2},-\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|𝝅
|180°
|{{radic|4}}
|2
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/9}=3{8/3}]]{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/3}{{=}}3{4} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|2}} chords. Each disjoint square can be seen as a skew {8/3} [[W:Octagram|octagram]] with {{radic|2}} edges: two open skew squares with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅, visible in the {24/9}{{=}}3{8/3} orthogonal projection.{{Efn|[[File:Regular_star_figure_3(8,3).svg|thumb|200px|Icositetragon {24/9}{{=}}3{8/3} is a compound of three octagrams {8/3}, as the 24-cell is a compound of three 16-cells.]]This orthogonal projection of a 24-cell to a 24-gram {24/9}{{=}}3{8/3} exhibits 3 disjoint [[16-cell#Helical construction|octagram {8/3} isoclines of a 16-cell]], each of which is a circular isocline path through the 8 vertices of one of the 3 disjoint 16-cells inscribed in the 24-cell.}} The octagram projects to a single square in two dimensions because it skews through all four dimensions. Those 3 disjoint [[16-cell#Helical construction|skew octagram isoclines]] are the circular vertex paths characteristic of an [[#Helical octagrams and their isoclines|isoclinic rotation in great square planes]], in which the 6 Clifford parallel great squares are invariant rotation planes. The great squares rotate 90° like wheels ''and'' 90° orthogonally like coins flipping, displacing each vertex by 180°, so each vertex exchanges places with its antipodal vertex. Each octagram isocline circles through the 8 vertices of a disjoint 16-cell. Alternatively, the 3 squares can be seen as a fibration of 6 Clifford parallel squares.{{Efn|name=three square fibrations}} This illustrates that the 3 octagram isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 6 squares.|name=octagram}}&lt;br&gt;[[File:Regular_star_figure_3(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6,-q4}&lt;/math&gt;&lt;br&gt;[72] 4𝝅 {8/3}
|colspan=4|&lt;math&gt;[144]R_{q6,-q4}&lt;/math&gt;{{Efn|The &lt;math&gt;[144]R_{q6,-q4}&lt;/math&gt; isoclinic rotation in great square invariant planes takes each vertex to a vertex 90° {{=}} {{radic|2}} away, without passing through any intervening vertices.{{Efn|At the mid-point of the isocline arc (45° away) it passes directly over the mid-point of a 24-cell edge.}} Each left square rotates 45° (like a wheel) at the same time that it tilts sideways by 45° (in an orthogonal central plane) into its corresponding right square plane. Repeated 8 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq6,-q4}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6}&lt;/math&gt;&lt;br&gt;[72] 2𝝅 {4}
|colspan=4|&lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q4}&lt;/math&gt;&lt;br&gt;[72] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,-\tfrac{\sqrt{2}}{2},-\tfrac{\sqrt{2}}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|𝝅
|180°
|{{radic|4}}
|2
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/1}={24}]]&lt;br&gt;[[File:Regular_polygon_24.svg|100px]]&lt;br&gt;&lt;math&gt;^{q4,q4}&lt;/math&gt;&lt;br&gt;[36] 4𝝅 {1}
|colspan=4|&lt;math&gt;[72]R_{q4,q4}&lt;/math&gt;{{Efn|The &lt;math&gt;[72]R_{q4,q4}&lt;/math&gt; isoclinic rotation in great square invariant planes takes each vertex through a 360° rotation and back to itself (360° {{=}} {{radic|0}} away), without passing through any intervening vertices. Each left square rotates 180° (like a wheel) at the same time that it tilts sideways by 180° (in an orthogonal central plane) into its corresponding right square plane. Repeated 2 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq4,q4}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q4}&lt;/math&gt;&lt;br&gt;[36] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q4}&lt;/math&gt;&lt;br&gt;[36] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|2𝝅
|360°
|{{radic|0}}
|0
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: #E6FFEE;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/2}=2{12}]]{{Efn|name=dodecagon}}&lt;br&gt;[[File:Regular_star_figure_2(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2,q7}&lt;/math&gt;&lt;br&gt;[48] 4𝝅 {12}
|colspan=4|&lt;math&gt;[96]R_{q2,q7}&lt;/math&gt;{{Efn|The &lt;math&gt;[96]R_{q2,q7}&lt;/math&gt; isoclinic rotation in great hexagon invariant planes takes each vertex to a vertex one vertex away (60° {{=}} {{radic|1}} away), without passing through any intervening vertices. Each left square rotates 30° (like a wheel) at the same time that it tilts sideways by 30° (in an orthogonal central plane) into its corresponding right hexagon plane.{{Efn|name=hybrid isoclinic rotation}} Repeated 12 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq2,q7}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2}&lt;/math&gt;&lt;br&gt;[48] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,0,1)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[48] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|- style=&quot;background: #E6FFEE;&quot;|
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2,-q2}&lt;/math&gt;&lt;br&gt;[9] 4𝝅 {2}
|colspan=4|&lt;math&gt;[18]R_{q2,-q2}&lt;/math&gt;{{Efn|The &lt;math&gt;[18]R_{q2,-q2}&lt;/math&gt; isoclinic rotation in great square invariant planes takes each vertex to a vertex 180° {{=}} {{radic|4}} away,{{Efn|name=quaternion group}} without passing through any intervening vertices. Each left square rotates 90° (like a wheel) at the same time that it tilts sideways by 90° (in an orthogonal central plane) into its corresponding right square plane, ''which in this rotation is the completely orthogonal plane''. Repeated 4 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq2,-q2}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2}&lt;/math&gt;&lt;br&gt;[9] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,0,1)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q2}&lt;/math&gt;&lt;br&gt;[9] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,0,-1)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|𝝅
|180°
|{{radic|4}}
|2
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2,q1}&lt;/math&gt;&lt;br&gt;[12] 4𝝅 {2}
|colspan=4|&lt;math&gt;[12]R_{q2,q1}&lt;/math&gt;{{Efn|The &lt;math&gt;[12]R_{q2,q1}&lt;/math&gt; isoclinic rotation in great digon invariant planes takes each vertex to a vertex 90° {{=}} {{radic|2}} away, without passing through any intervening vertices.{{Efn|At the mid-point of the isocline arc (45° away) it passes directly over the mid-point of a 24-cell edge.}} Each left digon rotates 45° (like a wheel) at the same time that it tilts sideways by 45° (in an orthogonal central plane) into its corresponding right digon plane. Repeated 8 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq2,q1}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2}&lt;/math&gt;&lt;br&gt;[12] 2𝝅 {2}
|colspan=4|&lt;math&gt;(0,0,0,1)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1}&lt;/math&gt;&lt;br&gt;[12] 2𝝅 {2}
|colspan=4|&lt;math&gt;(1,0,0,0)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/1}={24}]]&lt;br&gt;[[File:Regular_polygon_24.svg|100px]]&lt;br&gt;&lt;math&gt;^{q1,q1}&lt;/math&gt;&lt;br&gt;[0] 0𝝅 {1}
|colspan=4|&lt;math&gt;[1]R_{q1,q1}&lt;/math&gt;{{Efn|The &lt;math&gt;[1]R_{q1,q1}&lt;/math&gt; rotation is the ''identity operation'' of the 24-cell, in which no points move.|name=Rq1,q1}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1}&lt;/math&gt;&lt;br&gt;[0] 2𝝅 {2}
|colspan=4|&lt;math&gt;(1,0,0,0)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1}&lt;/math&gt;&lt;br&gt;[0] 2𝝅 {2}
|colspan=4|&lt;math&gt;(1,0,0,0)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|0
|0°
|{{radic|0}}
|0
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1,-q1}&lt;/math&gt;&lt;br&gt;[12] 2𝝅 {2}
|colspan=4|&lt;math&gt;[1]R_{q1,-q1}&lt;/math&gt;{{Efn|The &lt;math&gt;[1]R_{q1,-q1}&lt;/math&gt; rotation is the ''central inversion'' of the 24-cell. This isoclinic rotation in great digon invariant planes takes each vertex to a vertex 180° {{=}} {{radic|4}} away,{{Efn|name=quaternion group}} without passing through any intervening vertices. Each left digon rotates 90° (like a wheel) at the same time that it tilts sideways by 90° (in an orthogonal central plane) into its corresponding right digon plane, ''which in this rotation is the completely orthogonal plane''. Repeated 4 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq1,-q1}} 
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1}&lt;/math&gt;&lt;br&gt;[12] 2𝝅 {2}
|colspan=4|&lt;math&gt;(1,0,0,0)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q1}&lt;/math&gt;&lt;br&gt;[12] 2𝝅 {2}
|colspan=4|&lt;math&gt;(-1,0,0,0)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|𝝅
|180°
|{{radic|4}}
|2
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|}

In a rotation class &lt;math&gt;[d]{R_{ql,qr}}&lt;/math&gt; each quaternion group &lt;math&gt;\pm{q_n}&lt;/math&gt; may be representative not only of its own fibration of Clifford parallel planes{{Efn|name=quaternion group}} but also of the other congruent fibrations.{{Efn|name=four hexagonal fibrations}} For example, rotation class &lt;math&gt;[4]R_{q7,q8}&lt;/math&gt; takes the 4 hexagon planes of &lt;math&gt;q7&lt;/math&gt; to the 4 hexagon planes of &lt;math&gt;q8&lt;/math&gt; which are 120° away, in an isoclinic rotation. But in a rigid rotation of this kind,{{Efn|name=invariant planes of an isoclinic rotation}} all [16] hexagon planes move in congruent rotational displacements, so this rotation class also includes &lt;math&gt;[4]R_{-q7,-q8}&lt;/math&gt;, &lt;math&gt;[4]R_{q8,q7}&lt;/math&gt; and &lt;math&gt;[4]R_{-q8,-q7}&lt;/math&gt;. The name &lt;math&gt;[16]R_{q7,q8}&lt;/math&gt; is the conventional representation for all [16] congruent plane displacements.

These rotation classes are all subclasses of &lt;math&gt;[32]R_{q7,q8}&lt;/math&gt; which has [32] distinct rotational displacements rather than [16] because there are two [[W:Chiral|chiral]] ways to perform any class of rotations, designated its ''left rotations'' and its ''right rotations''. The [16] left displacements of this class are not congruent with the [16] right displacements, but enantiomorphous like a pair of shoes.{{Efn|A ''right rotation'' is performed by rotating the left and right planes in the &quot;same&quot; direction, and a ''left rotation'' is performed by rotating left and right planes in &quot;opposite&quot; directions, according to the [[W:Right hand rule|right hand rule]] by which we conventionally say which way is &quot;up&quot; on each of the 4 coordinate axes. Left and right rotations are [[chiral]] enantiomorphous ''shapes'' (like a pair of shoes), not opposite rotational ''directions''. Both left and right rotations can be performed in either the positive or negative rotational direction (from left planes to right planes, or right planes to left planes), but that is an additional distinction.{{Efn|name=clasped hands}}|name=chirality versus direction}} Each left (or right) isoclinic rotation takes [16] left planes to [16] right planes, but the left and right planes correspond differently in the left and right rotations. The left and right rotational displacements of the same left plane take it to different right planes.

Each rotation class (table row) describes a distinct left (and right) [[#Isoclinic rotations|isoclinic rotation]]. The left (or right) rotations carry the left planes to the right planes simultaneously,{{Efn|name=plane movement in rotations}} through a characteristic rotation angle.{{Efn|name=two angles between central planes}} For example, the &lt;math&gt;[32]R_{q7,q8}&lt;/math&gt; rotation moves all [16] hexagonal planes at once by {{sfrac|2𝝅|3}} = 120° each. Repeated 6 times, this left (or right) isoclinic rotation moves each plane 720° and back to itself in the same [[W:Orientation entanglement|orientation]], passing through all 4 planes of the &lt;math&gt;q7&lt;/math&gt; left set and all 4 planes of the &lt;math&gt;q8&lt;/math&gt; right set once each.{{Efn|The &lt;math&gt;\pm q7&lt;/math&gt; and &lt;math&gt;\pm q8&lt;/math&gt; sets of planes are not disjoint; the union of any two of these four sets is a set of 6 planes. The left (versus right) isoclinic rotation of each of these rotation classes (table rows) visits a distinct left (versus right) circular sequence of the same set of 6 Clifford parallel planes.|name=union of q7 and q8}} The picture in the isocline column represents this union of the left and right plane sets. In the &lt;math&gt;[32]R_{q7,q8}&lt;/math&gt; example it can be seen as a set of 4 Clifford parallel skew [[W:Hexagram|hexagram]]s, each having one edge in each great hexagon plane, and skewing to the left (or right) at each vertex throughout the left (or right) isoclinic rotation.{{Efn|name=clasped hands}}

== Visualization ==
[[File:OctacCrop.jpg|thumb|[[W:Octacube (sculpture)|Octacube steel sculpture]] at Pennsylvania State University]]

=== Cell rings ===
The 24-cell is bounded by 24 [[W:Octahedron|octahedral]] [[W:Cell (geometry)|cells]].  For visualization purposes, it is convenient that the octahedron has opposing parallel [[W:Face (geometry)|faces]] (a trait it shares with the cells of the [[W:Tesseract|tesseract]] and the [[120-cell]]).  One can stack octahedrons face to face in a straight line bent in the 4th direction into a [[W:Great circle|great circle]] with a [[W:Circumference|circumference]] of 6 cells.{{Sfn|Coxeter|1970|loc=§8. The simplex, cube, cross-polytope and 24-cell|p=18|ps=; Coxeter studied cell rings in the general case of their geometry and [[W:Group theory|group theory]], identifying each cell ring as a [[W:Polytope|polytope]] in its own right which fills a three-dimensional manifold (such as the [[W:3-sphere|3-sphere]]) with its corresponding [[W:Honeycomb (geometry)|honeycomb]]. He found that cell rings follow [[W:Petrie polygon|Petrie polygon]]s{{Efn|name=Petrie dodecagram and Clifford hexagram}} and some (but not all) cell rings and their honeycombs are ''twisted'', occurring in left- and right-handed [[chiral]] forms. Specifically, he found that since the 24-cell's octahedral cells have opposing faces, the cell rings in the 24-cell are of the non-chiral (directly congruent) kind.{{Efn|name=6-cell ring is not chiral}} Each of the 24-cell's cell rings has its corresponding honeycomb in Euclidean (rather than hyperbolic) space, so the 24-cell tiles 4-dimensional Euclidean space by translation to form the [[W:24-cell honeycomb|24-cell honeycomb]].}}{{Sfn|Banchoff|2013|ps=, studied the decomposition of regular 4-polytopes into honeycombs of tori tiling the [[W:Clifford torus|Clifford torus]], showed how the honeycombs correspond to [[W:Hopf fibration|Hopf fibration]]s, and made a particular study of the [[#6-cell rings|24-cell's 4 rings of 6 octahedral cells]] with illustrations.}} The cell locations lend themselves to a [[W:3-sphere|hyperspherical]] description. Pick an arbitrary cell and label it the &quot;[[W:North Pole|North Pole]]&quot;. Eight great circle meridians (two cells long) radiate out in 3 dimensions, converging at the 3rd &quot;[[W:South Pole|South Pole]]&quot; cell. This skeleton accounts for 18 of the 24 cells (2&amp;nbsp;+&amp;nbsp;{{gaps|8|×|2}}). See the table below.

There is another related [[#Geodesics|great circle]] in the 24-cell, the dual of the one above. A path that traverses 6 vertices solely along edges resides in the dual of this polytope, which is itself since it is self dual. These are the [[#Great hexagons|hexagonal]] geodesics [[#Geodesics|described above]].{{Efn|name=hexagonal fibrations}} One can easily follow this path in a rendering of the equatorial [[W:Cuboctahedron|cuboctahedron]] cross-section.

Starting at the North Pole, we can build up the 24-cell in 5 latitudinal layers. With the exception of the poles, each layer represents a separate 2-sphere, with the equator being a great 2-sphere.{{Efn|name=great 2-spheres}} The cells labeled equatorial in the following table are interstitial to the meridian great circle cells. The interstitial &quot;equatorial&quot; cells touch the meridian cells at their faces. They touch each other, and the pole cells at their vertices.  This latter subset of eight non-meridian and pole cells has the same relative position to each other as the cells in a [[W:Tesseract|tesseract]] (8-cell), although they touch at their vertices instead of their faces.

{| class=&quot;wikitable&quot;
|-
! Layer #
! Number of Cells
! Description
! Colatitude
! Region
|-
| style=&quot;text-align: center&quot; | 1
| style=&quot;text-align: center&quot; | 1 cell
| North Pole
| style=&quot;text-align: center&quot; | 0°
| rowspan=&quot;2&quot; | Northern Hemisphere
|-
| style=&quot;text-align: center&quot; | 2
| style=&quot;text-align: center&quot; | 8 cells
| First layer of meridian cells
| style=&quot;text-align: center&quot; | 60°
|-
| style=&quot;text-align: center&quot; | 3
| style=&quot;text-align: center&quot; | 6 cells
| Non-meridian / interstitial
| style=&quot;text-align: center&quot; | 90°
| style=&quot;text-align: center&quot; |Equator
|-
| style=&quot;text-align: center&quot; | 4
| style=&quot;text-align: center&quot; | 8 cells
| Second layer of meridian cells
| style=&quot;text-align: center&quot; | 120°
| rowspan=&quot;2&quot; | Southern Hemisphere
|-
| style=&quot;text-align: center&quot; | 5
| style=&quot;text-align: center&quot; | 1 cell
| South Pole
| style=&quot;text-align: center&quot; | 180°
|-
! Total
! 24 cells
! colspan=&quot;3&quot; |
|}
[[File:24-cell-6 ring edge center perspective.png|thumb|An edge-center perspective projection, showing one of four rings of 6 octahedra around the equator]]
The 24-cell can be partitioned into cell-disjoint sets of four of these 6-cell great circle rings, forming a discrete [[W:Hopf fibration|Hopf fibration]] of four non-intersecting linked rings.{{Efn|name=fibrations are distinguished only by rotations}} One ring is &quot;vertical&quot;, encompassing the pole cells and four meridian cells. The other three rings each encompass two equatorial cells and four meridian cells, two from the northern hemisphere and two from the southern.{{sfn|Banchoff|2013|p=|pp=265-266|loc=}}

Note this hexagon great circle path implies the interior/dihedral angle between adjacent cells is 180 - 360/6 = 120 degrees.  This suggests you can adjacently stack exactly three 24-cells in a plane and form a 4-D honeycomb of 24-cells as described previously.

One can also follow a [[#Geodesics|great circle]] route, through the octahedrons' opposing vertices, that is four cells long.  These are the [[#Great squares|square]] geodesics along four {{sqrt|2}} chords [[#Geodesics|described above]]. This path corresponds to traversing diagonally through the squares in the cuboctahedron cross-section.  The 24-cell is the only regular polytope in more than two dimensions where you can traverse a great circle purely through opposing vertices (and the interior) of each cell.  This great circle is self dual.  This path was touched on above regarding the set of 8 non-meridian (equatorial) and pole cells.

The 24-cell can be equipartitioned into three 8-cell subsets, each having the organization of a tesseract.  Each of these subsets can be further equipartitioned into two non-intersecting linked great circle chains, four cells long.  Collectively these three subsets now produce another, six ring, discrete Hopf fibration.

=== Parallel projections ===
[[Image:Orthogonal projection envelopes 24-cell.png|thumb|Projection envelopes of the 24-cell. (Each cell is drawn with different colored faces, inverted cells are undrawn)]]
The ''vertex-first'' parallel projection of the 24-cell into 3-dimensional space has a [[W:Rhombic dodecahedron|rhombic dodecahedral]] [[W:Projection envelope|envelope]]. Twelve of the 24 octahedral cells project in pairs onto six square dipyramids that meet at the center of the rhombic dodecahedron. The remaining 12 octahedral cells project onto the 12 rhombic faces of the rhombic dodecahedron.

The ''cell-first'' parallel projection of the 24-cell into 3-dimensional space has a [[W:Cuboctahedron|cuboctahedral]] envelope. Two of the octahedral cells, the nearest and farther from the viewer along the ''w''-axis, project onto an octahedron whose vertices lie at the center of the cuboctahedron's square faces. Surrounding this central octahedron lie the projections of 16 other cells, having 8 pairs that each project to one of the 8 volumes lying between a triangular face of the central octahedron and the closest triangular face of the cuboctahedron. The remaining 6 cells project onto the square faces of the cuboctahedron. This corresponds with the decomposition of the cuboctahedron into a regular octahedron and 8 irregular but equal octahedra, each of which is in the shape of the convex hull of a cube with two opposite vertices removed.

The ''edge-first'' parallel projection has an [[W:Elongated hexagonal dipyramidelongated hexagonal dipyramid|Elongated hexagonal dipyramidelongated hexagonal dipyramid]]al envelope, and the ''face-first'' parallel projection has a nonuniform hexagonal bi-[[W:Hexagonal antiprism|antiprismic]] envelope.

=== Perspective projections ===
The ''vertex-first'' [[W:Perspective projection|perspective projection]] of the 24-cell into 3-dimensional space has a [[W:Tetrakis hexahedron|tetrakis hexahedral]] envelope. The layout of cells in this image is similar to the image under parallel projection.

The following sequence of images shows the structure of the cell-first perspective projection of the 24-cell into 3 dimensions. The 4D viewpoint is placed at a distance of five times the vertex-center radius of the 24-cell.

{|class=&quot;wikitable&quot; width=660
!colspan=3|Cell-first perspective projection
|- valign=top
|[[Image:24cell-perspective-cell-first-01.png|220px]]&lt;BR&gt;In this image, the nearest cell is rendered in red, and the remaining cells are in edge-outline. For clarity, cells facing away from the 4D viewpoint have been culled.
|[[Image:24cell-perspective-cell-first-02.png|220px]]&lt;BR&gt;In this image, four of the 8 cells surrounding the nearest cell are shown in green. The fourth cell is behind the central cell in this viewpoint (slightly discernible since the red cell is semi-transparent).
|[[Image:24cell-perspective-cell-first-03.png|220px]]&lt;BR&gt;Finally, all 8 cells surrounding the nearest cell are shown, with the last four rendered in magenta.
|-
|colspan=3|Note that these images do not include cells which are facing away from the 4D viewpoint. Hence, only 9 cells are shown here. On the far side of the 24-cell are another 9 cells in an identical arrangement. The remaining 6 cells lie on the &quot;equator&quot; of the 24-cell, and bridge the two sets of cells.
|}

{| class=&quot;wikitable&quot; width=440
|[[Image:24cell section anim.gif|220px]]&lt;br&gt;Animated cross-section of 24-cell
|-
|colspan=2 valign=top|[[Image:3D stereoscopic projection icositetrachoron.PNG|450px]]&lt;br&gt;A [[W:Stereoscopy|stereoscopic]] 3D projection of an icositetrachoron (24-cell).
|-
|colspan=3|[[File:Cell24Construction.ogv|450px]]&lt;br&gt;Isometric Orthogonal Projection of: 8 Cell(Tesseract) + 16 Cell = 24 Cell
|}

== Related polytopes ==
=== Three Coxeter group constructions ===
There are two lower symmetry forms of the 24-cell, derived as a [[W:Rectification (geometry)|rectified]] 16-cell, with B&lt;sub&gt;4&lt;/sub&gt; or [3,3,4] symmetry drawn bicolored with 8 and 16 [[W:Octahedron|octahedral]] cells. Lastly it can be constructed from D&lt;sub&gt;4&lt;/sub&gt; or [3&lt;sup&gt;1,1,1&lt;/sup&gt;] symmetry, and drawn tricolored with 8 octahedra each.&lt;!-- it would be nice to illustrate another of these lower-symmetry decompositions of the 24-cell, into 4 different-colored helixes of 6 face-bonded octahedral cells, as those are the cell rings of its fibration described in /* Visualization */ --&gt;

{| class=&quot;wikitable collapsible collapsed&quot;
!colspan=12| Three [[W:Net (polytope)|nets]] of the ''24-cell'' with cells colored by D&lt;sub&gt;4&lt;/sub&gt;, B&lt;sub&gt;4&lt;/sub&gt;, and F&lt;sub&gt;4&lt;/sub&gt; symmetry
|-
![[W:Rectified demitesseract|Rectified demitesseract]]
![[W:Rectified demitesseract|Rectified 16-cell]]
!Regular 24-cell
|-
!D&lt;sub&gt;4&lt;/sub&gt;, [3&lt;sup&gt;1,1,1&lt;/sup&gt;], order 192
!B&lt;sub&gt;4&lt;/sub&gt;, [3,3,4], order 384
!F&lt;sub&gt;4&lt;/sub&gt;, [3,4,3], order 1152
|-
|colspan=3 align=center|[[Image:24-cell net 3-symmetries.png|659px]]
|- valign=top
|width=213|Three sets of 8 [[W:Rectified tetrahedron|rectified tetrahedral]] cells
|width=213|One set of 16 [[W:Rectified tetrahedron|rectified tetrahedral]] cells and one set of 8 [[W:Octahedron|octahedral]] cells.
|width=213|One set of 24 [[W:Octahedron|octahedral]] cells
|-
|colspan=3 align=center|'''[[W:Vertex figure|Vertex figure]]'''&lt;br&gt;(Each edge corresponds to one triangular face, colored by symmetry arrangement)
|- align=center
|[[Image:Rectified demitesseract verf.png|120px]]
|[[Image:Rectified 16-cell verf.png|120px]]
|[[Image:24 cell verf.svg|120px]]
|}

=== Related complex polygons ===
The [[W:Regular complex polygon|regular complex polygon]] &lt;sub&gt;4&lt;/sub&gt;{3}&lt;sub&gt;4&lt;/sub&gt;, {{Coxeter–Dynkin diagram|4node_1|3|4node}} or {{Coxeter–Dynkin diagram|node_h|6|4node}} contains the 24 vertices of the 24-cell, and 24 4-edges that correspond to central squares of 24 of 48 octahedral cells. Its symmetry is &lt;sub&gt;4&lt;/sub&gt;[3]&lt;sub&gt;4&lt;/sub&gt;, order 96.{{Sfn|Coxeter|1991|p=}}

The regular complex polytope &lt;sub&gt;3&lt;/sub&gt;{4}&lt;sub&gt;3&lt;/sub&gt;, {{Coxeter–Dynkin diagram|3node_1|4|3node}} or {{Coxeter–Dynkin diagram|node_h|8|3node}}, in &lt;math&gt;\mathbb{C}^2&lt;/math&gt; has a real representation as a 24-cell in 4-dimensional space. &lt;sub&gt;3&lt;/sub&gt;{4}&lt;sub&gt;3&lt;/sub&gt; has 24 vertices, and 24 3-edges. Its symmetry is &lt;sub&gt;3&lt;/sub&gt;[4]&lt;sub&gt;3&lt;/sub&gt;, order 72.

{| class=wikitable width=600
|+ Related figures in orthogonal projections
|-
!Name
!{3,4,3}, {{Coxeter–Dynkin diagram|node_1|3|node|4|node|3|node}}
!&lt;sub&gt;4&lt;/sub&gt;{3}&lt;sub&gt;4&lt;/sub&gt;, {{Coxeter–Dynkin diagram|4node_1|3|4node}}
!&lt;sub&gt;3&lt;/sub&gt;{4}&lt;sub&gt;3&lt;/sub&gt;, {{Coxeter–Dynkin diagram|3node_1|4|3node}}
|-
!Symmetry
![3,4,3], {{Coxeter–Dynkin diagram|node|3|node|4|node|3|node}}, order 1152
!&lt;sub&gt;4&lt;/sub&gt;[3]&lt;sub&gt;4&lt;/sub&gt;, {{Coxeter–Dynkin diagram|4node|3|4node}}, order 96
!&lt;sub&gt;3&lt;/sub&gt;[4]&lt;sub&gt;3&lt;/sub&gt;, {{Coxeter–Dynkin diagram|3node|4|3node}}, order 72
|- align=center
!Vertices
|24||24||24
|- align=center
!Edges
|96 2-edges||24 4-edge||24 3-edges
|- valign=top
!valign=center|Image
|[[File:24-cell t0 F4.svg|200px]]&lt;BR&gt;24-cell in F4 Coxeter plane, with 24 vertices in two rings of 12, and 96 edges.
|[[File:Complex polygon 4-3-4.png|200px]]&lt;BR&gt;&lt;sub&gt;4&lt;/sub&gt;{3}&lt;sub&gt;4&lt;/sub&gt;, {{Coxeter–Dynkin diagram|4node_1|3|4node}} has 24 vertices and 32 4-edges, shown here with 8 red, green, blue, and yellow square 4-edges.
|[[File:Complex polygon 3-4-3-fill1.png|200px]]&lt;BR&gt;&lt;sub&gt;3&lt;/sub&gt;{4}&lt;sub&gt;3&lt;/sub&gt; or {{Coxeter–Dynkin diagram|3node_1|4|3node}} has 24 vertices and 24 3-edges, shown here with 8 red, 8 green, and 8 blue square 3-edges, with blue edges filled.
|}

=== Related 4-polytopes ===
Several [[W:Uniform 4-polytope|uniform 4-polytope]]s can be derived from the 24-cell via [[W:Truncation (geometry)|truncation]]:
* truncating at 1/3 of the edge length yields the [[W:Truncated 24-cell|truncated 24-cell]];
* truncating at 1/2 of the edge length yields the [[W:Rectified 24-cell|rectified 24-cell]];
* and truncating at half the depth to the dual 24-cell yields the [[W:Bitruncated 24-cell|bitruncated 24-cell]], which is [[W:Cell-transitive|cell-transitive]].

The 96 edges of the 24-cell can be partitioned into the [[W:Golden ratio|golden ratio]] to produce the 96 vertices of the [[W:Snub 24-cell|snub 24-cell]]. This is done by first placing vectors along the 24-cell's edges such that each two-dimensional face is bounded by a cycle, then similarly partitioning each edge into the golden ratio along the direction of its vector. An analogous modification to an [[W:Octahedron|octahedron]] produces an [[W:Regular icosahedron|icosahedron]], or &quot;[[W:Regular icosahedron#Uniform colorings and subsymmetries|snub octahedron]].&quot;

The 24-cell is the unique convex self-dual regular Euclidean polytope that is neither a [[W:Polygon|polygon]] nor a [[W:simplex (geometry)|simplex]]. Relaxing the condition of convexity admits two further figures: the [[W:Great 120-cell|great 120-cell]] and [[W:Grand stellated 120-cell|grand stellated 120-cell]]. With itself, it can form a [[W:Polytope compound|polytope compound]]: the [[#Symmetries, root systems, and tessellations|compound of two 24-cells]].

=== Related uniform polytopes ===
{{Demitesseract family}}

{{24-cell_family}}

The 24-cell can also be derived as a rectified 16-cell:
{{Tesseract family}}

{{Symmetric_tessellations}}

==See also==
*[[W:Octacube (sculpture)|Octacube (sculpture)]]
*[[W:Uniform 4-polytope#The F4 family|Uniform 4-polytope § The F4 family]]

== Notes ==
{{Regular convex 4-polytopes Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite book | last=Kepler | first=Johannes | author-link=W:Johannes Kepler | title=Harmonices Mundi (The Harmony of the World) | title-link=W:Harmonices Mundi | publisher=Johann Planck | year=1619}}
* {{Cite book | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1973 | orig-year=1948 | title=Regular Polytopes | publisher=Dover | place=New York | edition=3rd | title-link=W:Regular Polytopes (book) }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1991 | title=Regular Complex Polytopes | place=Cambridge | publisher=Cambridge University Press | edition=2nd }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1995 | title=Kaleidoscopes: Selected Writings of H.S.M. Coxeter | publisher=Wiley-Interscience Publication | edition=2nd | isbn=978-0-471-01003-6 | url=https://archive.org/details/kaleidoscopessel0000coxe | editor1-last=Sherk | editor1-first=F. Arthur | editor2-last=McMullen | editor2-first=Peter | editor3-last=Thompson | editor3-first=Anthony C. | editor4-last=Weiss | editor4-first=Asia Ivic | url-access=registration }}
** (Paper 3) H.S.M. Coxeter, ''Two aspects of the regular 24-cell in four dimensions''
** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380–407, MR 2,10]
** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', [Math. Zeit. 188 (1985) 559-591]
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
* {{Cite book | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1968 | title=The Beauty of Geometry: Twelve Essays | publisher=Dover | place=New York | edition=2nd }}
* {{Cite journal | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1989 | title=Trisecting an Orthoscheme | journal=Computers Math. Applic. | volume=17 | issue=1–3 | pages=59–71 | doi=10.1016/0898-1221(89)90148-X | doi-access=free }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1970 | title=Twisted Honeycombs | place=Providence, Rhode Island | journal=Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics | publisher=American Mathematical Society | volume=4 }} 
* {{Cite journal|last=Stillwell|first=John|date=January 2001|title=The Story of the 120-Cell|url=https://www.ams.org/notices/200101/fea-stillwell.pdf|journal=Notices of the AMS|volume=48|issue=1|pages=17–25}}
*{{Citation | last=Goucher | first=A.P. | title=Spin groups | date=19 November 2019 | journal=Complex Projective 4-Space | url=https://cp4space.hatsya.com/2012/11/19/spin-groups/ }}
*{{Citation | last=Goucher | first=A.P. | title=Subsumptions of regular polytopes | date=1 October 2020 | journal=Complex Projective 4-Space | url=https://cp4space.hatsya.com/2020/10/01/subsumptions-of-regular-polytopes }}
*{{Citation | last=Johnson | first=Norman | author-link=W:Norman Johnson (mathematician) | title=Geometries and Transformations | year=2018 | place=Cambridge | publisher=Cambridge University Press | isbn=978-1-107-10340-5 | url=https://www.cambridge.org/core/books/geometries-and-transformations/94D1016D7AC64037B39440729CE815AB}}
* {{Citation | last=Johnson | first=Norman | author-link=W:Norman Johnson (mathematician) | year=1991 | title=Uniform Polytopes | edition=Manuscript }}
* {{Citation | last=Johnson | first=Norman | author-link=W:Norman Johnson (mathematician) | year=1966 | title=The Theory of Uniform Polytopes and Honeycombs | edition=Ph.D. }}
* {{cite book|last=Ghyka|first=Matila|title=The Geometry of Art and Life|date=1977|place=New York|publisher=Dover Publications|isbn=978-0-486-23542-4}}
* {{cite book|last=Banchoff|first=Thomas F.|chapter=Torus Decompostions of Regular Polytopes in 4-space|date=2013|title=Shaping Space|url=https://archive.org/details/shapingspaceexpl00sene|url-access=limited|pages=[https://archive.org/details/shapingspaceexpl00sene/page/n249 257]–266|editor-last=Senechal|editor-first=Marjorie|publisher=Springer New York|doi=10.1007/978-0-387-92714-5_20|isbn=978-0-387-92713-8}}
* {{Cite arXiv | eprint=1903.06971 | last=Copher | first=Jessica | year=2019 | title=Sums and Products of Regular Polytopes' Squared Chord Lengths | class=math.MG }}
* {{Cite thesis|url= http://resolver.tudelft.nl/uuid:dcffce5a-0b47-404e-8a67-9a3845774d89 |title=Symmetry groups of regular polytopes in three and four dimensions|last=van Ittersum |first=Clara|year=2020|publisher=[[W:Delft University of Technology|Delft University of Technology]]}}
* {{cite arXiv|last1=Kim|first1=Heuna|last2=Rote|first2=G.|date=2016|title=Congruence Testing of Point Sets in 4 Dimensions|class=cs.CG|eprint=1603.07269}}
* {{Cite journal|last1=Perez-Gracia|first1=Alba|last2=Thomas|first2=Federico|date=2017|title=On Cayley's Factorization of 4D Rotations and Applications|url=https://upcommons.upc.edu/bitstream/handle/2117/113067/1749-ON-CAYLEYS-FACTORIZATION-OF-4D-ROTATIONS-AND-APPLICATIONS.pdf|journal=Adv. Appl. Clifford Algebras|volume=27|pages=523–538|doi=10.1007/s00006-016-0683-9|hdl=2117/113067|s2cid=12350382|hdl-access=free}}
* {{Cite journal|last1=Waegell|first1=Mordecai|last2=Aravind|first2=P. K.|date=2009-11-12|title=Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem|journal=Journal of Physics A: Mathematical and Theoretical|volume=43|issue=10|page=105304|language=en|doi=10.1088/1751-8113/43/10/105304|arxiv=0911.2289|s2cid=118501180}}
* {{Cite book|title=Generalized Clifford parallelism|last1=Tyrrell|first1=J. A.|last2=Semple|first2=J.G.|year=1971|publisher=[[W:Cambridge University Press|Cambridge University Press]]|url=https://archive.org/details/generalizedcliff0000tyrr|isbn=0-521-08042-8}}
* {{Cite web|last=Egan|first=Greg|date=23 December 2021|title=Symmetries and the 24-cell|url=https://www.gregegan.net/SCIENCE/24-cell/24-cell.html|author-link=W:Greg Egan|website=gregegan.net|access-date=10 October 2022}}
* {{Cite journal | last1=Mamone|first1=Salvatore | last2=Pileio|first2=Giuseppe | last3=Levitt|first3=Malcolm H. | year=2010 | title=Orientational Sampling Schemes Based on Four Dimensional Polytopes | journal=Symmetry | volume=2 |issue=3 | pages=1423–1449 | doi=10.3390/sym2031423 |bibcode=2010Symm....2.1423M |doi-access=free }}
* {{Cite thesis|title=Applications of Quaternions to Dynamical Simulation, Computer Graphics and Biomechanics|last=Mebius|first=Johan|date=July 2015|publisher=[[W:Delft University of Technology|Delft University of Technology]]|orig-date=11 Jan 1994|doi=10.13140/RG.2.1.3310.3205}}
* {{Cite book|title=Elementary particles and the laws of physics|last1=Feynman|first1=Richard|last2=Weinberg|first2=Steven|publisher=Cambridge University Press|year=1987}}
* {{Cite journal|last=Dorst|first=Leo|title=Conformal Villarceau Rotors|year=2019|journal=Advances in Applied Clifford Algebras|volume=29|issue=44|doi=10.1007/s00006-019-0960-5 |s2cid=253592159 |doi-access=free}}
* {{Cite journal|last1=Koca|first1=Mehmet|last2=Al-Ajmi|first2=Mudhahir|last3=Koc|first3=Ramazan|date=November 2007|title=Polyhedra obtained from Coxeter groups and quaternions|journal=Journal of Mathematical Physics|volume=48|issue=11|pages=113514|doi=10.1063/1.2809467|bibcode=2007JMP....48k3514K |url=https://www.researchgate.net/publication/234907424}}
{{Refend}}

==External links==
* [https://bendwavy.org/klitzing/incmats/ico.htm ico], at [https://bendwavy.org/klitzing/home.htm Klitzing polytopes]
* [https://polytope.miraheze.org/wiki/Icositetrachoron Icositetrachoron], at [https://polytope.miraheze.org/wiki/Main_Page Polytope wiki]
* [http://hi.gher.space/wiki/Xylochoron Xylochoron], at [http://hi.gher.space/wiki/Main_Page Higher space]
* [https://www.qfbox.info/4d/24-cell The 24-cell], at [https://www.qfbox.info/4d/index 4D Euclidean Space]
* [https://web.archive.org/web/20051118135108/http://valdostamuseum.org/hamsmith/24anime.html 24-cell animations]
* [http://members.home.nl/fg.marcelis/24-cell.htm 24-cell in stereographic projections]
* [http://eusebeia.dyndns.org/4d/24-cell.html 24-cell description and diagrams] {{Webarchive|url=https://web.archive.org/web/20070715053230/http://eusebeia.dyndns.org/4d/24-cell.html |date=2007-07-15 }}
* [https://web.archive.org/web/20071204034724/http://www.xs4all.nl/~jemebius/Ab4help.htm Petrie dodecagons in the 24-cell: mathematics and animation software]

[[Category:Geometry]]
[[Category:Polyscheme]]</text>
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      <text bytes="29402" sha1="04dr71zd7r00q0amscsuh5u71z5a1c2" xml:space="preserve">{{title|Sound and perception of food and drink:&lt;br&gt;How does sound influence the taste and enjoyment of food and drink?}}
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__TOC__

==Overview==
{{robelbox|theme=9|title=Scenario: Sound and perception of food and drink}}
  &lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
    [[File:Caesar Salad (44907536925).jpg|thumb|'''Figure 1.''' Even a Caesar salad needs a good &quot;crunch&quot; to be fully enjoyable]]

Imagine sitting down to enjoy a carefully prepared meal at your favourite restaurant. The aroma is enticing, the presentation is highly appealing, and you're ready to savour every bite. 

But as you take that first bite, you're disappointed by the lack of &quot;crunch&quot; from the salad's croutons and the noise from a nearby table is making it hard to focus on the gorgeous flavours of your highly anticipated meal (see Figure 1). You might not realise it, but the sounds you hear - or don't hear - are largely impacting your dining experience.
&lt;/div&gt;
{{Robelbox/close}}

Enjoyment of food and drink is not only based on taste; it is a multi-sensory experience. From the fizz of a carbonated drink to the clatter of dishes in the background, the sounds associated with food and the dining environment can enhance or diminish enjoyment.

This book chapter explores how these sounds influence peoples{{gr}} perception of food and drink, with reference to underlying psychological theories and mechanisms that make certain sounds more satisfying, as well as how auditory cues even influence motivation to eat. Whether it's the perfect crunch, the right ambiance, or the subtle sounds that are barely noticed in surrounding environments, sound shapes dining experiences in more ways than expected.

{{RoundBoxTop|theme=9}}
'''Focus questions:'''
* Where does motivation for an enjoyable food and drink experience come from? 
* What are the cross-modal effects experienced during eating and drinking?
* How can eating behaviours and motivation change?{{vague}}
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==The origins of food and drink enjoyment==
The reasons behind food and drink enjoyment stem from the most basic human survival instincts. Early studies{{fact}} on the relationship between sound and flavour perception, combined with modern research into the psychological, cultural, and social significance of food, show just how complex and important consumption experiences are.  

=== The innate motivation for hunger and thirst ===
[[File:Maslow's Hierarchy of Needs2.svg|thumb|'''Figure 2.''' Maslow's hierarchy of needs (1943) places motivation for food and drink at the most basic level]]

Human motivation for food, drink, and enjoyment derives from the most basic survival instincts of hunger and thirst. This closely aligns with Maslow's (1943) hierarchy of needs (see Figure 2), where motivations to seek out food and drink are embedded in the human body's physiological need to maintain balance and ensure survival (Sternson et al., 2013). When an individual's body signals they need energy or hydration, motivation to eat and drink is powerful in directing their behaviour and decisions (Reeve, 2018). Biological disturbances such as thirst and hunger, are deficiency needs (Reeve, 2018) that arise when the body experiences a lack of essential nutrients, prompting us to take action to restore balance and ensure survival by seeking out food and drink. For more information, see:
* [[Motivation and emotion/Book/2010/Hunger motivation|Hunger motivation]] (Book chapter, 2010)
* [[Motivation and emotion/Book/2014/Dehydration and mood|Thirst and dehydration]] (Book chapter, 2014)

=== The study of hearing and flavour perception: A brief history ===
Food scientists began exploring how sound influences food and drink perception during the mid-20th century, with early studies largely focusing on how environment (background) noise affects taste (Spence, 2015). Birger Drake (1970) expanded on this research by analysing the sounds produced when food was chewed or crushed, discovering differences in amplitude, frequency, and timing (Spence, 2015; Yan et al., 2015). Zata Vickers (1991) furthered this work, showing that certain pitches of sounds could be linked to specific food-related textures (i.e., crunchiness and crispness) (Spence, 2015).

Later research also linked sound to flavour perception. For example, Ferber and Cabanac (1987) found loud noises to negatively impact the enjoyment of food. Crisinel and Spence (2009) and Woods and colleagues (2011) demonstrated associations between sound pitch and taste, suggesting auditory stimuli play a significant role in shaping someones{{gr}} tasting experience. These [[#Auditory cues|auditory cues]], combined with cultural and linguistic differences in texture perception, highlight the complexity of the food and drink experience (Spence, 2015; Yan et al., 2015). 

=== Why is enjoyment for food so important? ===
Eating and drinking habits are deeply intertwined with essential moral and social values. Research has consistently shown that humans have become an increasingly 'consumption-oriented society', whereby food and drink play an increasingly central role in peoples{{gr}} lives (Locher et al., 2005; Silver, 1996). Dining experiences are therefore a key element of connection, where restaurants and bars are popular spaces for socialising and unwinding over a nice meal or refreshing beverage. In many ways, dining can reinforce personal bonds as well as broader cultural values (Silver, 1996; Spence, 2015). 

Locher and colleagues (2005) also highlight the modern world's large dependence on comfort foods to cope with stress, psychological discomfort, and sadness, reflecting broader trends in society where food serves both nutritional and emotional purposes (Dunbar, 2017). Additionally, the things we consume, particularly food, can shape personal and social identities. Impulses and needs in this nature constitute the foundation for many forms of social behaviour and belonging (Locher et al., 2005). For more information see [https://www.ox.ac.uk/news/2017-03-16-social-eating-connects-communities Social eating connects communities] (University of Oxford) or in Dunbar (2017).

{{robelbox|theme=6|title=Case study: Jessica's Dining Experience|iconwidth=55px|icon=Think Outside the Box Flat Icon GIF Animation.gif}}
  &lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
Jessica is a 32 year old accountant, who occasionally loves visiting new restaurants around town. She's always seeking places with unique food and a nice ambiance. One Saturday evening, she invites her mother to come dine with her at a new trendy Asian fusion restaurant. It is currently her favourite cuisine and she's been craving some dumplings over the last couple of days. It has a huge dumpling menu, so she eagerly orders some pork dumplings with a fresh Asian side salad, while her mother chooses some sizzling pepper steak to follow ... &lt;/div&gt;
{{Robelbox/close}}

== Food and drink perception as a multisensory experience ==
The consumption of food and drink is one of the most multisensory perceptual experiences for humans, engaging all five senses to create a rich, integrated experience. That is, food and drink perception does not just depend on individual senses, but is a result from the [[wikipedia:Multisensory_integration|multisensory integration]] of all five (Vi et al., 2020; Pereira &amp; van der Bilt, 2016){{gr}}. Stated by world class chef, Heston Blumenthal, &quot;Eating is the only thing that we do that involves all of the senses. I don't think that we realise just how much influence the senses actually have on the way that we process information from mouth to brain&quot; (Spence, 2015, p. 2). This multisensory integration, understood through cross-modal effects, is grounded in psychological theories such as Ayres' Sensory Integration Theory and Grossberg's Adaptive Resonance Theory, which highlight the complex, psychologically driven nature of eating and drinking experiences.

=== Cross-modal effects ===
Cross-modal effects refer to interactions between different sensory modalities, such as sight, sound, taste, touch, and smell. In the context of perception, it means that the experience of interpreting one sense can influence or alter the perception of another (Zampini &amp; Spence, 2010). Cross-modal effects of taste and sound for example, explain how the crunchiness of food can be perceived as less intense if the sound associated with it is muffled, interrupted, or blatantly absent. These interactions highlight the complex nature of sensory perception and the brain's ability to integrate information from multiple senses to create a unified experience (Crisinel &amp; Spence, 2009; Zampini &amp; Spence, 2010). These cross-modal effects, especially during eating and drinking, have been thoroughly researched, revealing that what people hear - food-related or not - can significantly influence their perceptions of taste and flavour (Zampini &amp; Spence, 2010). 

=== Psychological underpinnings ===
Psychological theory helps to further explain these interactions across sensory modalities; 

==== Ayres' sensory integration theory ====
[[File:Jean Photos-1.jpg|thumb|245x245px|'''Figure 3.''' American occupational therapist and founder of ASI, Jean Ayres (1920-1988)|left]]
[[wikipedia:Anna_Jean_Ayres#Development_of_Sensory_Integration_theory|Sensory integration theory]] (commonly referred to as Ayres' Sensory Integration (ASI), developed by Jean Ayres, focuses on how the brain integrates sensory information from various modalities (i.e., sight, sound, smell, and touch). A large amount of Ayres work focused on developing intervention strategies to understand and treat children with learning and behavioural challenges (refer to Figure 3, or [https://raisingchildren.net.au/autism/therapies-guide/sensory-integration sensory integration therapy] for more information). 

According to ASI, difficulties in integrating sensory information can influence how people react to stimuli. For instance, sensory inputs such as the sound of chewing, background noise, and food textures all contribute to an individuals{{gr}} overall perception of food. The ASI framework suggests this integration of multiple sensory inputs is relied on for meaningful experience (Lane et al., 2019).

ASI supports the presence of cross-modal effects within food perception. For instance, studies have found sound-taste associations, where high-pitched sounds are linked to sweet and sour tastes, while low-pitched sounds are linked with bitterness (Crisinel &amp; Spence, 2009; Motoki et al., 2019). ASI helps explain how the brain naturally seeks to synthesise information from different senses to create a unified perception of food (Lane et al., 2019). Additionally, Knoeferle and colleagues (2015) found staccato (short and fast) sounds are associated with crunchiness, while legato (smooth and continuous) sounds evoke creaminess. These findings emphasise a connection between auditory and gustatory senses, reinforcing how auditory stimuli connect with textural sensations. Sensory integration therefore serves as a fundamental basis of the cross-modal effects that arise during food and drink perception.

==== Adaptive resonance theory ====
[[wikipedia:Adaptive_resonance_theory|Adaptive resonance theory]] (ART) is a more recent cognitive neural theory, developed by Stephen Grossberg (2013), explaining how the brain autonomously processes information based on prior experience and stored memories. ART can also explain how and why cross-modal effects emerge during sensory perception. That is, how expectations in one sensory modality (i.e., sound) influence perception in another modality (i.e., taste). As the brain is constantly integrating sensory inputs from multiple sources, perception remains stable and adaptive when the sensory information is consistent with expectations (Grossberg, 2013). However, when the sensory input from a sound does not align with what someone expects to taste, the brain may struggle to adapt and thus food/drink perception is altered. This process of using prior knowledge and expectations to interpret sensory input is known as [https://www.youtube.com/watch?v=0enXduVi4LE 'top-down processing]'. These top-down processes act like filters, guiding attention toward the most relevant cues in the environment (Grossberg, 2013). ART describes this process as &quot;biased competition&quot;, where certain stimuli are given priority over others based on how well they align with expectations. The brain is then focused on the most important information at any given time to form these 'expectations' (De Lange et al., 2018; Grosseberg, 2013).

Expectations, influenced by previous experiences or cultural cues, shape how food is perceived. Top-down processing helps explain how a person's past experiences, such as memory of a flavour, can influence or even enhance the way they perceive new tastes (Grossberg, 2013). If the salad (Figure 1) is expected to be crispy but isn't, it can lead to disappointment and reduced enjoyment due to sensory expectations being disrupted. If the sound (such as a crunch) matches the expectation, the perception is reinforced and leads to satisfaction.

{{tip|'''Quiz'''}}

&lt;quiz display=&quot;simple&quot;&gt;
{Multisensory integration is a psychological theory that explains how the brain combines information from multiple senses to create a unified perceptual experience:
|type=&quot;()&quot;}
+ True
- False

{Top-down processing is associated with which psychological theory:
|type=&quot;()&quot;}
- Multisensory Integration
+ Adaptive Resonance Theory (ART)
- Ayres' Sensory Integration (ASI)

&lt;/quiz&gt;

{{robelbox|theme=6|title=Case study: Jessica's Dining Experience|iconwidth=55px|icon=Think Outside the Box Flat Icon GIF Animation.gif}}
  &lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
 As she begins her meal, Jessica notices the noodles in her Asian salad are not satisfying to eat. They don't have the usual crunch to them and instead seem a bit soggy. As she continues to eat, she becomes increasingly aware of a loud conversation at the table next to them. She then starts to hear a baby crying loudly on the table directly behind her mother, and is also drawn to a constant clatter of dishes being cleared away at the same table. Jessica gives her mother a disappointed look upon realising that the noise in the restaurant is affecting her dining experience that she was initially so excited for. The loud background sounds are not only distracting her but also making the noodles seem less crunchy, the steak less sizzling, and the entire meal less enjoyable. Despite the food looking delicious, the auditory environment is really ruining her overall experience ... &lt;/div&gt;
{{Robelbox/close}}

== Auditory cues ==
The sounds that motivate someone to consume - or to refrain from it - come in various forms; 

=== Food/drink-related sounds ===
[[File:Opening coke.jpg|thumb|'''Figure 4.''' A can of Coke is expected to 'fizz' as it's opened, signaling its refreshing taste|234x234px]]

The sounds related to food and drink upon consumption, such as the crunch of a chip, fizz of a carbonated drink, sizzle of steak, or the snap of a carrot stick, often indicate the quality and overall freshness of what is being consumed. Research has shown the significant role these sounds play in how people evaluate food/drink quality. While they are shown to influence perception, conversely the masking of those sounds can also reduce enjoyment (Spence &amp; Shankar, 2010; Zampini &amp; Spence, 2010). 

This links to ART, which suggests that when the sensory inputs (e.g., the expected 'fizz' of a soft drink) match stored knowledge from past experiences, they result in a satisfying perception (of that fizzy beverage) (see Figure 4). If the input differs too much from expectations, the brain may either adjust its perception or experience a form of 'dissonance', diminishing enjoyment thereof (Grossberg, 2013). Spence and Shankar (2010) highlight this also applies to food packaging. For example, they reported a study where participants rated potato chips about 5% crispier when listening to the sound of a noisy packet (e.g., Kettles or Walkers) compared to white noise or the sound of a Pringles tube being opened. These auditory cues offer valuable insights into how sound influences eating motivation and behaviour, explaining why certain foods and drinks may be more enjoyable based on the sounds they make. 

==== Misophonia ====
[[File:Figure 1. Misophonia trigger, reflex, and emotions.JPG|thumb|'''Figure 5.''' Depiction of intense emotional response experienced by people with misophonia]]

While auditory cues like chewing, crunching, and slurping can enhance perception of food and drink for many, they can trigger strong, negative emotional responses in others. Misophonia, a condition involving heightened sensitivity to specific eating and drinking sounds, can cause intense discomfort, anxiety, and sometimes anger (see Figure 5). This further demonstrates the complex nature of sensory integration, whereby the same auditory cues that can enhance food and drink experience for most people can diminish it for others (Spence, 2020). Check out this [[Motivation and emotion/Book/2017/Misophonia|book chapter (2017)]] for a detailed analysis of misophonia.

=== Environmental sounds ===
Ambient noise and atmospheric effects such as music and background conversations also play a large role in food/drink perception. Auditory cues from the environment can influence people's perception of flavour and subsequent enjoyment (Zampini &amp; Spence, 2010). 

Sound has consistently been shown to be an important element for the ambiance, comfort, and setting of restaurants and bars. In fact, noise has become a major issue for patrons, ranking as the second most common complaint after poor service (Spence, 2014). This has led critics to frequently assess noise level, alongside food quality in their reviews. Whether it be the 'clatter' of dishes being cleared, loud music, or enthusiastic conversation, increased noise levels in restaurants is shown to impair peoples ability to smell, taste, and enjoy the flavours of what they eat and drink (Spence, 2014). The established connection between auditory and gustatory senses reinforces the relevance of ASI in understanding how environmental auditory cues affect food experiences (Lane et al., 2019).

==== Modifying taste through soundscapes ====
* &quot;Sonic seasoning&quot; is a more recent trend in restaurants, bars, design, and marketing where tailored soundtracks are paired with specific foods and beverages to modify peoples{{gr}} perception. This technique is growing, facilitating future innovations and the design of eating experience (Wang, 2017). 
* Crisinel and colleagues (2012) demonstrated the pitch of music to influence taste perception. They found that participants perceived toffee as sweeter when they listened to higher-pitched soundscapes, as opposed to lower-pitched ones. 
* Similarly, large-scale experiments with whisky and wine have demonstrated that background music or soundscapes can alter consumer perceptions across a range of taste and flavour characteristics; such as the 'woodiness' of whisky or the 'fruitiness' of wine (North, 2012; Spence et al., 2013; Velasco et al., 2013). 
* Spence and colleagues (2013) also found classical music to enhance the overall experience of drinking wine. For example, Tchaikovsky's ''String Quartet No.1'' matched well with red wine, while Mozart's ''Flute Quartet'' was better suited to white wine.
 
{{robelbox|theme=6|title=Case study: Jessica's Dining Experience|iconwidth=55px|icon=Think Outside the Box Flat Icon GIF Animation.gif}}
  &lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
Once they finish their meal, Jessica asks her mother if she enjoyed it. She says she loved it, and that was one of the best steaks she's had in a while! Jessica comes to realise that her own dissatisfaction wasn't at all due to the food itself but to the noise that overshadowed her meal. The experience makes her more conscious of how sound can interrupt her perception of food and as a result finds herself more drawn to quieter restaurants, where she can fully enjoy the crunch of her food and its rich flavours without any disruption. &lt;/div&gt;
{{Robelbox/close}}

{{RoundBoxTop|theme=9}}
[[Image:Nuvola apps xmag.png|left|48px|]][[File:2020 - Queen City Diner - 2 - Allentown PA.jpg|thumb|'''Figure 6.''' Structural factors in restaurants can influence noise and diminish patrons' experience]]

'''Real-life Case: Max's Eatery''' [https://kanopibyarmstrong.com/blogs/news/the-too-noisy-restaurant-revolution| (Kanopi by Armstrong World Industries)]

* Max's Eatery was an old-school diner, designed with hard surfaces and open-ceilings 
* This made for a loud and distracting dining experience, leaving their customers with ringing ears and lost conversations (see Figure 6)
* They had to install noise-reducing ceiling panels, designed to absorb 80% of the noise that hit them
* This led to vast improvements of a near 40% acoustical reduction
* As a result, overall noise levels were decreased and the dining experience of both patrons and servers was dramatically enhanced
{{RoundBoxBottom}}

==Conclusion==
The tastes people experience while dining are profoundly influenced by sound. Motivation for food and drink stems from basic survival instincts and has evolved into habits of deep cultural and social significance. The high-standards people now hold for dining experiences highlight the importance of senses in shaping their enjoyment. Psychological theories about cross-modal interactions reveal the intricate ways someones{{gr}} senses impact their perception of flavour. 

Often overlooked, sound emerges as a vital component of the eating experience, influencing not only how something tastes but also how enjoyable a meal is. Musical-taste combinations further reflect cross-modal effects that continuously shape human perception. A vast range of auditory cues from the sounds of consumption to the carefully curated soundscapes of dining environments allows restaurants and marketers to enhance customer satisfaction and engagement in more ways than expected. 

As research continues to explore the complex interplay between sound and taste, it has become clear that understanding this relationship can enhance and ultimately transform dining experiences. Through the multisensory nature of eating, it is evident that every crunch, fizz, and note of music has the power to elevate meals and forge deeper connections with food, each other, and the symphony of flavours that shape the culinary world.

==See also==
* [[wikipedia:Adaptive_resonance_theory|Adaptive resonance theory]] (Wikipedia)
* [[Motivation and emotion/Book/2014/Dehydration and mood|Dehydration and mood]] (Book chapter, 2014)
* [[Motivation and emotion/Book/2010/Hunger motivation|Hunger motivation]] (Book chapter, 2010)
* [[Motivation and emotion/Book/2017/Misophonia|Misophonia]] (Book chapter, 2017)
* [[wikipedia:Multisensory_integration|Multisenory integration]] (Wikipedia)
* [[wikipedia:Anna_Jean_Ayres#Development_of_Sensory_Integration_theory|Sensory integration theory]] (Wikipedia)

==References==
{{Hanging indent|1=

Crisinel, A. S., &amp; Spence, C. (2009). Implicit association between basic tastes and pitch. ''Neuroscience Letters'', ''464''(1), 39–42. https://doi.org/10.1016/j.neulet.2009.08.016

Crisinel, A. S., Cosser, S., King, S., Jones, R., Petrie, J., &amp; Spence, C. (2012). A bittersweet symphony: Systematically modulating the taste of food by changing the sonic properties of the soundtrack playing in the background. ''Food Quality and Preference'', ''24''(1), 201–204. https://doi.org/10.1016/j.foodqual.2011.08.009

De Lange, F. P., Heilbron, M., &amp; Kok, P. (2018). How do expectations shape perception?. ''Trends in Cognitive Sciences'', ''22''(9), 764–779. https://doi.org/10.1016/j.tics.2018.06.002

Dunbar, R. I. (2017). Breaking bread: the functions of social eating. ''Adaptive Human Behavior and Physiology'', ''3''(3), 198–211. https://doi.org/10.1007/s40750-017-0061-4

Grossberg, S. (2013). Adaptive Resonance Theory: How a brain learns to consciously attend, learn, and recognize a changing world. ''Neural Networks'', ''37'', 1–47. https://doi.org/10.1016/j.neunet.2012.09.017

Knoeferle, K. M., Woods, A., Käppler, F., &amp; Spence, C. (2015). That sounds sweet: Using cross‐modal correspondences to communicate gustatory attributes. ''Psychology &amp; Marketing'', ''32''(1), 107–120. https://doi.org/10.1002/mar.20766

Lane, S. J., Mailloux, Z., Schoen, S., Bundy, A., May-Benson, T. A., Parham, L. D., Roley, S. S., &amp; Schaaf, R. C. (2019). Neural foundations of Ayres' Sensory Integration. ''Brain Sciences'', ''9''(7), 153. https://doi.org/10.3390/brainsci9070153

Locher, J. L., Yoels, W. C., Maurer, D., &amp; Van Ells, J. (2005). Comfort foods: an exploratory journey into the social and emotional significance of food. ''Food &amp; Foodways'', ''13''(4), 273–297. https://doi.org/10.1080/07409710500334509

Maslow, A. H. (1943). Preface to Motivation Theory. ''Psychosomatic Medicine'', ''5''(1), 85–92. https://doi.org/10.1097/00006842-194301000-00012

Motoki, K., Saito, T., Nouchi, R., Kawashima, R., &amp; Sugiura, M. (2019). A sweet voice: The influence of cross-modal correspondence between taste and vocal pitch on advertising effectiveness. ''Multisensory Research'', ''32''(4-5), 401–427. https://doi.org/10.1163/22134808-20191365

North, A. C. (2012). The effect of background music on the taste of wine. ''British Journal of Psychology'', ''103''(3), 293–301. https://doi.org/10.1111/j.2044-8295.2011.02072.x

Pereira, L. J., &amp; Van der Bilt, A. (2016). The influence of oral processing, food perception and social aspects on food consumption: a review. ''Journal of Oral Rehabilitation'', ''43''(8), 630–648. https://doi.org/10.1111/joor.12395

Reeve, J. (2018). ''Understanding Motivation and Emotion''. John Wiley &amp; Sons. ISBN: Paperback 978-1-119-36760-4

Silver, I. (1996). Role transitions, objects, and identity. ''Symbolic Interaction'', ''19''(1), 1–20. https://doi.org/10.1525/si.1996.19.1.1

Spence, C., &amp; Shankar, M. U. (2010). The influence of auditory cues on the perception of, and responses to, food and drink. ''Journal of Sensory Studies'', ''25''(3), 406–430. https://doi.org/10.1111/j.1745-459X.2009.00267.x

Spence, C., Richards, L., Kjellin, E., Huhnt, A. M., Daskal, V., Scheybeler, A., Velasco, C., &amp; Deroy, O. (2013). Looking for crossmodal correspondences between classical music and fine wine. ''Flavour'', ''2'', 1–13. https://doi.org/10.1186/2044-7248-2-29

Spence, C. (2014). Noise and its impact on the perception of food and drink. ''Flavour'', ''3'', 1–17. https://doi.org/10.1186/2044-7248-3-9

Spence, C. (2015). Eating with our ears: Assessing the importance of the sounds of consumption on our perception and enjoyment of multisensory flavour experiences. ''Flavour'', ''4'', 1–14. https://doi.org/10.1186/2044-7248-4-3

Spence, C. (2020). Extraordinary emotional responses elicited by auditory stimuli linked to the consumption of food and drink. ''Acoustical Science and Technology'', ''41''(1), 28–36. https://doi.org/10.1250/ast.41.28

Sternson, S. M., Betley, J. N., &amp; Cao, Z. F. H. (2013). Neural circuits and motivational processes for hunger. ''Current Opinion in Neurobiology'', ''23''(3), 353–360. https://doi.org/10.1016/j.conb.2013.04.006

Velasco, C., Jones, R., King, S., &amp; Spence, C. (2013). The sound of temperature: What information do pouring sounds convey concerning the temperature of a beverage. ''Journal of Sensory Studies'', ''28''(5), 335–345. https://doi.org/10.1111/joss.12052

Vi, C. T., Marzo, A., Memoli, G., Maggioni, E., Ablart, D., Yeomans, M., &amp; Obrist, M. (2020). LeviSense: A platform for the multisensory integration in levitating food and insights into its effect on flavour perception. ''International Journal of Human-Computer Studies'', ''139'', 102428. https://doi.org/10.1016/j.ijhcs.2020.102428

Woods, A. T., Poliakoff, E., Lloyd, D. M., Kuenzel, J., Hodson, R., Gonda, H., Batchelor, J., Dijksterhuis, G. B., &amp; Thomas, A. (2011). Effect of background noise on food perception. ''Food Quality and Preference'', ''22''(1), 42–47. https://doi.org/10.1016/j.foodqual.2010.07.003

Yan, K. S., &amp; Dando, R. (2015). A crossmodal role for audition in taste perception. ''Journal of Experimental Psychology: Human Perception and Performance'', ''41''(3), 590. http://dx.doi.org/10.1037/xhp0000044

Zampini, M., &amp; Spence, C. (2010). Assessing the role of sound in the perception of food and drink. ''Chemosensory Perception'', ''3'', 57–67. https://doi.org/10.1007/s12078-010-9064-2

}}

==External links==
*[https://raisingchildren.net.au/autism/therapies-guide/sensory-integration Sensory integration therapy] (Raising Children Network Australia)
*[https://www.ox.ac.uk/news/2017-03-16-social-eating-connects-communities Social eating connects communities] (University of Oxford)
*[https://kanopibyarmstrong.com/blogs/news/the-too-noisy-restaurant-revolution The too-noisy restaurant revolution] (Kanopi by Armstrong World Industries)
*[https://www.youtube.com/watch?v=0enXduVi4LE Top-down processing] (YouTube)

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==Overview==
 {{RoundBoxTop}}
[[File:Carrot and stick motivation.svg|alt=A cartoon image of a carrot and a stick|thumb|150px|'''Figure 1'''. How much do rewards influence hard work? What role does learned industriousness play in terms of motivation and work ethic?]]

'''Case study'''

Laura and Nicole are colleagues at the Department of Human Services, {{g}} they are both 29 years old and work as project officers for the same team. Both employees are friendly, smart and graduated with the same bachelor degrees. Laura has gained a reputation for being reliable, putting in extra hours if needed and helping others with their work. Nicole, on the other hand often struggles to complete tasks, is easily distracted and shows a lack of enthusiasm for her work. Their manager, Melanie {{g}} recognises this, and as a result delegates more complex projects to Laura, praising her and knowing she will do a good job.
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Why do some people work so hard all the time, whereas others seem inherently lazy? Could this be a result of nature, nurture, personality ... or perhaps, acquired attitudes? Robert Eisenberger's theory of learned industriousness (1992) offers one explanation as to why some people work harder than others.

This chapter explores the following themes: 
* Overview of Learned industriousness as a theory
* Overview of how learned industriousness develops
* Definitions of motivation and work ethic
* Overview of how learned industriousness impacts work ethic and motivation based on literature
* Negative impact of learned industriousness in relation to motivation
* Practical applications of learned industriousness for personal and professional development

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'''Focus questions'''

* What is learned industriousness?
* How does learned industriousness influence work ethic and motivation?
* Are there any negative impacts of learned industriousness in relation to motivation?
* How does learning industriousness apply to real life situations?
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==What is learned industriousness?==
[[wikipedia:Learned_industriousness|'''Learned industriousness''']] posits that through experiences of effort and success, people learn to become motivated and hard-working (Eisenberger, 1992). Take the case study above as an example - two individuals have the same training and abilities, though {{g}} one becomes more motivated through their experience of positive feedback and success. The model of learned industriousness has been developed upon the [[wikipedia:Classical_conditioning|classical conditional reward framework]] (Eisenberger, 1992). This framework suggests that one learns to associate certain behaviours with positive reinforcement and reward (Figure 1). They may continue to practice those behaviours because they will bring positive outcome. The concept of learned industriousness provides insight to the way in which motivation and work ethic can be cultivated through reinforcement.  

== The relationship between effort and learned industriousness ==
Effort is a basic feeling. Many studies show that the sensation of effort is an aversive one{{f}}. Hull (1943) theorised the law of least effort, which suggested that given two opportunities for receiving a reward, animals select the option that requires the least effort. You might have experienced this yourself - imagine you have a dirty car and are feeling tired. Would you prefer to manually clean the car or sit scrolling on your phone as you go through the automatic car wash?

On the other hand, there are many situations where humans intentionally put themselves in uncomfortable or painful situations in order to achieve a long-term goal. Some examples include training for an ironman triathlon or a marathon. Sometimes humans willing choose to exert high level of effort. Learned industriousness suggests that as we get reinforced when putting in effort, exerting effort becomes less difficult (Eisenberger, 1992). This can push you to do harder, more ambitious things with higher targets. Effort allows people to achieve goals that they may not be naturally able to attain without training or perseverance.    
* It is likely that the most reasonable explanation for success in any line, is the formation of early work habits in youth, of working longer hours than others, and of practising more intensively than others (Watson, 1930).

==What is motivation and work ethic?==
Work ethic refers to the value of hard work, stigmatising idleness, completing obligations and the notion that work should be done in the best possible way; work ethic may involve approaching work as a duty or obligation, as well as a moral value (Weber, 2005).

Motivation is more complex. It is what propels people to act in a certain way, or to engage in goal driven behaviour (Reeves, 2024). Motivation is made up of environmental context and internal motive status, which gives behaviour energy, direction and persistence. 

==How does learned industriousness develop?==
Some research propose {{g}} that it develops as a result of positive reinforcement during childhood. One experiment found that both questionnaire responses and case studies of employees with various jobs who were exceptionally hard workers indicated that almost all had a childhood in which strong reinforcers were used to shape high performance in a variety of tasks (Cherrington, 1980). A plethora of studies suggest that aligning rewards with performance standards is simply not enough to facilitate industriousness (Clay et al., 2022; Cameron &amp; Pierce, 2002).

If the demands are too simple, people will not become intrinsically motivated as they lose interest; if the demands are too challenging people will think their efforts do not have any effect on the desired goal state or outcome - that the goal is beyond their control (Cameron et al., 2004). The task or demands must be moderately challenging.

In addition, positive reinforcement and experiences will teach people to become more hard-working and motivated. The motivation becomes self-sustaining as individuals who were rewarded for high effort in the past, generalise this high-effort behaviour to other tasks (Bustamante et al., 2014). Thus, moderately challenging tasks and positive reinforcement will lead to learned industriousness. Reinforced effort is very important in developing learned industriousness.

Persisting individual differences in industriousness may result from long-term differences in the degree of reinforced effort. An experiment with rats demonstrated the positive effect of longer-term effort training on industriousness, as well as the considerable generalisation of reinforced performance across very different situations (Eisenberger et al., 1992){{expand}}. The positive feedback allows people to experience a sense of rewards or satisfaction, increasing self-motivation.

{{Robelbox|theme={{{theme|2}}}|title= ''Quiz''}}

&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
{Which of the following statements best describes the concept of learned industriousness?
|type=&quot;()&quot;}
- People are born lazy or hard-working, and there is not much one can do to change it.
- It is important to teach children under 18 to have a strong work ethic, as once they hit 18 years they will not be able the change.
+ People who work hard and receive reinforcement/rewards will become more self-motivated.

Will completing easy, moderate or extremely challenging tasks be more likely to lead to learned industriousness?

&lt;quiz display=simple&gt;
{
|type=&quot;()&quot;}
+ Moderately difficult tasks.
|| That's correct.
- Easy tasks.
|| Incorrect - easy tasks may lead to a lack of engagement and a higher dropout rate.
- Extremely challenging tasks.
|| Incorrect - if the tasks are too challenging, one may feel that their efforts are making no difference in moving towards the goal state.

&lt;/quiz&gt;
&lt;/div&gt;
{{Robelbox/close}}

==The relationship between learned industriousness and motivation or work ethic==
[[File:Heart_Labyrinth.png|alt=A paper maze in the shape of a heart|120x120px|thumb|'''Figure 2'''. A paper maze in the shape of a heart]]

People can assign positive feelings to cognitive effort (Clay et al., 2022). This contradicts Hulls{{g}} theory of least effort (1943), demonstrating that one can learn to enjoy challenges.

There is a strong relationship between learned industriousness and motivation or work ethic. Here are two credible experiments which demonstrate the relationship:
* 73 undergraduate students were randomly assigned to complete tasks of either easy or moderate difficulty (Cameron et al., 2004). An ANOVA conducted on test performance found a significant interaction of reward by task difficulty, F(1, 69)=4.8, p=.03{{ic|Use APA style i.e., italicise statistical symbols}}. This means that participants who were rewarded for success performed better than those who were not rewarded when the task was of moderate difficulty. On the other hand, participants who participated in low difficulty tasks performed more poorly, had fewer correct responses and reduced levels of persistence.
* Learned industriousness encouraged motivation and work ethic in a study of 36 undergraduate students who were given pencils and paper mazes (Figure 2) to complete (Hickman, Stromme &amp; Lippman 1998). Those who received high-effort training attempted to complete more mazes than those in the control or low-effort conditions. The group was split into three and each group was given different sets of training material which was classified into high-effort, low-effort and control. The tasks were made up of anagrams, addition a cartoon-comparison task and pencil mazes to fill in. The high-effort was more challenging with a significant increase in difficulty, compared to the low-effort tasks which were in a similar format, but easier to solve. Results demonstrated that those who were given high-effort tasks persisted for longer on different tasks.

Taken together, these studies suggest that that successful completion of moderate tasks, when paired with rewards leads to industriousness and increased motivation. The conditioning history of an individual on one task can lead to high effort on another task. Notably, reinforcement in the form of verbal praise is the most effective strategy teachers use to motivate students in English Language centres and schools (Bhatti et al., 2021). This suggests potential cross-cultural validity of the theory.
{{RoundBoxTop}}

'''Case study'''
Laura has been given increased responsibilities and tasks by her manager, Melanie {{g}} who recognises her performance at work. Laura continues to challenge herself with the new responsibilities and builds her confidence. She recognises the value she brings into the workplace and is always happy to come to work to contribute. Laura is self-motivated and has a strong work ethic. A promotion becomes available, and Melanie immediately puts Laura forward as her recommended candidate.
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==Negative impacts of learned industriousness in relation to motivation==
[[File:Angry Emoji - FREE (50213827537).jpg|alt=An angry cartoon face|thumb|187x187px|'''Figure 3.''' Learned industriousness may have negative impacts if paired with extreme psychopathy]]

* When taken to extreme levels of psychopathology such as anorexia nervosa, learned industriousness may contribute to unhealthy behaviours, as it motivates one to maintain severe caloric restriction (Haynos et al., 2023). This could be self-justified by social praise one receives for losing weight.
* Learned industriousness may be linked to other eating disorders, such as bulimia though more research needs to be done (Haynos et al., 2023).
* Obsessive-compulsive personality types are linked with high levels of industriousness. There is a possible link to workaholism (Ng, H et al., 2007) (Figure 3). People may start to see their work ability as a large part of their identity, and attribute their self-worth to what they achieve, neglecting other areas of life. 

{{RoundBoxTop}}
'''Case study'''
Laura has been in her role with the Department of Human Services for several years. She loves getting feedback from her manager and colleagues, and often does work after hours and on weekends, despite not being compensated for it. Laura begins to neglect her social circle and familial responsibilities because she is so focused on work. She hasn't told her manager she works so much on the weekend; she would be embarrassed to do so. Laura hates sitting idle, doing nothing and has lately found the only thing that makes her feel good is working. Her family are getting frustrated with her absence and start to comment that she is addicted to work.
{{RoundBoxBottom}}

== Practical strategies to increase learned industriousness in the workplace or school ==
[[File:Wikipedia training group at Faversham public library.jpg|alt=A group of adults learning together on their laptops at a long table|thumb|'''Figure 4.''' Professional development and training can lead to increase self-efficacy]]

The {{what}} theory helps us understand subtle reward contingencies do play a part in situations and it's not just that someone has a natural affinity for hard work. Employers, teachers and others in positions of power can help developed learned industriousness in those around them by noting the following: 
* Reward systems are useful and positive, provided they promote, not limit human freedom (Cameron &amp; Pierce, 2002). Consider an award ceremony every six-months, financial bonuses or gift voucher for those who have worked hard.
* Feedback systems that are consistent and frequent can recognise efforts and achievements of students or staff. Recognising people for their efforts allows them to increase self-competence, feel valued and maintain motivation. 
* Professional development opportunities and training - letting employees decide their own goals at work, so they are intrinsically motivated. Then extrinsically motivate them through awards or monetary compensation. Skill development leads to increased self-efficacy (Figure 4).
* Provide rewards for only high difficulty tasks, not low difficulty ones to employees or students (Cameron, et al., 2004).
* Challenging yet achievable goals - push limits but ensure students or staff remain confident, not too much out of their depth.

==Conclusion==
Eisenberger's theory of learned industriousness (1992) explains that positive reinforcement and reward may lead to some people being more motivated and working harder than others. Working hard and persisting against obstacles can be driven by positive reinforcement and the reward sensation of putting effort in. Research suggests that to develop learned industriousness, individuals must complete moderately challenging tasks. Low-effort tasks lead to dropout, or boredom and overly challenging tasks may leave the individual thinking that their actions cannot contribute to a desired outcome.

Learned industriousness is closely related to motivation and work ethic. It creates a positive feedback loop, wherein people begin to positively associate hard work with reward or positive outcomes. Intrinsic motivation increases and people embrace challenges, seeing them as opportunities for growth, rather than painful obstacles. Learned industriousness is connected with concepts such as self-discipline, persistence, enhanced self-efficacy and a positive attitude towards hard work. Learned industriousness is a life skill that contributes to personal and professional growth. It allows one to take a proactive approach to challenges and contributes to a strong work ethic. 

Learned industriousness has practical applications for academic performance, sports and sporting training, career progression, and child development. However, it is important to recognise that if taken to extreme levels of psychopathy, learned industriousness may contribute to unhealthy behaviours such as anorexia nervosa and workaholism.

Understanding learned industriousness can facilitate a culture of motivation, productivity and healthy attitudes towards achievement. Learned industriousness is a tool that helps individuals achieve personal and professional goals. 

==See also==
* [[Motivation and emotion/Book/2019/Flexible work arrangements and work motivation|Flexible work arrangements and work motivation]] (Book chapter, 2019)
* [[w:Self determination theory|Self determination theory]] (Wikipedia)
* [[Motivation and emotion/Book/2023/Vocational identity|Vocational identity]] (Book chapter, 2023)
* [[Motivation and emotion/Book/2016/Vocational motivation and personality|Vocational motivation and personality]] (Book chapter, 2016)
* [[Motivation and emotion/Book/2011/Work motivation and work satisfaction|Work motivation and work satisfaction]] (Book chapter, 2021)

==References==
{{Hanging indent|1=

Bustamante, E. E., Davis, C. L., &amp; Marquez, D. X. (2014). A test of learned industriousness in the physical activity domain. ''International Journal of Psychological Studies, 6''(4), 12–25. https://doi.org/10.5539/ijps.v6n4p12

Cameron, J., &amp; Pierce, W.D. (2002). Rewards and intrinsic motivation: Resolving the controversy. Westport, CT: Bergin and Garvey, Greenwood.

Cameron, J., Pierce, W. D., &amp; So, S. (2004). Rewards, task difficulty, and intrinsic motivation: A test of learned industriousness theory. ''Alberta Journal of Educational Research, 50''(3), 317–320. https://doi.org/10.55016/ojs/ajer.v50i3.55091

Cherrington, D. J. (1980). The work ethic: Working values and values that work. New York: AMACOM.

Clay, G., Mlynski, C., Korb, F. M., Goschke, T., &amp; Job, V. (2022). Rewarding cognitive effort increases the intrinsic value of mental labor. ''Proceedings of the National Academy of Sciences - PNAS, 119''(5). https://doi.org/10.1073/pnas.2111785119

Eisenberger, R. (1992). Learned industriousness. ''Psychological review{{ic|Check and correct capitalisatio}}, 99''(2), 248–267. https://doi.org/10.1037/0033-295X.99.2.248

Haynos AF, Koithan E, Hagan KE. (2023). Learned industriousness as a translational mechanism in anorexia nervosa. ''Nat Rev Psychol''{{ic|Provide full journal title}}, 112-126. doi: 10.1038/s44159-022-00134-z. 

Ng, T. W. H., Sorensen, K. L., &amp; Feldman, D. C. (2007). Dimensions, antecedents, and consequences of workaholism: a conceptual integration and extension. ''Journal of Organizational Behavior, 28''(1), 111–136. https://doi.org/10.1002/job.424

Reeve, J. (2024). Understanding motivation and emotion. John Wiley &amp; Sons.{{ic|What edition?}}

Watson, J. B. (1930/1970). Behaviorism. New York: Norton.

Weber M. (2005). The Protestant ethic and the spirit of capitalism. London and New York: Routledge.{{ic|Remove publisher location}}

}}

==External links==
* [https://medium.com/@stevanpopo/learned-industriousness-ba43461dbb4e][https://www.linkedin.com/pulse/why-learned-industriousness-spreads-all-life-areas-paul-nispel/ Learned Industriousness] [https://www.linkedin.com/pulse/why-learned-industriousness-spreads-all-life-areas-paul-nispel/ (Medium)]
* [https://www.linkedin.com/pulse/why-learned-industriousness-spreads-all-life-areas-paul-nispel/#:~:text=Above%20all,%20intelligence%20and%20industriousness%20(i.e.%20diligence)%20are%20important Why Learned Industriousness spreads to all areas of life (Linkedin Article)]

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__TOC__

==Overview==
{{RoundBoxTop|theme=3}}

;Case study

[[File:Challenger explosion.jpg|thumb|200px|'''Figure 1'''. Space Shuttle ''Challenger'' explodes after take-off after warnings of launching in cold weather were ignored.]]

&quot;How could we have been so blind?&quot; President John F. Kennedy and his group of advisors reflected after the [[w:Bay of Pigs Invasion|Bay of Pigs Invasion]], a disastrous military operation against Cuba in 1961 (Janis, 1972).

The same sentiment reverberated through the world on 28th January 1986, when the [[w: Space Shuttle Challenger Disaster|Space Shuttle Challenger]] disintegrated just 73 seconds after launch (see Figure 1), leading to the tragic loss of seven astronauts (Janis, 1972). Despite repeated warnings from engineers about the dangers of launching in cold weather, NASA officials pressed on, swayed by the unanimity of groupthink and dismissed crucial dissenting opinions (Janis, 1972).

{{RoundBoxBottom}}

These cases highlight how group dynamics can severely undermine individual motivation and decision-making quality (Walker &amp; Main, 1973). However, this phenomenon extends beyond high-stake situations like space missions and military operations; it infiltrates everyday life, affecting organisational, legal, and social contexts (Walker &amp; Main, 1973). Juries deliver verdicts that contradict the evidence presented, while other groups adopt radical stances on issues without fully considering the consequences (Myers &amp; Lamm, 1976; Forsyth, 2024). Research also demonstrates that anonymity and confirmation bias have perpetuated group dynamics on social media platforms, leading to polarised opinions and reduced critical thinking (Sunstein, 2017). 

Psychological science provides valuable insights into the mechanisms that diminish individual motivation in groups and methods to address them. This chapter explores the psychological phenomena such as [[w:Groupthink|groupthink]], [[group polarisation]], [[social loafing]], [[w:Deindividuation|deindividuation]] and [[diffusion of responsibility]], and examine how they reduce individual motivation by diminishing accountability, critical thinking, and active participation. By understanding these dynamics, organisations can implement strategies to promote critical thinking, uphold individual accountability, and foster environments that value diverse perspectives. 

{{RoundBoxTop|theme=6}}

'''Focus questions:'''
* What drives individuals to seek inclusion in groups, and what psychological needs are fulfilled through group participation?
* What psychological theories explain how groups undermine individual motivation?
* In what specific ways do group dynamics undermine individual motivation in everyday life?
* What strategies can be used to mitigate the negative effects of group dynamics?

{{RoundBoxBottom}}

==The need to belong==
Humans have an inherent need to belong, and this need drives much of our behaviour, especially when it comes to group dynamics (Baumeister &amp; Leary, 1995). A simulation by Sandstrom and Dunn (2014) found that 71% of people feel happier with others than when alone. Schachter (1959) also found that when people were placed in uncertain, stressful situations and offered the choice to wait alone or with others, 63% of participants preferred to wait with others. This indicates a strong motivation to seek social support in challenging circumstances (Schachter, 1959).

=== Why do individuals gravitate towards groups? ===
Across individuals, societies, and throughout history, humans have consistently valued inclusion over exclusion and sought companionship over solitude (Sandstrom &amp; Dunn, 2014). Studies using [[Functional Magnetic Resonance Imaging|functional magnetic resonance imaging]] have found that individuals left out of group activities exhibit increased activity in the [[w:Insular_cortex|anterior insula]] and the [[w:Cingulate_cortex|dorsal anterior cingulate cortex]] (Eisenberger et.al., 2003). These regions are associated with the experience of physical pain (Eisenberger et.al, 2003). Being excluded from a group does not just hurt emotionally - it literally causes physical pain (Eisenberger et.al, 2003).

=== Groups vs individuals ===
[[File:Touwtrekken.jpg|thumb|303x303px|'''Figure 2:''' This game of tug-of-war demonstrates the benefits of working with groups. In this instance, a team can achieve more than a single person.]]

Groups often form for a specific purpose, whether it's solving problems, creating products or sharing knowledge (Sandstrom &amp; Dunn, 2014). In many instances, groups can accomplish more than people working alone (Latane, et.al., 1979). For instance, a single person in a game of tug-of-war would struggle to compete against a team (see Figure 2; for more benefits of groups, see [[Motivation and emotion/Book/2024/Groups and individual motivation enhancement|Groups and individual motivation enhancement]]). Research on [[social facilitation]] shows that working in groups can boost motivation and performance, especially when people know their efforts are being observed by others (Bond &amp; Titus, 1983). However, this dynamic changes when tasks require an even collective effort, where the contributions of individuals are less visible (Latane et.al., 1979).

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&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
Have you ever felt frustrated by the lack of effort from group members when working on a group assignment? Have you wondered why they are contributing less than if they were working on it individually? 

Studies have shown that people often exert up to 64% less effort when they believe their contributions are not easily identifiable or evaluated, which can significantly impact the quality of the group’s output (Latané et.al., 1979). Keep reading to find out ways to combat the &quot;doom and gloom&quot; of group assignments!
&lt;/div&gt;
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==Psychological theories==
To understand how group dynamics can impact individual motivation, it's crucial to examine several key psychological theories. These theories provide insights into how group processes can diminish individual motivation to actively participate, act accountably, and contribute meaningfully to group tasks. 

=== Groupthink ===
Groupthink occurs when a group values consensus and conformity over critical analysis, which can reduce individual motivation to share differing views (Grube &amp; Killick, 2023). In these situations, people refrain from sharing their disagreement because they believe their input may be met with resistance (Janis, 1972). As a result, individuals may become passive participants, leading to disengagement and less investment in the group's decisions, ultimately harming the quality of the outcomes (Grube &amp; Killick, 2023). 

Janis (1972) identified several characteristics that foster groupthink among intelligent groups which are applied to the case study of the 1986 Space Shuttle Challenger Disaster in Table 1 below:

Table 1

''Application of Janis' (1972) elements of groupthink to the 1986 Space Shuttle Challenger Case Study''

{| class=&quot;wikitable sortable&quot;
|+
!'''Janis' (1972) Groupthink Element'''
!Application to Challenger Disaster
|-
|Illusions of unanimity
|NASA's team believed there was unanimous agreement to launch despite the concerns about the cold weather. This led some engineers and scientists to doubt their objections and accept the decision to launch, rather than voicing their concerns.
|-
|Unquestioned beliefs
|The NASA team held a strong belief in the reliability of their shuttle program and their engineering solutions. This overconfidence led them to underestimate the risks posed by the cold weather, and ignore critical safety warnings.
|-
|Rationalisation
|The engineers concerns were rationalised as isolated incidents, rather than serious issues that could jeopardise the mission, minimising the perceived threat of potential failure.
|-
|Stereotyping
|Those who voice concerns about the launch were stereotyped as overly cautious or pessimistic. This stereotyping led to the dismissal of their viewpoints and reinforced the group's decision to proceed. 
|-
|Mindguards
|These mindguards prevented the full range of concerns from being openly discussed and considered, thus shielding the group from information that might have altered their decision
|-
|Illusions of invulnerability
|By maintaining an overly optimistic view of the shuttle program's success, the NASA team were led to an unjustified belief in the mission's success. 
|-
|Direct pressure
|The group were under pressure by the media and NASA leadership to launch successfully. 
|}

The Challenger disaster demonstrates how groupthink can lead to catastrophic outcomes when critical thinking is sacrificed for conformity (Janis, 1972). A thematic analysis of cabinet decisions confirmed that these dynamics can be used to predict poor decision-making within the United Kingdom Government (Grube &amp; Killick, 2023). Addressing these groupthink elements is crucial to preventing future failures in high-stakes decisions (Janis, 1972).  

=== Social loafing ===
Social loafing occurs when individuals exert less effort while working in a group compared to when they work alone (Karau &amp; Williams, 1993). When people believe that their individual contributions will not significantly impact the group's outcome or assume that peers will compensate for their lack of effort, their motivation to actively participate and contribute diminishes (Latane, et.al., 1979). Social loafing can lead to lower overall productivity and effectiveness within the group, and intensifies as group size increases (Latane, et.al., 1979). Social loafing is common in group settings, including workplaces, academic projectsm and sports teams, where individual contributions seem less critical (Karau &amp; Williams, 1993). 

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'''Case study:'''

Latané and colleagues (1979) investigated social loafing through an experiment where students were instructed to cheer or clap, either alone or in groups of different sizes. As group size increased, individual effort decreased: participants in pairs exerted only 66% of their potential effort, and in groups of six, this dropped to 36%. Even when participants merely believed they were in a group, their effort still decreased, demonstrating that social loafing stems from reduced motivation rather than coordination issues (Latané et al., 1979).

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=== Group polarisation ===
[[File:Man holding sign during Iranian hostage crisis protest, 1979.jpg|thumb|402x402px|'''Figure 3''': Man holding a provocative sign during the Iranian hostage crisis protest 1979, demonstrating the extreme political opinions that can form by group polarisation]]

Researchers have also found that group members tend to adopt views that are more extreme than their initial beliefs after discussion with other group members (Myers &amp; Lamm, 1976). Moscovici and Zavalloni's (1969) research with 140 students demonstrated that group discussions intensified negative opinions towards Americans while simultaneously increasing positive views of the French government. A metanalysis found that prejudiced individuals who discussed racial issues with like-minded peers developed even stronger negative biases, whereas those with more tolerant views became even more accepting of diversity (Mullen &amp; Salas, 1991; see Figure 3).  

This research demonstrates that group polarisation can undermine individual motivation by compelling members to conform to more extreme group views or behaviours, even if these are more radical than their initial beliefs (Myers &amp; Lamm, 1976). Festinger's [[w:social_comparison_theory|social comparison theory]] (1954) supports this, suggesting that people seek groups to validate their own beliefs and attitudes. As a result, the need for validation often outweighs critical thinking, diminishing individuals' intrinsic motivation to question or moderate their views (Festinger, 1954).

=== Deindividuation ===
Deindividuation occurs when people in a group lose their sense of personal identity, which diminishes their motivation to act ethically, often leading them to engage in behaviours they would not typically exhibit alone (Festinger, et.al.,1952). This loss of individuality reduces personal responsibility and increases the likelihood of impulsive or violent behaviour, especially when people feel anonymous within the group (Goldstein, 2002). Zimbardo's study (1973) demonstrates how group contexts and anonymity foster detachment from one's usual self-regulatory mechanisms, leading individuals to reflect the group’s dynamics rather than adhere to their own values.

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'''Case study:'''

Zimbardo's (1973) [[w:Stanford Prison Experiment|Stanford Prison Experiment ]] demonstrated how deindividuation can create a state of altered consciousness. College students assigned as &quot;guards&quot; in a mock prison quickly adopted aggressive and authoritarian behaviours, imposing harsh and degrading punishments on the &quot;prisoners.&quot; The guards' anonymity, reinforced by their uniforms and mirror sunglasses, led to a loss of personal responsibility. The motivation to act in morally right ways was undermined by the collective identity and the power dynamics established within the group. The prisoners, dehumanised by being referred to by numbers instead of names, became submissive and emotionally distressed. The experiment was intended to last two weeks but was terminated after just six days due to the extreme behaviour exhibited by the participants.
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=== Diffusion of responsibility ===
[[Diffusion of responsibility]] occurs when people in a group feel less responsible to take action because they assume that others will respond instead (Darley &amp; Latane, 1968). This undermines individual motivation to act in critical situations because as responsibility is spread across the group, the likelihood of any single person acting decreases (Darley &amp; Latane, 1968). This perceived reduction in personal responsibility can result in mass inaction, as seen in the Genovese case:

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'''Case study:'''

In 1964, [[w:Murder_of_Kitty_Genovese|Kitty Genovese]] was brutally attacked and murdered outside her New York apartment. Despite multiple neighbours hearing her cries for help, none intervened or called the police, assuming someone else would take action. This case study became notorious for what was perceived as the community's apathy, sparking widespread media attention and public outrage (Mullen et.al., 1998).
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{{Robelbox|width=10|theme={{{theme|4}}}|title=Test yourself!}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;

What phenomenon occurs when individuals in a group reduce their effort because they believe their contributions are less noticeable?
|type=&quot;()&quot;}
- Social facilitation
- Group polarisation
- Groupthink
+ Social loafing

{Which psychological theory explains how group discussions can lead to more extreme positions than individuals initially held?
|type=&quot;()&quot;}
- Deindividuation
- Groupthink
+ Group polarisation
- Diffusion of responsibility 

{According to the Stanford Prison Experiment, what psychological effect led participants to act in ways they normally wouldn’t?
|type=&quot;()&quot;}
+ Deindividuation
- Groupthink
- Social loafing
- Diffusion of responsibility
&lt;/quiz&gt;
&lt;/div&gt;
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These psychological theories offer a foundational understanding of how group dynamics can undermine individual motivation. The next section explores how these concepts manifest in everyday life and provide strategies to overcome these effects. 

== Group dynamics in practice ==
{{expand}}

=== The impact of social media on group dynamics ===
Social media has become a significant arena for group dynamics and has profoundly impacted individual motivation and behaviour (Bastug, et.al., 2020). With its vast reach and algorithm-driven content, these platforms allow users to create [[wikipedia:Echo_chamber_(media)|echo chambers]] - online spaces where their existing beliefs are reinforced by like-minded individuals. Bastug and colleagues' (2020) study of 51 Canadian extremists demonstrated that group polarisation is intensified on social media, as users tend to engage with content that reinforces their existing views, making opinions and attitudes more extreme over time. Sunstein (2017) further argues that this selective exposure of information can lead to a narrowing of perspectives, reducing motivation to seek out diverse viewpoints or question personal beliefs.  

Furthermore, the anonymity provided by social media platforms can increase deindividuation, often exacerbating toxic behaviour. Suler (2004) describes the [[wikipedia:Online_disinhibition_effect|online disinhibition effect]] in which anonymity allows people to act more aggressively or unethically than they would in person. The group dynamic diffuses personal responsibility for such actions and reduces individual motivation to avoid behaviour like online harassment or bullying (Bastug et.al., 2020). 

=== Group dynamics in political and legal contexts ===
Group dynamics also play a powerful role in political and legal settings, where they can have significant consequences on decision-making processes. Walker and Main's (1973) conducted a study of 521 U.S. Federal District court judges' decisions to investigate group polarisation. When making decisions alone, judges took extreme actions 35% of the time, but when deliberating in groups, this increased to 65% (Walker &amp; Main, 1973). This reinforces previous findings and has demonstrated that group polarisation is prevalent even among those expected to be impartial and measured in their judgements. 

In politics, Abramowitz and Saunder's (2008) analysis of United States election results from 1952-2004 demonstrates that partisan loyalty often leads people to support their party's stance without question, simply because it aligns with their group's identity. This blind allegiance suppresses individual thinking and leads people to ignore alternative policies that might better serve the public (Brams, 1991). Forsyth (2024) reinforces this, observing that political environments are becoming more polarised, with individuals increasingly entrenched in their views.  

The implications of these group dynamics extend to the broader democratic process. Sunstein (2009) notes that groupthink and partisan loyalty can undermine democratic principles by stifling the diversity of perspectives and critical evaluation necessary for a healthy democracy. When freedom of speech is stifled, the erosion of critical discourse and diversity of opinion weakens the democratic process, potentially leading to decisions that are less reflective of the population's true desires (Sunstein, 2009). 

Reflecting on these dynamics is crucial for fostering environments that encourage individual responsibility, critical thinking and the consideration of diverse perspectives. As social media continues to evolve and influence our interactions, and as political and legal landscapes become increasingly polarised, it is essential to remain vigilant about the ways in which group dynamics can shape our behaviours and decisions.  

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As you scroll through social media this week, take a moment to spot the group dynamics in action! 

Can you see how your algorithm might be reinforcing your opinions? Notice how people can be harsher in the comments because of the anonymity online. Keep an eye out for how people might rally behind a trending topic, quickly jumping on the bandwagon without much thought. Or maybe you'll spot how group pressure influences people to share or like content that everyone else seems to be supporting. 

Happy scrolling, and remember—you're now equipped to see beyond the screen! 🧐📱  
&lt;/div&gt;
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==Overcoming group dynamics==
Fortunately, research has found effective strategies (Table 2) to counteract the effects of group dynamics, ensuring that group work remains productive, inclusive, and balanced. 

'''Table 2'''. 

''Strategies to Overcome Group Dynamics'' 
{| class=&quot;wikitable&quot;
|+
!Group dynamic
!Strategy to overcome the group dynamic 
|-
|Social loafing
|
* Clearly define each member's role and responsibilities to ensure accountability. For example, in group projects, assign specific tasks to individuals and regularly review progress (Latane, et.al., 1979).
|-
|Groupthink and polarisation
|
* Promote open discussion that considers all alternative viewpoints (Janis, 1972).
* Admit to the possibility of failure and actively seek out diverse perspectives to avoid bias (Myers &amp; Lamm, 1976).
* Allow time for reflection and individual consideration before finalising decisions to prevent hasty choices driven by group pressures (Sunstein, 2009).
|-
|Deindividuation and diffusion of responsibility
|
* Encourage personal accountability by setting clear participation guidelines, fostering transparency, and providing individual feedback (Darley &amp; Latané, 1968). When individuals are aware of their specific contributions and responsibilities, they are more likely to be motivated to act ethically (Darley &amp; Latané, 1968).
* Use the [[Delphi method|Delphi Method]] which gathers anonymous input from all group members to reduce bias and encourage independent thinking, minimising the influence of dominant voices (Linstone &amp; Turoff, 1975).
|}

=== The role of leaders ===
Leaders are pivotal in shaping group behaviour and individual motivation, and can even influence the overall mood of the group (George, 1995). To combat groupthink, leaders should ensure consider appointing a &quot;[[w:Devil's_advocate|devil's advocate]]&quot; or breaking the group into smaller discussion teams to bring out diverse perspectives (Janis, 1972). Leaders should avoid expressing their preferences early on to avoid biasing the group (Janis, 1972). In the Space Shuttle Challenger case, pro-launch opinions by leaders discouraged open discussion and contributed to the tragedy (Moorhead et.al., 1991). 

=== Future research avenues ===
As group dynamics evolve with changing social climates and the rise of social media, it is essential for research to adapt existing strategies to align with the modern environment. Some meta-analyses indicate that these strategies remain effective (Gerber et al., 2018; McComb, 2023). However, these findings must be interpreted with caution given the lack of participant blinding and potential publication bias from omitting key studies. Therefore, more rigorous and comprehensive research is needed to fully understand the applicability and effectiveness of these strategies in contemporary settings. 

== Conclusion ==
The desire to seek inclusion in groups, share experiences, and receive validation fulfills the human need for social support and interpersonal attachments (Baumeister &amp; Leary, 1995). However, key psychological theories reveal that group dynamics can diminish individual motivation by reducing accountability, critical thinking, and active participation. These dynamics are increasingly prevalent in social media and politics, where they not only reinforce ideological conformity and suppress diverse perspectives, but also exacerbate polarisation, and undermine democratic principles. Moving forward, research should adapt existing strategies to the modern landscape. Meanwhile, groups must implement practices that promote individual accountability, encourage open debate, and foster an environment where diverse perspectives are valued. Organisations and individuals alike can actively manage group dynamics to foster healthier group environments, informed decision-making, and contribute to more effective collaboration.  

==See also==
* [[wikipedia:Social_loafing|Diffusion of responsibility]] (Wikipedia)
* [[wikipedia:Deindividuation|Deindividuation]] (Wikipedia)
* [[wikipedia:Group_polarization|Group polarisation]] (Wikipedia)
* [[wikipedia:Groupthink|Groupthink]] (Wikipedia)
* [[wikipedia:Social_loafing|Social loafing]] (Wikipedia)
* [[Motivation and emotion/Book/2024/Groups and individual motivation enhancement|Groups and individual motivation enhancement]] (Book chapter, 2024)

==References==
{{Hanging indent|1=

Abramowitz, A., &amp; Saunders, K. (2008). Is polarization a myth? ''Journal of Politics'', ''70''(2), 542–555. https://doi.org/10.1017/s0022381608080493

Baumeister, R., &amp; Leary, M. (1995). Desire for interpersonal attachments as a fundamental human motivation. ''Psychological Bulletin'', ''117''(3), 497–529. https://doi.org/10.1037/0033-2909.117.3.497

Bastug, M., Douai, A., &amp; Akca, D. (2020). Exploring the &quot;demand side&quot; of online radicalisation: Evidence from the Canadian context. ''Studies in Conflict &amp; Terrorism'', ''43''(7), 616–637. https://doi.org/10.1080/1057610X.2018.1494409

Brams, S. (1991). Alternative voting systems. In L. S. Maisel (Ed.), ''Political parties and elections in the United States: An encyclopedia'' (pp. 23–31) Garland.

Darley, J. &amp; Latané, B. (1968). Bystander intervention in emergencies: Diffusion of responsibility. ''Journal of Personality and Social Psychology'', ''8''(4), 377–383. https://doi.org/10.1037/h0025589

De Dreu, C., &amp; West, M. (2001). Minority dissent and team innovation: The importance of participation in decision making. ''Journal of Applied Psychology'', ''86''(6), 1191–1201. https://doi.org/10.1037/0021-9010.86.6.1191

Eisenberger, N., Lieberman, M., &amp; Williams, K. (2003). Does rejection hurt? An fMRI study of social exclusion. ''Science'', ''302''(5643), 290–292. https://doi.org/10.1126/science.1089134

Festinger, L. (1954). A theory of social comparison processes. ''Human Relations'', ''7''(2), 117–140. https://doi.org/10.1177/001872675400700202

Festinger, L., Pepitone, A., &amp; Newcomb, T. (1952). Some consequences of de-individuation in a group. ''The Journal of Abnormal and Social Psychology'', ''47''(2), 382–389. https://doi.org/10.1037/h0057906

Forsyth, D. (2024). The psychology of groups. In R. Biswas-Diener &amp; E. Diener (Eds.), ''Noba textbook series: Psychology''. DEF publishers.

George, J. (1995). Leader positive mood and group performance. ''Journal of Applied Social Psychology'', ''25''(9), 778–794. https://doi.org/10.1111/j.1559-1816.1995.tb01775.x

Gerber, J., Wheeler, L., &amp; Suls, J. (2018). A social comparison theory meta-analysis 60+ years on. ''Psychological Bulletin'', ''144''(2), 177–197. https://doi.org/10.1037/bul0000127

Goldstein, A. (2004). ''The psychology of group aggression''. John Wiley &amp; Sons. https://doi.org/10.1002/0470013451

Grube, D. C., &amp; Killick, A. (2023). Groupthink, polythink and the challenges of decision making in cabinet government. ''Parliamentary Affairs'', ''76'', 211-231. https://doi.org/10.1093/pa/gsab047

Janis, I. L. (1972). ''Victims of groupthink: A psychological study of foreign-policy decisions and fiascos.'' Houghton-Mifflin

Karau, S., &amp; Williams, K. (1993). Social loafing: A meta-analytic review and theoretical integration. ''Journal of Personality and Social Psychology'', ''65''(4), 681–706. https://doi.org/10.1037/0022-3514.65.4.681

Latané, B., Williams, K., &amp; Harkins, S. (1979). Many hands make light the work: The causes and consequences of social loafing. ''Journal of Personality and Social Psychology'', ''37''(6), 822–832. https://doi.org/10.1037/0022-3514.37.6.822
Linstone, H., &amp; Turoff, M. (1975). ''The Delphi method: Techniques and applications.'' Addison-Wesley.

McComb, C. (2023). A meta-analysis of the effects of social media exposure to upward comparison targets on self-evaluations and emotions. ''Media Psychology'', ''26''(5), 612–635. https://doi.org/10.1080/15213269.2023.2180647

Moorhead, G., Ference, R., &amp; Neck, C. (1991). Group decision fiascoes continue: Space Shuttle Challenger and a revised groupthink framework. ''Human Relations'', ''44''(6), 539–550. https://doi.org/10.1177/001872679104400601

Moscovici, S., &amp; Zavalloni, M. (1969). The group as a polarizer of attitudes. ''Journal of Personality and Social Psychology'', ''12''(2), 125–135. https://doi.org/10.1037/h0027568

Mullen, B. &amp; Salas, E. (1998). Meta-analysis and the study of group dynamics. ''Group Dynamics: Theory, Research, and Practice'', ''2''(4), 213–229. https://doi.org/10.1037/1089-2699.2.4.213

Myers, D. &amp; Lamm, H. (1976). The group polarization phenomenon. ''Psychological Bulletin'', ''83''(4), 602–627. https://doi.org/10.1037/0033-2909.83.4.602

Sandstrom, G., &amp; Dunn, E. (2014). Is efficiency overrated?: Minimal social interactions lead to belonging and positive affect. ''Social Psychological and Personality Science'', ''5''(4), 437–442. https://doi.org/10.1177/1948550613502990

Schachter, S. (1959). ''The psychology of affiliation''. Stanford University Press.

Suler, J. (2004). The online disinhibition effect. ''CyberPsychology &amp; Behavior'', ''7''(3), 321–326. https://doi.org/10.1089/1094931041291295

Sunstein, C. (2009). Deliberative trouble? Why groups go to extremes. ''The Yale Law Journal'', ''110''(1), 71–119. https://doi.org/10.2307/797343

Sunstein, C. (2017). ''#Republic: Divided democracy in the age of social media''. Princeton University Press.

Walker, T. &amp; Main, E. (1973). Choice shifts and extreme behavior: Judicial review in the federal courts. ''The Journal of Social Psychology'', ''91''(2), 215–221. https://doi.org/10.1080/00224545.1973.9923044

Zimbardo, P., Haney, C., &amp; Jaffe, D. (1973). The psychology of imprisonment: A study of the social dynamics of the prison environment. ''International Journal of Criminology and Penology'', ''1''(4), 269–278.
}}

==External links==
* [https://www.researchgate.net/publication/258170531_Exploring_Negative_Group_Dynamics Exploring negative group dynamics] (Article, Cornell University)
* [https://openaccess.pirireis.edu.tr/xmlui/bitstream/handle/20.500.12960/156/00156.pdf?sequence=1&amp;isAllowed=y Group dynamics and behaviour] (Universal Journal of Educational Research)
* [https://nobaproject.com/modules/the-psychology-of-groups The psychology of groups] (NOBA Project, University of Richmond)

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__TOC__

==Overview==
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'''Case study'''

[[File:BeReal. Logo.svg|thumb|Figure 1. The BeReal Application Logo]]

BeReal{{ic|Add link to Wikipedia article}} is a photo-sharing social media application (Figure1) that allows users to upload a photo taken within a 2 minute time period and share it among friends. The design is prompted to  “show their friends who they really are, for once,” by taking away the chance to edit or add filters. This captures an insight on what others are up to in different points in time. 

The BeReal app incorporated the Fogg behaviour model in persuasive technology as well as product design. All 3 areas are encapsulated 

# Trigger – A notification appears every day at different time, even if you miss the initial time period more notifications come after a period of time to further remind you. 
# Ability – The user interface is very easy to use as in the click of one button a front facing photo (selfie) and a  photo from the back camera are taken simultaneously 
# Motivation – This an easy way to connect with friends on a social media platform in a short amount of time. BeReal also allows users to connect with celebrities and share songs all within the same app.
{{RoundBoxBottom}}

[[File:Fogg-Behavior-Model.jpg|thumb|''Figure 2.'' The Fogg Behaviour Model Graph]]

The [https://behaviormodel.org/ Fogg behaviour model] (FBM) (Figure 2) produces an understanding for human behaviour and how its anticipated / created with 3 key principals, these include Motivation, ability and triggers (Fogg, 2009). Furthermore, these categories are split into subcomponents, Motivation can be influenced by pleasure / pain, hope / fear and acceptance / rejection, Ability is all about simplicity so time, money, physical effort all factor into this with brain cycles, social deviance and non-routine. Triggers are categories into sparks , facilitators and signals.{{f}}

In conjunction these three areas can influence behaviour to shift in many facets such as building habits, Consumer behaviour, the design of persuasive technology and building public policy, these industries heavily aided the use of FBM for a multitude of reasons{{g}}. The FBM’s simple design and message makes it easy for people to adapt and effetely incorporate it into what they wanting to achieve. Generally, this can be adopted if (1) In order for a behaviour to occur the person needs to be adequately motivated,(2) the person can perform the behaviour In full secession and (3) a trigger that the person can respond to do the behaviour.{{f}}

[[File:Fogg Behaviour Equation.png|left|thumb|''Figure 3.'' The Fogg behaviour model equation]]

The {{which}} graph shows an ideal depiction of how the behaviour will have a favourable outcome. Thus an acceptable behaviour will only occur if little ability is needed in combination with high level of motivation and a an {{g}} effective trigger that the person can act upon. If a more challenging behaviour is bestowed upon them one of the 3 principals{{sp}} will be altered.{{example}}

“Behaviour happens when Motivation, Ability, and a Prompt come together at the same time. When a behaviour does not occur, at least one of those three elements is missing.” – Fogg 

The Fogg behaviour Model (FBM)was theorised by [[wikipedia:B._J._Fogg|Dr. BJ Fogg]]  who is behavioural scientist at Stanford university. Fogg's early work was in persuasive technology {{g}} then he transitioned into the health habits of humans and how they are maintained.

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'''Focus questions:'''
* What is the Fogg behaviour model? 
* How can the Fogg behaviour model be used in persuasive technologies / social media? 
* How can it benefit individuals using this method? 

{{RoundBoxBottom}}

== What is the Fogg behaviour model? ==
The FBM makes it easier to understand behaviour on a general scale. It was developed on the prominent psychosocial and cognitive theories (e.g., behaviorist learning principles (Skinner, 1938), social cognitive theory (Bandura, 1999), cognitive dissonance theory (Festinger, 1957),{{g}}it further considers persuasive design techniques (Mallawaarachchi et al., 2023). The  FBM encompassed 3 core principals of motivation, ability and triggers. The principles coming together allow for favourable behaviour to occur. The principles can intertwine in a various number of ways to achieve a good result for example, if motivation is high, the ability of the task can be low. Allowing for persuasive technologies to cleverly use this to their advantage. The world is full of persuasion, everywhere you look, something as simple as walking into a grocery store, or talking to a friend. These simple moments can influence your behaviour.{{f}}

The 3 main principals are listed below along with their subcomponents.

=== Motivation ===
Motivation within the FBM is very important as behaviour should align with the motivation, yet it must be made very clear, so the individual can change in a promptly matter{{rewrite}}. At least one of the 3 subcategories of pleasure / pain, hope / fear or social acceptance / rejection should be targeted to ensure motivation a closer sense of individualisation to the consumer{{f}}. Common motivators in persuasive technologies are more targeted extrinsically as a reward can be seen or something to work towards. The value (Schwartz, 1992) and goal framing (Linden burg, 2001) theories were explored while creating the FBM{{f}}.

==== Pleasure / Pain ====
The pleasure and pain aspect of motivation acts as an immediate response to the behaviour without any thinking behind it. Eg. exercising with energising music may make exercising more pleasurable to perform){{g}}{{f}}

==== Hope / Fear ====
The hope and fear aspect encompasses the anticipation of what the behaviour result will be. This is the very present among everyday behaviour e.g. fear of getting a flu shot. E.g. hope joining a dating a site. Hope is most like the most ethical an empowering motivator{{g}}{{f}}

==== Social Acceptance / Rejection ====
This one is very individualised as every person has, they {{gr}} own concept of what is socially acceptable. People are more motivated to be seen as a winner in society but do everything they can to avoid being rejected{{f}}. Social media has heavily influenced many people to buy products, try a new workout routine or try something new. Humans like to be a part of groups that accept them .{{f}}

=== Ability ===
The ability principal{{sp}} of FBM address how the behaviour can be performed. Five subcomponents of apply to the ability principle these are, time, money, physical effort, brin cycles, social deviance, and non-routine{{g}}. The Simplicity of the behaviour is one of the biggest factors of getting a behaviour done. Yet training and teaching in a work perspective isn’t that helpful (Fogg, 2009). In persuasive design the behaviour is usually easier to do, for example, 1 click shopping. The behaviour that is wanted needs to be inclusive of everyone, so anyone is capable.{{f}}

==== Time ====
One of the biggest factors from to prevent a behaviour being performed. It needs to be simple and quick.{{f}}

* How often the excuse of time is used?{{expand}}

==== Money ====
If money is required for a behaviour to be carried it may be an issue for those in low socio-economic areas. Yet wealthy individual can use money to make tasks easier{{g}}. In persuasive technology a wide array of individuals “simplicity” should be evaluated{{g}}{{f}}

==== Physical Effort ====
If an exertion is needed for a behaviour may not considered simple enough for some people.{{f}}

==== Brain Cycles ====
Thinking hard for a long time on one behaviour isn’t the nicest feeling when many other things may be on someone’s mind. Individuals all have different brain capacity to hold or release information{{g}}{{f}}

==== Social Deviance ====
Similar to social acceptance this one is for going against the norms even if the behaviour requires something outside the usual .{{g}}{{f}}

==== Non-routine ====
An easy to implement behaviour can be helpful for those who follow routine and can be flexible but if it can’t fit oats{{huh}} not that simple for people to adapt to{{g}}{{f}}

* What are “easy” things that can be added to a routine ?

=== Trigger ===
The core princip{{g}}{{f}}le of trigger is very important as it’s a call to action or prompt that the consumer knows it time to perform the behaviour. The three subcategories of spark, facilitator and signal act as different types of triggers that all have a different purpose. In persuasive technologies one of these can be used or a combination of all 3 to ensure the message is getting to the consumer in a timely manner. An activation / call to action sign is very helpful for people to keep going with the behaviour or something to come backater.{{g}}{{f}}

==== Spark ====
This is for those who lack motivation, it help to try  to tailor the message just to them. Persuasive technology use positive sparks to uplift others (forms of pleasure, sense of hope and social acceptance){{g}}{{f}}

==== Facilitator ====
This trigger is for those who ack ability to do the behaviour effectively by making it more approachable to those who have forgotten or feeling doubt e.g “make a delicious dessert with items you have on hand.”{{g}}{{f}}

==== Signal ====
This {{what}} acts as friendly reminder, this is targeted towards those who have a motivation and ability to complete the behaviour. An ordinary example of a signal is a traffic light that turns red or green. The traffic light is not trying to motivate me.; it simply indicates when a behaviour  is appropriate.{{f}}

{{RoundBoxTop|theme=8}}
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&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
&lt;quiz display=simple&gt;
{What subcategory is in ability category?{{ic|Provide quiz questions about the main take-home messages rather than specific aspects}}}
+ Time
- Hope/fear
- Spark

&lt;/quiz&gt;
&lt;/div&gt;&lt;/div&gt;
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== How can the Fogg behaviour model be used in persuasive technologies / social media? ==
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'''Case Study - Duolingo'''
Duolingo is a language learning platform (Figure 4 ) that has executed the Fogg behaviour model very efficiently for the user to have a fun and interactive experience while learning a language. 

Motivation - The hope/fear aspect of motivation is tapped into as the hope of learning a new language is very prevalent. Earning points with the hope of leveling up and being competitive are all motivators to become better{{g}}.

Ability - The way a user learns the language is by participating in easy lessons that can be performed anytime and all you need is a phone to complete the exercise{{g}}.

Triggers - Daily prompts  help remind you do another lesson or two to further your knowledge and keep you streak going while learning. {{RoundBoxBottom}}

The FBM is widely used in persuasive technologies and in social media and marketing strategies in a positive way.

In the 21&lt;sup&gt;st&lt;/sup&gt; century more and more these days {{awkward}} you see children having their heads buried in smart devices, with over a third of Australian aged between 3 -6 having access to a smart device (Rhodes, 2017 ) which can be problematic in some cases. A study by Mallawaarachchi et al., 2023 asses 132 free and paid apps to depict the FBM persuasive features carried by each. This resulted a widespread presence of passive motivational features such as music and vibrant colours. The ability aspect was quite inclusive with many repetitive tasks and in game suggestions. Triggers were more prevalent in free apps for in-app purchases compared to paid apps. The FBM model has been used effectively. [[wikipedia:Gamification|Gamification]] is highly used and defined as “ adding game mechanics into nongame environments, like a website, online community, learning management system or business' intranet to increase participation”. This links with FBM as a user engagement model, AlMarshedi et al. (2016) and Muntean (2011) found that it had a positive influence on consumers, epically in the health and e-learning space. Although it is aimed at positive engagement behaviours it also feasible that it can promote behavioural that require excessive engagement levels (Mallawaarachchi et al., 2023).

[[File:AIS (Advertising Impact survey).png|thumb|''Figure 5.'' The AIS{[explain}} survey ]]

In the health space {{g}} FBM has predominantly been used in health inventions in high income countries (Boerger et al.,2018; Kemler &amp; Gouttebarge, 2018) as its{{g}} easier {{ic|than what?}} to for the FBM to apply to{{g}}. In lower income-countries has not been executed as highly. Agha et al. (2019) put the FBM into use in order to assess the social marketing campaign of condom use on Pakistan. The impact was assessed though a ‘very in your face’ marketing campaign with ''Touch'' Condoms with the first instalment being a long advertisement, then a shorter advertisement during a cricket tournament. Then an AIS (Advertising Impact survey) (Figure 4) was sent out to hundreds of married men in Urban Pakistan to help establish a motivation and ability level, the trigger was the advertisement . This resulted in condom use being 34 times higher in men who had a high motivation and high ability compared to those with low motivation and low ability. Moreover, The trigger did lead to a higher level of motivation. This is supported by previous research that states that having easy access to condoms will help the adoption of successful condom uptake. (Carvalho et al., 2014; Charania et al., 2011).

Following the health sector during the COVID-19 lockdown it was obviously a lot harder to access doctors, health services and access family planning providers (Nanda et al., 2020). Ability was also very limited during this time as income was strained. A lower access to contraception was apparent yet this led to an opportunity to improve contraceptive social marketing in Nigeria (Meekers et al., 2020). The effects of family planning can deter if COVID-19 makes people relucent{{sp}} to visit or use contraception without the proper knowledge. The FBM was implemented to help create a structure to ensure this was being rolled out efficiently. Motivation was increased with DKT{{explain}} Nigeria call centre creating a youth-friendly website that is accessible to all along with a strong social media presence on Facebook, X, YouTube and Instagram. The social media also acted a trigger that helps reminds individuals. Accessibility was made easier for women during the lockdown period they were allowed to travel in order to obtain family planning services. The FBM allows DKT to easily adapt to the changing circumstances to ensure that contraception was still easily available during the troubling times{{g}}

It is clear to see a strong correspondence in how the FBM can be utilised in numerous amounts of ways{{vague}}. All of them {{what}} generated in a favourable behaviour outcome, or leading to a favourable outcome.{{f}}

== How can it benefit individuals using this method? ==
[[File:Adaptability icon.png|thumb|''Figure 6.'' Adaptability Process]]

The FBM has had many applications, but the benefits are extraordinary{{vague}}. A bigger {{ic|than what?}} focus is on aiding the consumer on how the behaviour can be more manageable and approachable. Breaking the behaviour in reasonable steps can further teach the individual how easy and adaptable it {{what}} can be (van Gent et al., 2019). The Fogg behaviour grid is another instance in which behaviour can be phased in or out (Fogg, 2009c) (Table 1). For persuasive technology use it simple to adapt (Figure 6) and understand by following the 3 principals of motivation, ability and triggers{{g}}. The clarity helps organisations to focus on the essential elements if{{sp}} behaviour change. The FMB{{sp}} is more holistic {{ic|than?}} as it considers more than motivation so persuasive technologies must think {{ic|a technology can't think}} about the ability and triggers to make it appealing to the consumer. Although it follows 3 core principals it also tallows{{huh}} to experiment with the FMB{{sp}} and find the most effective method to get consumers clicking, buying or changing their behaviour whatever it needs to be. This steamily{{huh}} simple deign considers fields in psychology, technology and design fostering a collaboration among different disciplines. The FBM framework allows for the transform observations concise linguistic information with a high concertation{{sp}} on ability and motivation (Toledo et al., 2018){{rewrite}}. Persuasive Technologies are more effective when they are interactive {{g}} for example children using smart devices with learning apps (Mallawaarachchi et al., 2023). This further allows persuaders to adjust influence if need be (Guimaraes et al., 2018){{vague}}. 

'''Table 1'''. Fogg Behaviour Grid{{f}}{{explain}}
{| class=&quot;wikitable&quot;
|+
!
|'''Green behaviour'''
Do &lt;u&gt;new&lt;/u&gt; behaviour, one that is &lt;u&gt;unfamiliar&lt;/u&gt;
|'''Blue behaviour'''
Do &lt;u&gt;familiar&lt;/u&gt; behaviour
|'''Purple behaviour'''
&lt;u&gt;Increase&lt;/u&gt; behaviour intensity or duration
|'''Grey behaviour'''
&lt;u&gt;Decrease&lt;/u&gt; behaviour intensity or duration
|'''Black behaviour'''
&lt;u&gt;Stop&lt;/u&gt; doing a behaviour
|-
|'''Dot behaviour'''
is done &lt;u&gt;one-time&lt;/u&gt;
|GreenDot 
do new behaviour one time 
|BlueDot 
Do familiar behaviour one time 
|PurpleDot
Increase behaviour one time 
|GreyDot
Decrease behaviour one time
|BlackDot
Stop doing behaviour at one time 
|-
|'''Span behaviour'''
has &lt;u&gt;duration&lt;/u&gt; such as 40 days 
|GreenSpan
Do new behaviour for a period of time 
|BlueSpan
Do familiar behaviour for a period of time 
|PurpleSpan
Increase behaviour for a period of time
|GreySpan
Decrease behaviour for a period of time
|BlackSpan
Stop a behaviour for a period of time 
|-
|'''Path behaviour'''
is a &lt;u&gt;permanent change&lt;/u&gt; 
|GreenPath
Do new behaviour from now on 
|BluePath
do familiar behaviour from now on
|PurplePath
Increase behaviour from now on
|GreyPath
Decrease behaviour from now on
|BlackPath 
Stop a behaviour from now on
|}

== Conclusion ==
The Fogg behaviour model brings to light a new and reimagined way to improve and increase favourable behaviour. Fogg {{g}} extensive history of persuasive design and input allowed for him to create this model that encompasses the 3 core principals{{sp}} of behaviour change. Motivation, ability and triggers all hold{{awkward}} some of influence when a change occurs. A persuasive technology company would assume that the {{what}} biggest motivator for their audience, then create and accessible binding for the behaviour to be set on. Lastly, a catchy trigger in which it reminds people for the behaviour to act upon{{example}}. The FBM model structure is as follows {{g}} motivation containing 3 subcomponents of pleasure / pain, hope / fear or social acceptance / rejection, secondly ability which consider time, money, physical effort, brain cycles, social deviance, and non-routine. Lastly triggers, where they are categorised into spark, facilitator and signal{{g}}.

The Model can be easily adapted into many domains, {{g}} some of the listed in the chapter such as the use of social media apps such as Duolingo and BeReal, but mainly lie within the health sector such as the importance of family planning within Nigeria during COVID-19 and condom use in Pakistan. These all have very different mission {{g}} as to what they are trying to portray yet the FBM has been used effectively in all circumstances to portray an improvement / awareness in behaviour.

== See also ==
* [[wikipedia:B._J._Fogg|B. J. Fogg]] (Wikipedia)
* [[Motivation and emotion/Book/2024/Habit stacking|Habit stacking]] (Book chapter, 2024)
* [[Motivation and emotion/Book/2022/Gamification and work motivation|Gamification and work motivation]] (Book Chapter, 2022)

== References ==
{{Hanging indent|1=

Agha, S., Tollefson, D., Paul, S., Green, D., &amp; Babigumira, J. B. (2019). Use of the Fogg Behaviour Model to assess the impact of a social marketing campaign on condom use in Pakistan. Journal of Health Communication, 24(3), 284–292. https://doi.org/10.1080/10810730.2019.1597952

AlMarshedi, A., Wanick, V., Wills, G. B., &amp; Ranchhod, A. (2016). Gamification and behaviour. In Progress in IS (pp. 19–29). https://doi.org/10.1007/978-3-319-45557-0_2

Boerger, N. L., Barleen, N. A., Marzec, M. L., Moloney, D. P., &amp; Dobro, J. (2018). The impact of specialized telephonic guides on employee engagement in corporate well-being programs. Population Health Management, 21(1), 32–39. https://doi.org/10.1089/pop.2017.0027

Carvalho, T., Alvarez, M.-J., Barz, M., &amp; Schwarzer, R. (2014). Preparatory behavior for condom use among heterosexual young men. Health Education &amp; Behavior, 42(1), 92–99. https://doi.org/10.1177/1090198114537066

Charania, M. R., Crepaz, N., Guenther-Gray, C., Henny, K., Liau, A., Willis, L. A., &amp; Lyles, C. M. (2010). Efficacy of structural-level condom distribution interventions: A meta-analysis of U.S. and international studies, 1998–2007. AIDS and Behavior, 15(7), 1283–1297. https://doi.org/10.1007/s10461-010-9812-y

Filippou, J., Cheong, C., &amp; Cheong, F. (2016). Combining the Fogg behavioural model and hook model to design features in a persuasive app to improve study habits. arXiv preprint arXiv:1606.03531.

Fogg, B. (2009). A behavior model for persuasive design. Proceedings of the 4th International Conference on Persuasive Technology - Persuasive ’09, 40(40), 1–7. https://doi.org/10.1145/1541948.1541999

Fogg, B. (2009c). The Behavior Grid. Proceedings of the 4th International Conference on Persuasive Technology - Persuasive ’09. https://doi.org/10.1145/1541948.1542001 

Fogg, B. J., &amp; Euchner, J. (2019). Designing for behavior change—New models and moral issues: An interview with B.J. Fogg. Research-Technology Management, 62(5), 14–19. https://doi.org/10.1080/08956308.2019.1638490

Guimaraes, M., Emmendorfer, L., &amp; Adamatti, D. (2018). Persuasive agent based simulation for evaluation of the dynamic threshold line and trigger classification from the Fogg Behavior Model. Simulation Modelling Practice and Theory, 83, 18–35. https://doi.org/10.1016/j.simpat.2018.01.001

Ji, K., Rosalam Che Me, &amp; Khairul Manami Kamarudin. (2023). A review of persuasive technology and design to healthy lifestyle. International Journal of Art and Design, 7(2), 101–113. https://doi.org/10.24191/ijad.v7i2.1059

Kemler, E., &amp; Gouttebarge, V. (2018). A tailored web-based advice tool for skiers and snowboarders: Protocol for a randomized controlled trial. JMIR Research Protocols, 7.

Mallawaarachchi, S. R., Tieppo, A., Hooley, M., &amp; Horwood, S. (2023). Persuasive design-related motivators, ability factors, and prompts in early childhood apps: A content analysis. Computers in Human Behavior, 139, 107492. https://doi.org/10.1016/j.chb.2022.107492

Meekers, D., Onuoha, C., &amp; Olutola, O. (2020). Applying the Fogg Behavior Model to improve contraceptive social marketing during the COVID-19 lockdown in Nigeria: A case study. Gates Open Research, 4, 141. https://doi.org/10.12688/gatesopenres.13186.1

Mogles, N., Padget, J., Gabe-Thomas, E., Walker, I., &amp; Lee, J. (2017). A computational model for designing energy behaviour change interventions. User Modeling and User-Adapted Interaction, 28(1), 1–34. https://doi.org/10.1007/s11257-017-9199-9

Nanda, K., Lebetkin, E., Steiner, M. J., Yacobson, I., &amp; Dorflinger, L. J. (2020). Contraception in the era of COVID-19. Global Health: Science and Practice, 8(2), 166–168. https://doi.org/10.9745/GHSP-D-20-00119

Plak, S., van Klaveren, C., &amp; Cornelisz, I. (2022). Raising student engagement using digital nudges tailored to students’ motivation and perceived ability levels. British Journal of Educational Technology, 54(2). https://doi.org/10.1111/bjet.13261

Sittig, S., &amp; Franklin, A. L. (2020). Persuasive technology: Designing mobile health triggers to impact health behavior.

Toledo, F. P. de, Devincenzi, S., Kwecko, V., Mota, F. P., &amp; Botelho, S. S. da C. (2018). A framework for modeling persuasive technologies based on the Fogg Behavior Model. 2018 IEEE Frontiers in Education Conference (FIE). https://doi.org/10.1109/fie.2018.8659195

Van Bon, I. (2015). PLEASE REMIND ME TO GET ACTIVE (Doctoral dissertation, Eindhoven University of Technology).

van Gent, P., Farah, H., van Nes, N., &amp; van Arem, B. (2019). A conceptual model for persuasive in-vehicle technology to influence tactical level driver behaviour. Transportation Research Part F: Traffic Psychology and Behaviour, 60, 202–216. https://doi.org/10.1016/j.trf.2018.10.004

}}

== External links ==
* [https://behaviormodel.org/ Fogg behaviour model] (behaviormodel.org)
* [https://www.boranikolic.com/modeling-behavior Modeling Behaviour] (Bora Nikolic)
*[https://www.isaca.org/resources/news-and-trends/industry-news/2024/persuasive-technology-the-technology-that-connects-and-controls-us Persuasive technologies] (Sunil Arora)

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{{title|Empathy versus sympathy: &lt;br&gt; What's the difference and how do they influence behaviour and relationships?}}
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==Overview==
[[File:Arthur Hughes - Back from Sea.jpg|thumb|figure 1: ''Friend B offers empathy by sitting with the distressed person, illustrating emotional support.'']]

'''Ever wondered why some people make us feel truly understood, while others, despite good intentions, leave us feeling alone in our struggles?''' This difference is rooted in the distinction between empathy and sympathy.

Empathy brings us closer and improves our behaviour, while sympathy can create distance—understanding the difference is key to promoting positive behaviours and building stronger relationships.

{{Font color|purple|&lt;blockquote&gt;'''Imagine two friends, both trying to help, but only one leaves you feeling truly supported. Why is that? The answer lies in the difference between empathy and sympathy, and how these responses shape our relationships and influence our behaviour.''' &lt;/blockquote&gt;}}

{{RoundBoxTop|theme=7}}
You’re having a really bad day—everything feels overwhelming, and nothing is going right. Just as you feel it couldn't get worse, you spill your coffee on your favourite white shirt. In the whirlwind of it all, you fall to the ground and break down.

Friend A notices how distressed you are and says, &quot;I know how you feel; I spilled my coffee last week on my white shirt. Please don't cry; everything will be alright.&quot;

Friend B sits with you on the cold, hard floor and says, &quot;It sounds like you're going through a really tough time. I'm here to listen if you want to talk.&quot;

As shown in Figure 1, Friend B’s empathetic behaviour allows for a deeper emotional connection, strengthening the relationship. In comparison, Friend A’s well intended sympathy, while comforting in the short term, may unintentionally create distance.{{RoundBoxBottom}}

{{RoundBoxTop|theme=11}}

Now, consider this:
Which friend's response do you feel had a greater impact on your behaviour after you calmed down?

Which response would lead to a more meaningful, lasting connection?

How did Friend A’s response differ from Friend B’s in terms of emotional support?

Who would you turn to next time for support—Friend A or Friend B?
{{RoundBoxBottom}}

{{Font color|purple|&lt;blockquote&gt;But why does this happen? What is it about empathy that develops stronger bonds, while sympathy, despite its kindness, can fall short?..&lt;/blockquote&gt;}}

Note:
Friend A displayed sympathy. Friend B displayed empathy.

== Empathy vs sympathy: What’s the difference? ==
Empathy and sympathy are often used interchangeably, yet they represent two distinct psychological processes that, although linked, have significantly different impacts on our relationships and behaviour.

[[File:Dalian Liaoning China Two-Chinese-at-Xinghai-Bay-01.jpg|thumb|figure 2: In moments of quiet reflection, sometimes the greatest comfort is simply having someone by your side]]

[[Empathy|Empathy]] involves understanding and sharing another person’s feelings, while [[wikipedia:Sympathy|sympathy]] acknowledges distress without full emotional engagement (Batson, 2009). Friend B’s empathy fosters a deeper connection, while Friend A’s sympathy, though well-intended, may unintentionally create distance.

Empathy goes beyond mere acknowledgment of distress. It requires us to step into another person’s emotions, truly sharing their experience. I invite you to look at these two scenarios:

In Figure 2, one person sits quietly next to another who gazes out at the sea. No words are exchanged, but their presence offers silent support. This is an example of sympathy, where comfort is offered through being present, but there’s less emotional connection.

[[File:There's no crying in baseball! (4549295140) 2.jpg|thumb|figure 3: (child hugging another child):''&quot;Empathy isn’t always in words; sometimes, a simple hug says everything.&quot;'']]

In Figure 3, a child, visibly upset after a tough moment, is hugged by a friend. The friend not only acknowledges their distress but also embraces them with understanding. This is empathy a deeper connection that shows a true effort to feel what the other person is going through.

Figure 2: &quot;In moments of quiet reflection, sometimes the greatest comfort is simply having someone by your side.&quot;

Figure 3: &quot;Empathy isn’t always in words; sometimes, a simple hug says everything.&quot;

'''Why does the second response resonate more?''' Because it shows that the person is not just acknowledging your feelings. They’re actively trying to connect with your emotional experience. Sympathy, on the other hand, while supportive, often lacks this emotional depth.

{{Font color|purple|&lt;blockquote&gt;Understanding these broad definitions is one thing, but how do empathy and sympathy show up in our everyday behaviour and interactions?&lt;/blockquote&gt;}}

To further understand the distinction between empathy and sympathy, watch this video: [https://youtu.be/KZBTYViDPlQ Empathy vs. Sympathy: What’s the Difference?.] The video explains these emotional processes through clear examples, helping to clarify why empathy builds stronger emotional connections than sympathy (Brené Brown, 2013).

=== Core differences ===
Empathy and sympathy, though often confused, have distinct characteristics that affect how we relate to others and how we respond to their suffering. The table below outlines the core differences between the two:  

{| class=&quot;wikitable&quot;
|+[https://journals.sagepub.com/doi/full/10.1177/0269216316663499 key compassion]
!Aspects 
!Sympathy
!Empathy
|-
|Definition
|A feeling of pity or sorrow for someone else’s distress, but without fully understanding or sharing their emotions.
|The ability to deeply understand and share the feelings of another person, fostering emotional connection.
|-
|Emotional Engagement
|Superficial emotional engagement, often distant.
|Deep emotional engagement, involving emotional resonance and shared understanding.
|-
|Response to Suffering
|Acknowledgment of another’s suffering, often followed by attempts to comfort or reassure.
|Acknowledgment of suffering, combined with understanding and emotional resonance (“feeling with” the person).
|-
|Type of Response
|Reactive and often detached; tends to focus on the observer’s own emotions (e.g., pity)
|Affective and connected; focuses on the emotions of the person suffering, aiming to understand them.
|-
|Emotional State of Observer
|Emotional dissonance; the observer’s emotional state is often separate from the person in distress.
|Emotional resonance; the observer experiences emotional contagion, feeling with the person in distress
|-
|Motivators of Response
|Pity, obligation, and self-preservation.
|Compassion, duty, and a desire to connect or help the other person
|-
|Impact on Relationships
|Can create emotional distance or make the person in distress feel patronized or overwhelmed.
|Strengthens relationships by fostering deeper emotional connections and understanding.
|-
|Examples
|“I’m so sorry.”

“This must be awful.”

“I can’t imagine what it must be like.”
|“I understand what you're going through.”
“Help me understand your situation.”

“I feel your sadness.”
|}
'''Note.''' Adapted from Sinclair, S., Beamer, K., Hack, T. F., McClement, S., Bouchal, S. R., Chochinov, H. M., ... &amp; Hagen, N. A. (2016). Sympathy, empathy, and compassion: A grounded theory study of palliative care patients' understandings, experiences, and preferences. ''Palliative Medicine'', 31(5). https://doi.org/10.1177/0269216316663499

This table illustrates that while both empathy and sympathy are responses to another's suffering, they differ significantly. Empathy inspires prosocial behaviours, such as active listening and emotional regulation, which create stronger bonds in relationships. Sympathy, while helpful in providing short-term comfort, often leads to less meaningful emotional engagement and behavioural support. Ultimately, while sympathy can provide short-term comfort, it is empathy that helps us build deeper, more supportive relationships that endure.

== Psychological insights into empathy and sympathy ==
Empathy and sympathy are fundamental to social interactions, yet they operate through distinct psychological processes that have vastly different effects on human behaviour and relationships. Understanding these differences is essential for enhancing emotional well-being and developing healthier relationships (Decety &amp; Cowell, 2014).

In the coffee spill scenario, Friend A’s sympathetic response, &quot;I know how you feel,&quot; shifts focus away from you, while Friend B’s empathetic response, &quot;I'm here to listen,&quot; demonstrates deeper emotional engagement.

According to Decety and Cowell (2014), Empathy involves several key components that shape how we interact in relationships:

* '''Emotional sharing''': Feeling what the other person feels. Friend B shares your frustration, strengthening the bond by validating your experience.
* '''Self–other awareness''': Recognising the difference between your own emotions and those of others. Friend B maintains an awareness of your feelings without projecting their own emotions onto you.
* '''Perspective-taking''': Understanding the other person’s situation from their viewpoint. Friend B’s ability to see the situation through your eyes fosters deeper understanding.
* '''Emotional regulation''': Managing your own emotions while supporting another. Friend B’s calm presence prevents the situation from becoming overwhelming, allowing for more meaningful support.

By integrating these elements, empathy enhances prosocial behaviour and deepens relationships, whereas sympathy may create emotional distance.

'''How do these psychological processes shape relationships?''' 

Batson’s Empathy-Altruism Hypothesis (1991) demonstrates that empathy drives prosocial behaviour, as seen in Friend B’s response. It fosters trust, emotional resonance, and strengthens relationships. 

By practising '''[[wikipedia:Active_listening|active listening,]]''' '''[[wikipedia:Perspective-taking|perspective-taking]]''' and genuine concern, we move beyond sympathy and develop empathetic connections that meaningfully impact others. These behaviours shape both immediate and long-term relationship dynamics.

&lt;blockquote&gt;{{Font color|purple|So why does it matter? Understanding the distinction between empathy and sympathy goes beyond simple emotional responses. it’s essential for building lasting, fulfilling relationships. Let’s dive deeper into why recognising the difference between these two is crucial for our emotional well-being and connection with others}}&lt;/blockquote&gt;]

'''The importance of understanding empathy and sympathy'''

Recognising the differences between empathy and sympathy is essential for emotional well-being and building stronger, more supportive relationships. While empathy involves truly understanding and sharing another’s emotional experience, sympathy acknowledges distress without fully engaging with the other person’s emotions (Decety &amp; Cowell, 2014).

Empathy encourages active listening and perspective-taking, promoting trust and deepening emotional bonds. Sympathy, despite good intentions, can sometimes widen the gap between people by focusing on comfort rather than fully addressing emotional needs. Over time, this can lead to disconnection.

As seen in the coffee spill scenario, Friend A’s sympathetic response shifted focus away from your distress, offering reassurance without emotional depth. In contrast, Friend B’s empathetic approach develops a stronger emotional connection and meaningful support.

Understanding these distinctions allows us to develop deeper, more emotionally supportive relationships in both personal and professional environments. While sympathy can be well-meaning, empathy enhances emotional closeness and connection.

'''How psychological science can enhance our understanding'''

Research such as Batson’s Empathy-Altruism Hypothesis (1991) demonstrates that individuals who act with empathy, like Friend B, are more likely to engage in prosocial behaviours, which build trust and deepen emotional connections over time. Empathy develops mutual support and strengthens relationships by encouraging emotional resonance and active listening.

In sympathy, though it may provide immediate comfort, often lacks the emotional depth needed for long-term relationships. This can result in emotional disconnection, as seen in Friend A’s response, which was well-intentioned but detached from the other person’s feelings (Batson, 1991).

Understanding these distinctions is important as empathy not only improves relational dynamics but also promotes behaviours that enhance emotional well-being in personal and professional relationships (Decety &amp; Cowell, 2014).

=== Key theories and research ===
Various psychological theories help explain the complexities of empathy and sympathy:

'''[[wikipedia:Empathy-altruism|Empathy-Altruism Hypothesis]] (Batson, 1991)''' This theory suggests that empathy drives altruistic behaviour. When we truly empathise, we help others without expecting anything in return. Friend B’s empathetic response, “I’m here to listen if you want to talk,” illustrates this, as empathy fosters prosocial behaviour, deepens trust, and strengthens relationships. In compassion, Friend A’s sympathetic response, “Please don’t cry; everything will be alright,” may have been more about easing their own discomfort rather than addressing the other person’s needs, potentially creating emotional distance. 

'''[[wikipedia:Theory_of_mind|Theory of Mind]] (Premack &amp; Woodruff, 1978):''' Theory of Mind refers to our ability to understand the mental states of others—such as their beliefs, desires, and intentions. Closely tied to cognitive empathy, it helps us grasp another person's perspective. Empathy engages this theory by allowing individuals to predict and understand how others might react, leading to stronger, more nuanced connections. Sympathy, while recognising emotions, may not engage this cognitive process as deeply, often resulting in more superficial relationships., leading to more superficial relationships that don't fully address the other person's experience. 

'''[[wikipedia:Emotional_contagion|Emotional Contagion Theory]] (de Greck et al., 2012)''' This theory explains how emotions spread between people. Empathy allows individuals to resonate with another person’s feelings, as seen in Friend B’s ability to absorb and share the distressed person’s emotions, strengthening their bond. Sympathy, however, lacks this deeper emotional engagement, which can lead to a more detached response and weaker connection. 

'''[[wikipedia:Attachment_theory|Attachment Theory]] (Bowlby, 1969):''' This theory states that our early relationships with caregivers influence our ability to form secure emotional bonds in adulthood. Those with secure attachment styles tend to show more empathy in relationships, having experienced consistent emotional support. In contrast, individuals with insecure attachments may lean more towards sympathy but without the same emotional engagement, impacting the depth and quality of relationships. Attachment theory helps explain how empathy fosters secure, trusting relationships, while sympathy may reflect less emotionally attuned interactions.

'''[[wikipedia:Empathy|Cognitive vs. Affective Empathy]] (Decety &amp; Cowell, 2014):''' Cognitive empathy involves understanding another’s situation, while affective empathy is about sharing their emotions. Friend B demonstrated both, building a stronger emotional connection. In contrast, Friend A, relying mostly on cognitive empathy, provided support but didn’t fully connect emotionally. This distinction shows that empathy, by engaging both thought and feeling, leads to more meaningful and supportive relationships, while sympathy often lacks this emotional depth.

'''[[wikipedia:Compassionate_love|Compassionate Love Theory]] (Underwood, 2009):''' Compassionate love is rooted in genuine care and concern for others, without personal gain. It overlaps with empathy but stands out through its sustained commitment to helping others. Compassionate love draws on both cognitive and affective empathy, fostering long-term supportive behaviour that strengthens relationships. Sympathy may offer temporary comfort, but compassionate love, driven by empathy, nurtures deeper, more enduring connections.

These psychological theories illustrate the key differences between empathy and sympathy in shaping behaviour and relationships. Empathy develops deeper emotional connections and trust, allowing individuals to genuinely support one another. By understanding both the emotional and cognitive experiences of others, empathy creates lasting bonds. Sympathy, while offering temporary comfort, often lacks the depth needed for strong, enduring relationships. Recognising the impact of these responses is essential for building healthier, more supportive connections that promote mutual understanding and trust.

{{RoundBoxTop|theme=11}}'''As you read further, consider these questions:''' 
* '''How does empathy and sympathy shape your interactions with others?'''
* '''Which type of support do you tend to offer or seek?'''
* '''How can understanding these differences improve your relationships?'''
{{RoundBoxBottom}}

{{Font color|purple|&lt;blockquote&gt;Now that we understand these differences, how do empathy and sympathy play out in our everyday relationships? Let’s explore how these emotional responses impact romantic relationships, friendships, family dynamics, and even therapeutic settings&lt;/blockquote&gt;}}

== Impact of empathy and sympathy on behaviour and relationships ==
Empathy and sympathy significantly impact how we interact in various types of day-to-day relationships. As illustrated in the scenario with Friends A and B, these emotional responses determine the depth and quality of our connections with others, influencing our overall well-being.  

=== Case study 1: empathy in romantic relationships ===
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Empathy plays a crucial role in building emotional intimacy and maintaining a strong connection in romantic relationships. 

A study by Cohen et al. (2012) examined the effects of empathy on conflict resolution among couples. The researchers found that partners who displayed higher levels of empathy, such as taking the time to genuinely understand their partner’s emotional experiences, were better able to resolve conflicts and maintain a healthy emotional connection.

For example, consider a situation where one partner comes home after a long day and expresses frustration around work. An empathetic partner would say, &quot;I understand you're feeling stressed, it sounds like you had a really tough day. How can I support you?&quot; This response mirrors Friend B’s empathetic approach, deepening trust and strengthening the emotional bond between partners, which is vital for a healthy relationship

The study highlighted that couples who regularly practise empathy reported fewer feelings of isolation and were more likely to view conflicts as opportunities for growth, rather than threats to the relationship. In compassion, couples who responded with more sympathetic, statements often experienced greater relationship strain.
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'''After reading this, do you tend to respond with empathy or sympathy in your romantic relationships, and how do you think this affects the emotional intimacy between you and your partner?'''

=== Case study 2: sympathy in friendships ===
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While empathy strengthens relationships, sympathy can sometimes unintentionally weaken friendship bonds. A study by Smith and Davidson (2016) explored how sympathy, in comparison to empathy, affects friendships over time. They found that when one friend consistently responds to another's struggles with sympathy, it often leads to feelings of isolation and emotional disconnection.

For example, imagine a situation where one friend shares that they are overwhelmed with family and work responsibilities. A sympathetic response might be, &quot;I feel bad for you, but you’ll get through it!&quot; This aligns with Friend A's response in the earlier coffee spill scenario, where the attempt to comfort was superficial and centred around minimising the situation internally.

Friendships grow with emotional connection. Sympathy, while supportive, often falls short of creating the emotional depth needed to build trust and strengthen friendships, leaving the person feeling distanced rather than connected. Over time, friends who consistently receive sympathy may feel less inclined to open up, leading to a more emotionally distant relationship.
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 '''Think about your own friendships. Do you find that you respond more with empathy or sympathy? How has this influenced the depth and quality of your friendships?'''

=== Case study 3: family dynamics and emotional well-being ===
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Empathy and sympathy also play distinct roles in family relationships, influencing how family members support each other through difficult times. Research by Thomas et al. (2018) found that parents who responded empathetically to their children’s struggles were more likely to raise resilient and emotionally healthy children.

For instance, when a child comes home upset after a bad day at school, an empathetic parent might say, &quot;I can see that this has really upset you. Let’s sit down and talk about what happened.&quot; This mirrors Friend B’s response in the original scenario, where the intent was to connect emotionally rather than immediately offering solutions. On the other hand, a sympathetic response, such as, &quot;I’m sorry you’re feeling bad, but don’t worry, it will all be okay,&quot; may provide short-term comfort but lacks the depth required to address the child’s emotional needs.
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'''In your family relationships, are you more likely to respond with empathy or sympathy? How has this affected the emotional well-being of the family members you support?'''

=== Case study 4: the role of empathy in building rapport ===
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Empathy is essential in therapeutic settings because it allows psychologists to establish trust, develop openness, and create a non-judgmental space for clients to explore their feelings. A case study by Norcross and Lambert (2011) examined Dr. Williams, a psychologist who worked with Sarah, a client experiencing severe anxiety following the loss of her partner.

In one early session, Sarah expressed her feelings of guilt and grief. Instead of offering comforting words or advice (a sympathetic response) Dr. Williams responded empathetically, saying, &quot;It sounds like you're feeling a lot of guilt right now, and that must be incredibly heavy to carry. I'm here to help you process this in a way that makes sense for you.&quot; This empathetic response allowed Sarah to feel heard, encouraging her to open up more in future sessions and build rapport.

Empathy in therapy, like Friend B’s response in the coffee spill scenario, builds deeper emotional connections and trust. It enables client’s emotional exploration, contributing to their psychological healing
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'''In your own experiences, whether personal or professional, how might using empathy rather than sympathy affect the rapport you build with others?'''

The effects of empathy and sympathy extend beyond individual relationships and influence overall well-being. When we experience empathy in our close relationships, whether with a partner, friend, or family member. we feel more understood and supported, which enhances our mental health. Empathy creates emotional closeness and trust, contributing to '''[[wikipedia:Psychological_resilience|psychological resilience]]''' and long-term well-being.

Excessive sympathy, especially if perceived as pity, can lead to feelings of loneliness and emotional disconnection. This happens because sympathy often lacks the emotional engagement necessary for deep, meaningful relationships, leaving the person in need feeling misunderstood or patronised. Just as seen in the coffee spill scenario, sympathy may unintentionally create a gap in emotional connection, while empathy bridges that gap, developing stronger, healthier relationships.

{{RoundBoxTop|theme=7}}
;Quiz: Empathy or Sympathy? 

&lt;quiz display=&quot;simple&quot;&gt;
{When a friend shares their bad day, you reply:
|type=&quot;()&quot;}
- I know how you feel. I had a terrible day I had one last week too&quot;
+ That sounds really tough. I’m here if you want to talk&quot;.
&lt;/quiz&gt;

&lt;quiz display=&quot;simple&quot;&gt;
{Your partner seems stressed after work. You:
|type=&quot;()&quot;}
- Suggest they &quot;just relax and forget about it.&quot; 
+ Ask them to share what’s on in their mind and listen without interrupting.
&lt;/quiz&gt;

&lt;quiz display=&quot;simple&quot;&gt;
{A family member is struggling with a personal issue. You:
|type=&quot;()&quot;}
- Offer advice, saying &quot;I’m sure everything will work out fine.&quot; 
+ Sit with them and say &quot;I’m here to support you however you need.&quot;
&lt;/quiz&gt;
{{RoundBoxBottom}}

Empathy creates meaningful, emotionally fulfilling relationships across various relationships. By incorporating empathy into our daily interactions, we develop deeper connections, promote well-being, and foster long-term emotional health. Sympathy, while helpful in some contexts, lacks the emotional depth that empathy provides and can sometimes lead to emotional disconnection. As illustrated by the case studies, practicing empathy leads to more supportive, resilient relationships that enhance the well-being of all individuals involved.

{{Font color|purple|&lt;blockquote&gt;However, empathy and sympathy manifest differently across cultures. Let’s explore how various cultural perspectives shape the expression of these emotions.&lt;/blockquote&gt;}}

== Cultural perspectives on empathy and sympathy ==
Empathy and sympathy vary across cultures, shaping behaviour and relationships differently. In '''[[wikipedia:Individualistic_culture|individualistic cultures]]''', empathy is personal and emphasises emotional validation (de Greck et al., 2012). It is highly valued in healthcare, where empathetic listening improves patient outcomes. Open emotional expression strengthens relationships by addressing individual needs. 

In contrast, '''[https://simple.wikipedia.org/wiki/Collectivism collectivist cultures]''' empathy focuses on group harmony, with subtle expressions to maintain social cohesion (Mesquita &amp; Karasawa, 2002). Emotional restraint is prioritised, and sympathy often leads in professional settings where hierarchy and harmony are emphasised. Families in collectivist cultures favour indirect emotional support, while individualistic families prefer open expression (de Greck et al., 2012; Mesquita &amp; Karasawa, 2002). 

Regardless of culture, empathy builds stronger emotional bonds, while sympathy, although supportive, can sometimes create emotional distance by not fully engaging with the other person's feelings. 

'''Reflect on how your cultural background influences how you offer emotional support. Do you prioritise individual emotional needs or group harmony when offering empathy or sympathy?

'''{{Font color|purple|    &lt;blockquote&gt;So how do empathy and sympathy affect our motivation and emotions? Understanding this can reveal why we react the way we do?&lt;/blockquote&gt;}}'''Impact on motivation and emotion'''

The way empathy and sympathy are expressed in different cultural settings directly impacts [[wikipedia:Motivation|motivation]] and [[wikipedia:Emotional_self-regulation|emotional regulation]]. In '''individualistic cultures''', empathy motivates individuals to engage in prosocial behaviour, driven by personal emotional needs. This leads to open communication in relationships, where verbal validation is key to emotional support.

In '''collectivist cultures''', the motivation for empathy stems from a desire to preserve group harmony. Here, emotional restraint reduces conflict, with empathy often conveyed through actions rather than words (de Greck et al., 2012). These differences illustrate how empathy and sympathy shape emotional regulation and relationship dynamics, whether focused on personal emotional fulfilment or collective well-being.

'''The role of motivation in empathetic and sympathetic responses'''

Motivation plays a key role in how empathy and sympathy are expressed. In individualistic cultures, empathy often stems from a desire to build emotional intimacy and meet personal emotional needs. This aligns with Batson's Empathy-Altruism Hypothesis (1991), which suggests that empathy drives altruistic behaviour, fostering stronger relationships by focusing on individual support.

In collectivist cultures, motivation for empathy is group-based, aimed at maintaining social harmony rather than individual emotional fulfilment. This cultural difference impacts how empathy is expressed, either through emotional resonance to strengthen personal bonds or through subtle actions that benefit the group.

Understanding these motivations helps clarify how empathy influences behaviour and relationships: In individualistic settings, empathy enhances personal emotional connections, while in collectivist settings, empathy maintains group balance and cohesion

{{Font color|purple|&lt;blockquote&gt;Just as motivation influences the expression of empathy and sympathy, it also shapes the emotional outcomes that follow. Let’s now explore how these emotions impact long-term behaviour and relationship dynamics&lt;/blockquote&gt;}}

'''Emotional consequences of empathy and sympathy'''

The emotional consequences of empathy and sympathy vary across cultures, influencing long-term behaviour and relationship dynamics. In individualistic cultures, empathy enhances deeper emotional connections, leading to stronger, more emotionally fulfilling relationships. This openness allows for emotional support that enhances individual well-being.

In collectivist cultures, empathy’s long-term effects focus on group harmony, limiting personal emotional fulfilment to some extent. While empathy may strengthen group bonds, it can sometimes prevent deeper one-on-one relationships, as individual emotional needs are often subordinated to the collective.

Sympathy, in both contexts, can create emotional distance. It tends to offer superficial support without fully engaging in the other person’s emotional experience. Over-reliance on sympathy may leave individuals feeling misunderstood or emotionally disconnected, negatively impacting relationships over time (Mesquita &amp; Karasawa, 2002).

{{Font color|purple|&lt;blockquote&gt;Empathy and sympathy clearly shape our relationships in profound ways. So, what key lessons can we take from this to develop stronger, more supportive connections?&lt;/blockquote&gt;}}

== '''key takeaways''' ==
{{RoundBoxTop|theme=11}}
* Understanding Differences: Recognising the distinction between empathy and sympathy is essential for building stronger, more supportive relationships.
* Empathy Builds Connection: Practising empathy enhances emotional bonds and encourages prosocial behaviours, leading to deeper, more meaningful relationships.
* Limitations of Sympathy: While sympathy can provide immediate comfort, it often lacks the emotional depth necessary for long-term connection and can lead to feelings of emotional disconnection.
* Practical Strategies:
Active Listening: Pay attention to what others are saying and respond thoughtfully.
Perspective-Taking: Strive to understand situations from the other person's viewpoint.
Show Genuine Concern: Demonstrate care and interest in the emotions and experiences of others.

{{RoundBoxBottom}}

== Conclusion ==
Empathy and sympathy are fundamentally different in their effects on behaviour and relationships. Empathy fosters emotional resonance and prosocial behaviours, while sympathy, though well-meaning, may create emotional distance. This distinction is essential for understanding how we build deeper, more meaningful connections.

The answer to the question, &quot;What's the difference and how do empathy and sympathy influence behaviour and relationships?&quot; lies in the way each emotion motivates behaviour. Empathy encourages prosocial actions, emotional support, and stronger, more resilient relationships, while sympathy, though well-meaning, may lead to less engaged, surface-level support, which can limit emotional depth and connection.

Practical takeaways include the importance of active listening, perspective-taking, and showing genuine concern to foster empathetic relationships. In both personal and professional settings, empathy enhances emotional well-being and promotes deeper, more supportive connections. Conversely, relying too heavily on sympathy can lead to misunderstandings or emotional disconnection, especially when the emotional engagement is lacking.

Empathy empowers us to build meaningful, supportive connections that not only enhance our well-being but also strengthen the emotional bonds we share with others. By practising empathy over sympathy, we can cultivate deeper, more resilient relationships that not only withstand challenges but grow stronger over time. The key to building lasting, fulfilling relationships lies in understanding and practicing empathy, which ultimately leads to more positive behaviour and stronger relational bonds.

==References==
{{Hanging indent|1=

Batson, C. D. (1991). The altruism question: Toward a social-psychological answer. Erlbaum.

Beail, N. (1988). Empathy and its development (N. Eisenberg &amp; J. Strayer, Eds.). Cambridge University Press. https://doi.org/10.1192/S0007125000224951

Bresnahan, M. J., Shearman, S. M., Lee, S. Y., Ohashi, R., &amp; Mosher, D. (2002). Personal and cultural differences in responding to criticism in three countries. Asian Journal of Social Psychology, 5(2), 93–105. https://doi.org/10.1111/1467-839X.00097

Brown, B. (2013, December 10). *Empathy vs. sympathy: What’s the difference?* [Video]. YouTube. https://youtu.be/KZBTYViDPlQ

Cohen, P., Schulz, M. S., Weiss, E., &amp; Waldinger, R. J. (2012). Empathy and conflict resolution in romantic relationships. Journal of Family Psychology, 26(4), 626–633. https://doi.org/10.1037/a0028667

de Greck, M., Shi, Z., Wang, G., Zuo, X., Yang, X., Wang, X., Northoff, G., &amp; Han, S. (2012). Culture modulates brain activity during empathy with anger. NeuroImage, 59(3), 2871–2882. https://doi.org/10.1016/j.neuroimage.2011.09.052

Decety, J., &amp; Cowell, J. M. (2014). Friends or foes: Is empathy necessary for moral behavior? Perspectives on Psychological Science, 9(5), 525–537. https://doi.org/10.1177/1745691614545130

Decety, J., Ickes, W., Batson, C. D., Blair, R. J. R., Bozarth, J. D., Buysse, A., Butler, S. F., Carlin, M., Carter, C. S., &amp; Craig, K. D. (2009). The social neuroscience of empathy (1st ed.). MIT Press. https://doi.org/10.7551/mitpress/9780262012973.001.0001

Decety, J., &amp; Jackson, P. L. (2006). A social-neuroscience perspective on empathy. Current Directions in Psychological Science, 15(2), 54–58. https://doi.org/10.1111/j.0963-7214.2006.00406.x

Mesquita, B., &amp; Karasawa, M. (2002). Different emotional lives. Emotion Review, 1(3), 255–268. https://doi.org/10.1177/1754073909103598

Smith, R., &amp; Davidson, J. (2016). The impact of sympathy and empathy on friendships. Journal of Social and Personal Relationships, 33(7), 897–913. https://doi.org/10.1177/0265407515615730

Thomas, S., Jackson, A., &amp; Harris, M. (2018). Parenting styles and children's emotional resilience: The role of empathy. Journal of Family Studies, 24(3), 314–329. https://doi.org/10.1080/13229400.2017.1350982

Wren, T. E. (2003). Empathy and moral development: Implications for caring and justice [Review of Empathy and moral development: Implications for caring and justice]. Ethics, 113(2), 417–419. https://doi.org/10.1086/343014

}}

==Exterenal{{sp}} links==

video: Brown, B. (2013, December 10). *Empathy vs. sympathy: What’s the difference?* [Video]. YouTube. https://youtu.be/KZBTYViDPlQ

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{{MECR3|1=https://www.youtube.com/watch?v=F1vM9LmVF7o}}
__TOC__

==Overview==
{{RoundBoxTop|theme=4}}

;Case study 

[https://en.wikipedia.org/wiki/7_October_Hamas-led_attack_on_Israel#:~:text=On%207%20October%202023%2C%20Hamas,the%201948%20Arab%E2%80%93Israeli%20War. On the 7th of October 2023], Israel and Hamas have been immersed in a horrific violence of war and over 1400 lives were lost, 240 people abducted, dozens missing and countless others left traumatised ''(Awwad-Tabry et al., 2024)''. The incident had left health and mental health professionals no choice but a daunting task of delivering distressing news to civilian families who have been impacted by the war and trauma ''(Awwad-Tabry et al., 2024)''. Traditionally, in Israel, it is the responsibility of the military to inform families about the loss or abduction of their loved ones ''(Awwad-Tabry et al., 2024)''.However due to the magnitude of casualties and abductions, breaking bad news extended beyond the military protocols ''(Awwad-Tabry et al., 2024)''. The daunting task of breaking bad news was given to a unique group of social workers in a particular city''(Awwad-Tabry et al., 2024)''.

Delivering negative news requires a unique skill sets such as balancing compassion, professionalism and psychological insight ''(Rosenzweig., 2012)''. For social workers, being met with such a difficult task has a profound effect on both sides of parties ''(Awwad-Tabry et al., 2024)''. The social workers who lack formal training on such areas of delivering negative news, were met with an extraordinary demand since the social workers were facing their own chaos and potential threats to their own families due to the catastrophic event''(Awwad-Tabry et al., 2024)''.

A qualitative case study design was conducted with the  purpose of examining the intricacy of delivering bad news on a single entity ''(Awwad-Tabry et al., 2024)''. The finding showed that the magnitude and the complexity of the event made it challenging to deliver bitter news  Irrespective of training, simulation and adequate preparation for such events, the task was alarming ''(Awwad-Tabry et al., 2024)''. The study suggested that delivering bad news in such events should be actioned by a formation of experienced and seasoned social workers. People who deliver bad news need to be fully prepared for the intense, difficult, painful and intimate moments for such cases ''(Awwad-Tabry et al., 2024)''.
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Delivering negative news is an inevitable aspect of both professional and personal life, and doing so effectively requires sensitivity, clarity, and empathy (''Ghanbari et al., 2023)''. Whether the person is informing the sad news to a team, friend, colleagues, or family, breaking bad news depends on how it is communicated ''(Ghanbari et al., 2023)''.  [[Communication skills|The method of communicating]] bad news to a person or team can significantly impact the recipient's emotional response and future relationship ''(Ghanbari et al., 2023)''. The challenge lies in balancing honesty with compassion, ensuring that the recipient understands the gravity of the situation without feeling overwhelmed or demoralise ''(Ghanbari et al., 2023)''. This chapter investigates the best ways of breaking bad news. Such as preparation, selecting the correct environment, utilising [https://www.verywellmind.com/what-is-empathy-2795562 empathetic language], and providing support for moving forward ''(Ghanbari et al., 2023)''. Following these principles enables a person to approach difficult conversations with confidence and foster an atmosphere of understanding and respect, even in challenging circumstances ''(Ghanbari et al., 2023)''. 

{{RoundBoxTop|theme=3}}
'''Focus questions:'''
* What is bad news?
* How to deliver bad news empathically?
* What psychological theories frames breaking bad news?
{{RoundBoxBottom}}

==What is bad news?==

===Diagnosis===
Bad news is defined as information which is negative, unfavourable and distressing for individuals or groups that are receiving it ''(Abdel Wahab et al., 2022)''.This means that bad news can involve personal, social, economic or political situations ''(Awwad-Tabry., 2024)''.  

For instance, in the medical field, breaking bad news to patient is a difficult and a regular duty for health care workers (''Cavallaro., 2017''). Breaking bad news can be health related issues, for example diagnosing a serious illness for a patient such as cancer ''(Abdel Wahab et al., 2022)''. An Oncologist would have to inform a patient about a negative test results from lab test or imaging which reveals an issue regarding an organ dysfunction or a present of a disease ''(Abdel Wahab et al., 2022)''.  

Informing a patient about a condition which is not getting better,  Meaning the patient's current health problem has declined since the treatment is ineffective ''(Abdel Wahab et al., 2022)''. The role of the practitioner is to analyse the emotional and the psychological reaction to bad news experienced by the patient. The assessing help practitioners to determine what the patient needs in order to adjust to the new reality(''Cavallaro., 2017''). While the doctor might see minor non-fatal diseases and slightly disorders, the patients might have different mindset. Therefore to understand the patient mindset, healthcare workers have to examine how the illness relates in the context of the individual's life(''Cavallaro., 2017'').  

Bad news can provoke a range of emotional responses which may include sadness, anxiety, anger and fear ''(Ghanbari et al., 2023)''. When individuals are faced with such problems it requires them to process the information and decide how to react and cope with the condition ''(Ghanbari et al., 2023)''. Hence, breaking bad news in the medical setting needs to be approached by sensitivity and compassion since it has a significant impact on a patient's psychological and emotional well-being ''(Ghanbari et al., 2023)''. 

Apparently, most physicians, clinicians, oncologist, nurses and other health care providers hardly receives adequate training on minimising emotional impact of life changing news (''Cavallaro., 2017''). Sadly, due to the lack of training, health practitioners don’t get to witness the value of training application in terms of accomplishing goals in managed care (''Cavallaro., 2017''). 

{{Robelbox|width=50|theme=
{{{theme|3}}}|title=Case study}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
A mixed methods study design was conducted using a cross-sectional design to assess the training and practice of doctors in breaking bad news (BBN) ''(Abdullah et al., 2024)''.The study was carried out in five different hospitals, where data were collected in eight weeks ''(Abdullah et al., 2024)'' .The participants were selected through a simple random sampling which included medical personnel involved in the selected hospital ''(Abdullah et al., 2024)''. The data collection involved a 25-item self-administered questionnaire consisting of two main sections ''(Abdullah et al., 2024)''. The initial phase focused on recording participants demographic information (Age, gender, designation and specialty including the years of experience ''(Abdullah et al., 2024)''. The second phase contained questions regarding the healthcare worker familiarity with protocol concerning guidelines about BBN ''(Abdullah et al., 2024)''.

The validity and reliability of the study was measured by administering a pilot study with ten work physicians in the general practice ''(Abdullah et al., 2024)''. The sample size was determined based on a 95% confidence level with an estimated population of 11% with a 5% margin error. Over all the population sample size was estimated to be 200, 000. It was estimated after using the design effect, the population size(N), the hypothesised Proportion (P), The margin Error (d) and the critical value (Z) ''(Abdullah et al., 2024)''. The study determined that the required sample size for the desired confidence level would approximately be 151 participants ''(Abdullah et al., 2024)''. After the data gathering, the information was analysed using SPSS version 22.0 descriptive statistics, frequencies table and percentages were computed to gain an insight about BBN ''(Abdullah et al., 2024)''. Qualitative data were collected through an in depth interview.

The results of the demographic data revealed the participants out 151 to be 62.3% males than females.
The overall outcome revealed that most health care workers rely on personal experience rather than formal training''(Abdullah et al., 2024)''. It suggested the need for structuring educational programs in the guidelines in BBN ''(Abdullah et al., 2024)''.
&lt;/div&gt;
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It is recommended that healthcare providers communicate bad news clearly and supportively. This involves implementing strategies like the [https://www.youtube.com/watch?v=9afuudUCKm4 SPIKES protocol] ''(Baile et al., 2000)''. The SPIKES is a six-step protocol which stands for setting, patient’s perception, invitation, knowledge, exploring or empathy and finally, strategy or summary ''(Baile et al., 2000)''. This protocol is a framework designed to guide practitioners on how to effectively discuss bad news with patients in a positive light ''(Baile et al., 2000)''.

'''Table 1.'''  
A descriptive table for the SPIKES protocol by ''Baile et al., 2000.''


The SPIKES protocol serves as a tool for breaking bad news in four components''(Baile et al., 2000)''.Gathering details from patients, transmitting the medical information and providing support to the patient ''(Baile et al., 2000)''. Additionally, it elicits patient collaboration and develops a strategy and treatment for the future ''((Baile et al., 2000)''.

The evolutionary theory of Emotion, explained by &amp;nbsp;Charles Darwin and later scholars, suggests that emotions have evolved to facilitate social communication and survival ''(Shackelford et al., 2015)''. Emotions are seen as adaptive responses to environmental challenges, helping individuals navigate social interactions and threats ''(Shackelford et al., 2015)''.

==How should bad news be delivered?==
===Private setting===
Since breaking bad news is a sensitive and crucial task that can dramatically impact the emotional and cognitive well- being of a person, health professionals take great consideration on how and where such negative matter needs to be delivered effectively ''(Leoniuk &amp; Sobczak., 2023)''. One of the components of delivering bad news is actioned in a private setting, a [[Privacy, Security, and Implied Mutual Exclusion|quiet space]] where the conversation can not be overheard by unwelcome bystanders ''(Leoniuk &amp; Sobczak., 2023)''. It allows the patient to process the information in a manner which makes them feel unexposed but respected for their privacy ''(Leoniuk &amp; Sobczak., 2023)''. The degree of comfort can be offered to a patient in comfortable environment such as a quiet room in a healthcare facility ''(Leoniuk &amp; Sobczak., 2023)''. The space should provide a sense of safety and security. Furthermore, healthcare workers must think about time consideration to ensure that there is a sufficient duration for discussing the news without rushing ''(Leoniuk &amp; Sobczak., 2023)''. It provides an open conversion where the patient can ask questions and express their emotions without being perceived as another statistical object on the topic. 

=== Allow present support===
Health professionals must listen to the wishes of the patient when breaking bad news, for example, allowing patients to have a present support, for instance allowing patients to have a family member or friend to be present during the conversation ''(Leoniuk &amp; Sobczak., 2023)''. Having a present support can assist in enabling the patient to process the information without feeling isolated ''(Leoniuk &amp; Sobczak., 2023)''. Healthcare workers need to be culturally sensitive when breaking bad news as some cultures may prefer to have a family member participating in the discussion. Lastly, a good healthcare professional must allocate an appropriate setting for follow-up discussion ''(Leoniuk &amp; Sobczak., 2023)''. The consideration of where the follow up should take place and the type of follow-up matter whether it needs to be an ongoing conversation ''(Leoniuk &amp; Sobczak., 2023)''. Ongoing conversation required a private setting to address treatment options, questions and emotional support. In total, breaking bad news, healthcare workers should constantly prioritise the patient’s emotional response and mental safety ''(Leoniuk &amp; Sobczak., 2023)''. Ensuring a private, comfortable and supportive environment is provided for the patient. It facilitates a more compassionate and effective conversation for both parties ''(Leoniuk &amp; Sobczak., 2023)''.

{{RoundBoxTop|theme=4}}Case study
In the article titled  ''Delivering bad news to patient'', ''(Cox et al., 2016)''. it examines the importance of healthcare professionals, chiefly physicians, being equipped with the necessary training when tasked with the unenviable role of telling an individual life altering news.  In the study,''(Cox et al., 2016)'', implemented a questionnaire at the Baylor University Medical Centre to deduce if an educational intervention should be undertaken at the facility. ''(Cox et al., 2016)'' the theorised based on their research that a patient centred approach was the ideal, highlighting the SPIKES protocol (Setting, Perception, Invitation, Knowledge, Empathy &amp; Staggery) and the ABCDE approach (Advanced preparation, Build a rapport, Communicate, Deal with reaction &amp; Encourage and validate emotions). They concluded that while there was an abundance of online resources at a physician’s fingertips there was no certainty that those at the university medical centre were actively seeking them out and implementing them ''(Cox et al., 2016)''.  A questionnaire was undertaken involving fifty-four participants ''(Cox et al., 2016)''. The results yielded that an overwhelming 93% of the sample size believed the ability to effectively deliver bad news was essential, however only 43% believed they presently had adequate training to perform such a task with 85% conceding they felt they required additional training ''(Cox et al., 2016)''.  It was concluded that a follow up study would be undertaken to gauge the effectiveness of the aforementioned ABCDE approach by using simulated patients and three altering bad news scenarios that would be filmed and feedback provided ''(Cox et al., 2016)''.  If this further study proved fruitful, ''(Cox et al., 2016)'' determined it would become a staple method of training moving forward at the university.    
{{RoundBoxBottom}}

==How to deliver bad news empathically==

===Preparation===
Empathy is an essential skill for a health practitioner to contain in order to deliver bad news with soft impact and making the discussion session more constructive ''(Aoun &amp; Breen., 2020)''. In order to enhance empathy, the medical practitioner would need to prepare themselves before breaking bad news to patients ''(Aoun &amp; Breen., 2020)''. Taking a moment to gather their thoughts, understand the facts clearly and anticipate the emotional reactions which may arise is an important step for health workers to consider before breaking bad news. Patients will have emotional reactions when responding to bad news delivered to them ''(Aoun &amp; Breen., 2020)''. For instance, experiencing silent shock, substantial crying and sobbing.

A relevant theory that is planted in the area of empathy when breaking bad news is the [[wikipedia:Carl_Rogers|person-centred therapy]] or the client-centred therapy ''(Aoun &amp; Breen., 2020)''. The theory of Person-centred therapy was established by an influential American psychologist and the founders of the humanistic approach to psychology Carl rogers ''(Dulmen et al., 2015)''. He developed several concepts and practices that have had a significant impact on therapy and counselling ''(Dulmen et al., 2015)''. 

These emotional responses can create a potentially awkward moment for the health practitioner but can be diminished through engaging in an empathetic communication ''(Aoun &amp; Breen., 2020)''. For example, empathy can be revealed by acknowledging the impact of the news through phrases. “ I can imagine how difficult it is for you,” or “ I’m really sorry to break this horrific news for you.’ The usage of simple and clear language can help the process of breaking bad news to be less complicated ''(Aoun &amp; Breen., 2020)''. Being direct and honest ensures understanding and can avoid beating around the bush to minimise confusion and frustration ''(Aoun &amp; Breen., 2020)''.

=== Active listening===
Another valuable component of revealing empathy is being an active listener. Medical workers should listen to the patient's emotional and general response during such times ''(Aoun &amp; Breen., 2020)''. Encourage them to express their feelings and validate their emotions. Utilise phrases such as “ I understand this is a lot to take in and it's okay to be upset.”&amp;nbsp; Offer them support and solutions by providing options and resources which might be healthy to cope with the negative situation ''(Aoun &amp; Breen., 2020)''. For instance, directing them to see a psychologist and notify them that you will be there to support them. Finally a health practitioner should reflect on the experience. After the discussion, it is a positive practice to take time to reflect on how it went and how it can be improved next time. The habitat of reflection can help to develop the skills in delivering difficult news empathetically ''(Aoun &amp; Breen., 2020)''. Being compassionate and thoughtful can assist in mitigating the distress that comes with breaking bad news. It fosters a supportive relationship and maintaining trust moving onward.

The Facial Feedback, this theory suggests that facial expressions can influence emotional experiences ''(Coles &amp; Lench., 2019)''. For instance, smiling can make a person feel happier, while frowning may lead to feelings of sadness.The idea is that feedback from facial expressions can increase or decrease emotional experiences ''(Coles &amp; Lench., 2019)''.

=== Quizzes===
{{RoundBoxTop}}&lt;quiz display=simple&gt;
What framework is often use in guiding healthcare professionals in breaking bad news? 
|type=&quot;()&quot;}
- SMILE
- CARE
+ SPIKE
- RELAX

{Breaking bad news can be a daunting task for most healthcare practitioner
|type=&quot;()&quot;}
+ True
- False

{What actions should healthcare worker do if a person reacts very emotional to bad news? 
|type=&quot;()&quot;}
- Get frustrated and leave
+ Validate their feelings and offer support
- Minimize their emotions
- Change the topic
&lt;/quiz&gt;
{{RoundBoxBottom}}

==Conclusion==
This chapter focused on exploring the best ways of breaking bad news. Breaking bad news to patients requires the skills of being empathetic, having safe space and providing support. Health practitioners are recommended to have strong knowledge of the SPIKES protocols when breaking bad news to clients. Compassion and empathetic are highly regarded to facilitate and support relationships and maintain trust when breaking bad news.

==See also==
*[[Motivation and emotion/Book/2024/Empathy versus sympathy|Empathy versus sympathy]] (Book chapter 2024)
*[[Motivation and emotion/Book/2024/Emotional self-care|Emotional self-care]] (Book chapter 2024)
*[[Motivation and emotion/Book/2021/Empathy-altruism hypothesis|Empathy-altruism hypothesis]] (Book chapter 2021)

==References==
{{Hanging indent|1=

Abdel Wahab et al. (2022). ''Breaking Bad News of a Cancer Diagnosis: A Mixed-Methods Study of Patients' Perspectives. Patient preference and adherence,'' 16, 3357–3369. https://doi.org/10.2147/PPA.S394170

Abdullah, M. A., Khan, K. R., Shaikh, B. T., &amp; Yasin, M. A. (2024). ''Breaking bad news: A mixed methods study reporting the need for improving communication skills among doctors in Pakistan. BMC Health Services Research,'' 24(1), 588–588. https://doi.org/10.1186/s12913-024-11056-2

Aoun, S., &amp; Breen, L. (2020). ''A person-centred approach to breaking bad news.''http://hdl.handle.net/20.500.11937/9107

Awwad-Tabry, S. ,  Elyoseph, Z., Levkovich, I. , &amp; Weisman-Moschkovich, M.(2024). Breaking Bad News: ''A Case Study of Social Workers Communicating Bereavement and Distressing News in the Aftermath of Hamas Attack in Israel. Psychology,'' 15, 915-923. doi: 10.4236/psych.2024.156054.

Baile, et al. (2000). SPIKES—A Six‐Step Protocol for Delivering Bad News: Application to the Patient with Cancer. The Oncologist (Dayton, Ohio), 5(4), 302–311. https://doi.org/10.1634/theoncologist.5-4-302

Barclay, L. J., Breitsohl, H. &amp; Kitz, C. C. (2023). ''The delivery of bad news: An integrative review and path forward. Human Resource Management Review'', 33(3), 100971-. https://doi.org/10.1016/j.hrmr.2023.100971

Cavallaro, M. J. (2017). How to present negative medical news in a positive light: a prescription for health care providers. Atlantic Publishing Group, Inc.

Coles, N. A., Larsen, J. T., &amp; Lench, H. C. (2019). A Meta-Analysis of the Facial Feedback Literature: Effects of Facial Feedback on Emotional Experience Are Small and Variable. Psychological Bulletin, 145(6), 610–651. https://doi.org/10.1037/bul0000194​

Cox, T. R.,  Gentry, L., &amp; Monden, K. R . (2016). ''Delivering bad news to patients. Proceedings'' (Baylor University. Medical Center), 29(1), 101–102. https://doi.org/10.1080/08998280.2016.11929380

Dulmen, S. A., Lukersmith, S., Muxlow, J., Santa Mina, E., Nijhuis‐van der Sanden, M. W. G., &amp; Wees, P. J. (2015). ''Supporting a person‐centred approach in clinical guidelines. A position paper of the Allied Health Community – Guidelines International Network (G‐I‐N). Health Expectations : An International Journal of Public Participation in Health Care and Health Policy,'' 18(5), 1543–1558. https://doi.org/10.1111/hex.12144

Equipe de Marketing. (2022, November 17). Consumerism in the health area with Ninsaúde Apolo. Tips to Open Your Clinic and Medical Marketing - Ninsaúde Clinic. https://english.apolo.app/consumerism-in-the-health-area-with-ninsaude-apolo/​

Ghanbari Jolfaei, A., Mansoursamaei, A., Mansoursamaei, M., Salehian,R., &amp; Zandi, M.(2023). ''Self-assessment of residents in breaking bad news; skills and barriers. BMC Medical Education,'' 23(1), 1–740. https://doi.org/10.1186/s12909-023-04720-4

Healthcare professionals: Hone your advance care planning skills. (n.d.). VITAS Healthcare. https://www.vitas.com/about-us/newsroom/webinar-spikes-protocol-for-national-healthcare-decisions-day-2020​

Leoniuk, K. &amp; Sobczak, K. (2023.''Doctors’ attitudes in the situation of delivering bad news: patients’ experience and expectations. Archives of Medical Science,'' 19(4), 921–929. https://doi.org/10.5114/aoms/112756

New ML improves cancer drug effectiveness predictions. (2021, November 10). AI Powered Healthcare {{!}} Healthcare IT News. https://www.healthcareitnews.com/ai-powered-healthcare/new-ml-improves-cancer-drug-effectiveness-predictions​

Rosenzweig M. Q. (2012). ''Breaking bad news: a guide for effective and empathetic communication. The Nurse practitioner,'' 37(2), 1–4. https://doi.org/10.1097/01.NPR.0000408626.24599.9e

Shackelford, T. K., Welling, L. L. M., &amp; Zeigler-Hill, V., (2015). Evolutionary perspectives on social psychology. Springer. https://doi.org/10.1007/978-3-319-12697-5

}}

==External links==
* [https://www.youtube.com/watch?v=MKnWkrPLGOs Breaking Bad News Demonstration] ( YouTube video)
* [https://www.youtube.com/watch?v=9afuudUCKm4 Breaking Bad News - SPIKES Overview -OSCE Guide] ( YouTube Video)
* [https://www.bradfordvts.co.uk/wp-content/onlineresources/communication-skills/breaking-bad-news/how%20do%20i%20break%20bad%20news.pdf How Do I Break Bad News] (Hospice friendly Hospitals Book)
* [https://www.verywellmind.com/what-is-empathy-2795562 Empathy] (very well Mind)
* [https://litfl.com/osce-breaking-bad-news-ich/ Procedures explaining Breaking Bad News] (Life in the Fastlane)
* [https://northyorkshireccg.nhs.uk/wp-content/uploads/2021/02/Top_tips.pdf Top Tips for Difficult Conversation] (South Tees Hospitals)

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{{CountryHeader|File:South Africa (orthographic projection).svg|https://en.wikipedia.org/wiki/South Africa}}
{{HTitle|General Information}}South Africa (SA), the southernmost country in Africa, is among the four nations with the continent’s largest gross domestic product (GDP) (Cooper et al. 2020). Known for its remarkable diversity, SA is divided into nine provinces, each with its own legislature, premier, and executive council. This diversity is also reflected in its 12 official languages: Afrikaans,
English, Ndebele, Pedi, Sotho, South African Sign Language, Swati, Tsonga, Tswana, Venda, Xhosa, and Zulu. The late Archbishop Desmond Tutu famously called SA “The Rainbow Nation” in recognition of its rich cultural, linguistic, and ethnic variety (Dixon, 2023).

One of the most significant issues in South African history is apartheid, a system of racial segregation, meaning &quot;apartness.&quot; This ideology or law was introduced and supported by the National Party and implemented in 1948 (South African History Online, 2022). During this regime, the apartheid law forced the different racial groups to live separately and develop. Apartheid ended in the early 1990s, culminating in the first democratic elections in 1994, when Nobel Peace Prize laureate Dr. Nelson Rolihlahla Mandela became South Africa’s first black president.

SA shares borders with Botswana, Zimbabwe, Namibia, Lesotho, Eswatini, and Mozambique. Its population is estimated at 63.02 million (StatsSA, 2024). The country is also renowned for its mineral wealth, with mining dating back to the 1800s. Diamonds were discovered in the Northern Cape in 1867, and gold was found in Gauteng in 1884. As such, mining was reported to be the second most influential industry, with manufacturing being the largest in the country (StatsSA, 2017). Due to the nature of this work, both in the mining and manufacturing industries, earliest reports on noise-induced hearing loss (NIHL) were documented among gold
miners in the 1980s (Hessel &amp; Sluis-Cremer, 1987).

{{HTitle|Incidence and Prevalence of Hearing Loss}}Hearing loss is a widespread public health concern, with Sub-Saharan Africa contributing significantly to global estimates (WHO, 2021). The World Health Organization (WHO) reports that approximately 15.7% of adults aged 15 and older in this region experience hearing loss (WHO, 2021). In South Africa, an estimated 12 million people are affected by some degree of hearing loss, including about 4 million individuals with hearing disabilities, of whom fewer than 600,000 use South African Sign Language (SASL) (World Hearing Report, 2022).

There are notable regional disparities in hearing loss prevalence across South Africa. Less developed provinces generally report higher rates compared to more developed areas. In Cape Town, located in the developed Western Cape province, the overall prevalence of hearing loss
in the population was reported to be 12.35% (95% CI: 11.06%- 13.64%), and the prevalence of disabling hearing loss was 4.57% (95% CI: 3.75%- 5.39%) amongst individuals ≥ 4 years old (Ramma &amp; Sebothoma, 2016). In primary health care settings within urban and peri-urban facilities in Tshwane, the prevelance of hearing loss has been been reported at 17.5%, with the majority of cases being bilateral (70.0%) and sensorineural in nature (84.2%) (Louw et al. 2018). Conversely, the overall prevalence of hearing loss in the Elias Motsoaledi Local Municipal (EMLM) area in rural Limpopo province, was reported to be 19.88% (95% confidence interval [CI]: 0.15–0.2) and
8.94 (95% CI: 0.08–0.12) for disabling hearing loss. The prevalence of ear disease was 13.19% (95% CI: 0.10–0.15), with impacted cerumen and otitis media reported as the most prevalent cause (Joubert &amp; Botha, 2019).

Similar patterns of disparities are observed across age groups, as illustrated in table 1 below. 

{| class=&quot;wikitable&quot;
|+ Table 1. Prevalence rates across age groups for Limpopo and Gauteng Province
|-
! Limpopo Province (Joubert &amp; Botha, 2019) !! Gauteng Province (Louw et al, 2018)
|-
| 0-14.11 years = 14.01% || 3-14 years = 4.8%
|-
| 15-64.11 years = 20.22% || 15-39 years=5.7%
|-
| 65 years and older = 64.65% || 40 years and above = 15%
|-
| Overall prevalence = 19.88% || Overall prevalence = 17.5%
|}

These findings underscore the critical need for comprehensive hearing care services, including prevention, early detection, and intervention, to address the rising prevalence of hearing loss across South Africa.

{{HTitle|Information About Audiology}}
==== Landscape of Audiological Care ====
Hearing healthcare services in South Africa began with limited availability, primarily emerging in the mid-20th century. The development of audiology was closely linked to the establishment of university training programs, which began at the University of the Witwatersrand (Wits) in the late 1930s and early 1940s. In those early years, hearing healthcare services were often provided through hearing aid fitting and assessment programs, and much of the clinical work was associated with hospitals, schools for the deaf, and other special education facilities. Throughout the 1970s and 1980s, more formalized audiology clinics began to emerge in hospitals across South Africa, often as part of larger healthcare systems. During the 1990’s the government started to recognize the need for comprehensive hearing care services, and more initiatives to improve accessibility in both urban and rural settings were developed.

Today, audiology services in South Africa are more widespread, however they remain concentrated in urban areas. In 2024, 947 audiologists were registered with the Health Professions Council of South Africa (HPCSA), with the majority practicing in private settings rather than public healthcare facilities. This distribution underscores the ongoing gap in access to services. To meet the diverse needs of individuals with hearing and balance issues, South Africa relies on a network of hearing healthcare professionals who work collaboratively to provide comprehensive care. These include:
	
* Audiologists who are central to hearing healthcare, offering services such as hearing assessments, cerumen management, hearing intervention (invasive and non-invasive hearing devices), aural rehabilitation, vestibular evaluations and interventions. These professionals are trained through accredited university programs and work in a variety of settings, including public and private hospitals, private practices, and community health centers. 
* Hearing aid acousticians specialize in the assessment, fitting and maintenance of hearing aids and other assistive listening devices for adults. They typically work in private practices or audiology clinics.
* Ear-, Nose-, Throat, Specialists (otolaryngologists/otologists/otoneurologists) focus on complex ear and balance disorders, managing advanced cases of hearing loss or vestibular conditions in urban hospitals and private clinics. ENT specialists often collaborate with audiologists, particularly for patients requiring surgical interventions such as cochlear implants or treatments for chronic otitis media. These specialists provide services in both public and private healthcare settings, with their training conducted through accredited medical schools and specialized ENT programs within the country. 
* Community healthcare workers (CHWs) and early childhood development (ECD) practitioners, where available, support audiologists and hearing healthcare professionals in underserved areas. They may serve as the first point of contact, conducting basic hearing screenings and referring individuals for further evaluation when necessary. Their community-based position also enables them to monitor at-risk populations, provide early intervention, and raise awareness through health education campaigns on hearing loss prevention, hearing protection, and the importance of early screening.

==== Education and Training ====
The field of speech therapy in South Africa began in 1937, when Professor Pierre de Villiers Pienaar introduced the first diploma in Logopaedics at the University of the Witwatersrand (Wits). This program focused primarily on speech and language disorders, and he also established the Speech, Voice, and Hearing Clinic at Wits, laying the groundwork for the profession. Audiology was later incorporated as a distinct discipline, and in 1959, Professor Pienaar further advanced these fields by heading the newly established Department of Speech Science, Logopedics, and Audiology at the University of Pretoria. These developments were instrumental in formalizing education and clinical training in both speech therapy and audiology in South Africa.

Today, six (6) universities in South Africa offer degree programs in audiology, including the University of Pretoria, the University of the Witwatersrand, the University of KwaZulu-Natal, Stellenbosch University, University of Cape Town, and Sefako Makgatho Health Sciences University. Since 2006, all these institutions have transitioned to training audiologists and speech-language therapists separately, moving away from the previous dual qualification model (Swanepoel, 2006). The programs now consist of a four-year undergraduate degree, followed by a mandatory year of community service in public healthcare facilities. This system ensures graduates gain practical experience as community-service audiologists or speech-language therapists, addressing the needs of underserved populations. Despite the progress in education, there is still a shortage of audiologists to meet the country’s healthcare needs (Pillay et al., 2020; Swanepoel, 2006).

{| class=&quot;wikitable&quot;
|+ Table 2. Institutions offering training in Audiology
|-
! Institution !! Degree Name !! Estimated Number of Annual Graduates
|-
| University of Pretoria || B: Audiology || 35-40
|-
| University of Witwatersrand || B: Audiology || 25
|-
| University of Cape Town || BSc: Audiology || 20-30
|-
| University of Kwazulu Natal || B: Audiology || 35
|-
| Sefako Makgatho Health Sciences University || B: Audiology || 25-30
|}

===== Scope of Practice =====
In South Africa, the scope of practice for audiologists is clearly defined and regulated by the Health Professions Council of South Africa (HPCSA). Audiologists are authorized to provide or be involved in the following:
# Hearing Assessment and Diagnosis
# Hearing Rehabilitation and Management
# Vestibular Assessment and Rehabilitation
# Neonatal and Paediatric Audiology
# Public Health and Education
# Interdisciplinary collaboration

=== Audiological Services === 
Audiology services in South Africa encompass both core and advanced diagnostic and rehabilitative options to address a range of hearing and balance disorders. These services play a crucial role in improving the quality of life for individuals affected by hearing loss and balance disorders.

===== Core Audiology Services =====
* Pure-tone audiometry (PTA): A standard test to determine hearing thresholds.
* Tympanometry: Evaluation of middle-ear function, including eardrum movement and pressure within the middle ear. Impedance audiometry: Assessment of middle-ear reflexes and compliance.
* Otoacoustic emissions (OAE): Screening for cochlear (inner ear) function, particularly for newborn hearing programs, and used for differential diagnostic purposes in older populations.
* Screening auditory brainstem response (ABR): Early detection of auditory pathway integrity, especially for infants and individuals unable to perform standard audiometric tests.
* Hearing aid assessment and dispensing: Comprehensive evaluation and fitting of hearing aids tailored to individual hearing needs.
* Aural rehabilitation: Therapy and counselling to maximize the use of residual hearing and optimize communication skills.

==== Advanced Audiology Services ====

Advanced audiology services are available at selected practices and hospitals, these services expand diagnostic and rehabilitative options:	
* Diagnostic auditory brainstem response (ABR): A detailed evaluation of the auditory pathway, aiding in the diagnosis of neurological and cochlear disorders.
* Auditory steady-state response (ASSR): Assessment of hearing thresholds, particularly in difficult-to-test populations, including infants.
* Implantable devices: Evaluation, programming, and management of cochlear implants, bone-anchored hearing aids (BAHA), and other implantable hearing solutions.
* Vestibular audiology: Comprehensive assessment and management of balance disorders, including:
**Computerized Dynamic Visual Acuity (cDVA): Evaluation of visual stability during head movements.
**Video head impulse testing (vHIT): Assessment of semicircular canal function.
**Vestibular evoked myogenic potentials (VEMPs): Measurement of vestibular function through muscle responses.
**Electrocochleography (EcoG): Diagnosis of endolymphatic hydrops and other inner ear conditions.
**Videonystagmography (VNG): Analysis of eye movements to assess vestibular function.
**Posturography: Evaluation of balance and postural control.
**Fall Risk Assessment: Identification of individuals at risk of falling using standardized tools, including gait and balance evaluations, timed up-and-go (TUG) test, Berg Balance Scale (BBS), and functional reach tests. Audiologists assess the impact of vestibular dysfunction on postural stability and recommend appropriate interventions to mitigate fall risk.

*Vestibular rehabilitation: Customized therapy programs to address balance dysfunction and dizziness, incorporating exercises for gaze stabilization, balance improvement, and compensation strategies.
*Central auditory processing disorder (CAPD) testing and management: Identification and treatment of difficulties in the brain’s ability to process auditory information.
*Tinnitus management: Multi-faceted approach to alleviate tinnitus symptoms, including sound therapy, counselling, and habituation strategies.
This comprehensive list reflects the range of audiology services available in South Africa, showcasing the country's capacity to provide both foundational and advanced care across diverse populations. These services are critical for addressing the needs of individuals with hearing and balance disorders, contributing to improved quality of life.

The public sector provides audiology services primarily in hospitals and community clinics, but access can be inconsistent, especially in rural areas. While government hospitals offer these services, they are often limited due to resource constraints, including equipment shortages and understaffing. This disparity is accentuated in rural and underserved areas, where audiology services may be entirely unavailable.

In contrast, private audiology practices are more equipped and accessible in urban and peri-urban areas, offering a broader range of diagnostic and rehabilitative services. Private practitioners often include tinnitus management, vestibular assessments, auditory processing evaluations, and hearing aid fittings as part of their comprehensive care. However, these services are typically funded out-of-pocket or through medical aid schemes, limiting access for economically disadvantaged individuals.

=== Regulatory Body === 
The Health Professions Council of South Africa (HPCSA) is the primary regulatory authority for healthcare professionals, including audiologists. The HPCSA oversees the registration, scope of practice, accreditation of higher education programmes, continuing professional development (CPD), and disciplinary processes for practitioners.
Based on the regulatory framework an audiologist must:
#Complete Accredited Education: Obtain a degree in audiology from a recognized South African university.
#Community service: Fulfil a compulsory community service year, providing audiological services in public healthcare facilities after completing a degree in Audiology.
#Register with the HPCSA: Registration is mandatory to practice legally. Audiologists are listed under the Professional Board for Speech, Language, and Hearing Professions.
#Engage in Continuing Professional Development (CPD): Practitioners must participate in ongoing education to maintain their registration and stay updated on advancements in the field.
#Ethical guidelines: Audiologists must adhere to the ethical guidelines set out by the HPCSA which emphasizes patient confidentiality and informed consent, non-discriminatory practices and evidence-based decision making.

The HPCSA may register persons holding qualifications that are not prescribed, that is, qualifications obtained from outside of South Africa. In this regard, Section 25 of the Health Professions Act No. 56 of 1974 (as amended) states, “the Minister may, after consultation with the council by regulation provide that any person who holds a qualification which the council may accept by virtue of the fact that such qualification, in the opinion of the council, indicates a satisfactory standard of professional education and training”. This allows registration of such a person, at the discretion of a relevant professional board, but subject to any regulations and national health policy and international protocols. A professional board may require such a person to pass an evaluation before persons appointed by the professional board, to determine whether such person possesses adequate professional knowledge, skill, and competence to practice in South Africa. Holding a foreign qualification does not guarantee registration with the HPCSA unless the above requirements are met.

=== Professional Associations === 
South Africa has several professional bodies that support and regulate the practice of audiology and speech-language therapy. These organizations play a crucial role in professional development, advocacy, and ensure that high standards of practice are maintained within the industry. They provide resources, networking opportunities, and continuing education to audiologists, speech-language therapists, and related professionals.
*'''South African Speech-Language-Hearing Association (SASLHA):''' A professional organization representing speech-language therapists and audiologists. SASLHA supports its members through advocacy, education, and collaboration, promoting excellence in the professions. 
*'''South African Association of Audiologists (SAAA):''' A dedicated body for audiologists, providing support, networking opportunities, and resources for members. SAAA also advocates for the audiology profession and promotes evidence-based practice. 


{{HTitle|Audiology Research}}Much of the audiology research in South Africa is conducted at universities, with independent clinical audiologists and hearing aid companies also actively contributing. This research spans the full range of audiological practice, often through student projects at the undergraduate, master’s, and doctoral levels. Notable innovations in particular in the field of TeleAudiology and mHealth have resulted from research pioneered by South African Audiologists (https://www.hearxgroup.com/about-us). 

South African Audiology researchers publish widely in several peer-reviewed international audiology-related journals, as well as in the South African Journal of Communication Disorders (SAJCD). SAJCD is an open-access double-blinded peer-reviewed local South African journal with an impact factor of 1.0. The journal has a dual focus and includes “reports and papers concerned with research, and critically evaluative theoretical, philosophical and conceptual issues dealing with aspects of human communication and its disorders, dysphagia, service provision, training and policy.” (https://sajcd.org.za/index.php/sajcd). 

Some of the themes published in SAJCD in recent years have focused on the following topics:
*''Early Hearing Detection and Intervention (EHDI)''. Topics covered include: Newborn hearing screening (NHS) programs, targeted vs. universal NHS, follow-up challenges (Khan &amp; Joseph 2024; Kgare &amp; Joubert 2024; Kanji 2022; Petrocchi-Bartel &amp; Khoza Shangase, 2014).
*''Public Awareness and Knowledge of Hearing Health''. Key topics reported were: Awareness of audiology professions, community education on hearing loss (Ehlert 2017).
*''Hearing Conservation and Occupational Hearing Health''. Topics covered: Noise-induced hearing loss, hearing conservation in workplaces (A Special Edition on this topic was published in 2020 https://sajcd.org.za/index.php/sajcd/issue/view/71; Mahomed &amp; Panday 2024). 
*''Barriers to Accessing Audiological Services:'' Topics include: Socioeconomic, cultural, and systemic barriers to care  (Mtimkulu &amp; Khoza-Shangase 2024; Joubert et al 2017).
*''Pediatric Hearing Loss.'' Including topics of: Parental knowledge, intervention in early childhood (Ehlert &amp; Coetzer 2024; Van Zyl et al 2024)
*''Rural and Underserved Populations.'' Topics included: Hearing impairment prevalence, community-based approaches (Joubert 2023; Petrocchi 2023).
*''Technological and Methodological Advances.'' Key Topics: Tele-audiology, improved diagnostics (Moll et al 2024,Naude et al 2024, Kuschke et al 2023; Khoza-Shangase &amp; Moroe 2020).

{{HTitle|Audiology Charities}}There are several organizations in South Africa that are dedicated to supporting audiology and enhancing hearing healthcare services. Below are some notable organizations and their contributions:

# '''HiHopes''' offers early intervention programs that provide free, home-based support to families with infants or toddlers diagnosed with hearing loss. Their mission is to optimize the development of children with hearing loss by offering care, support, and partnership. 
# '''hearX Foundation''' is focused on creating access to hearing care services in underserved communities. They provide community-based hearing screenings, referrals, and awareness programs to address educational barriers related to hearing impairments. 
# '''Hearing Africa''' is dedicated to improving the lives of individuals with hearing loss by providing affordable hearing aids and support services. 
# '''DeafSA''' acts as the national research, information, and community action organization facilitating services to the South African Deaf and hard-of-hearing communities.  The organization's mission is to preserve, protect, and promote the civil, human, and linguistic rights of Deaf, Deafblind, Hard of hearing and deafened people in South Africa.
# '''DEAFinition Organization''' is a non-profit organization that empowers the Deaf community through education, advocacy, and support services. Their work aims to create an inclusive society where Deaf individuals have equal opportunities and access to resources. 
# '''DEAFability''' works to promote the rights and well-being of Deaf individuals through various programs and services. Their initiatives focus on enhancing the lives of people with hearing loss by providing educational support and advocacy. 
# '''South African National Deaf Association (SANDA)''' provides quality services, ensuring public accessibility and increasing awareness of issues affecting Deaf people at all levels in South Africa. As an advocacy organisation, SANDA is at the forefront in promoting and advancing the rights of Deaf people at all levels of society.
# '''‘Give an Ear Foundation’''' is dedicated to improving the lives of African children with Microtia/Atresia and related conditions. They aim to raise awareness about Microtia/Atresia and provide access to life-changing corrective surgeries and hearing aids.
# '''Hear Us''' is a non-profit organisation based in the Western Cape, established in 2001 by parents of deaf children who received cochlear implants. Hear Us is committed to financially supporting disadvantaged individuals with severe-to-profound hearing loss to afford a Cochlear Implant and maintain them lifelong in order to realise their full potential in the hearing world. They also give support to those with hearing loss and their families. 
# '''Dischem Foundation:''' The gift of hearing, as part of their commitment to “Better Health Starts Here”, the Dis-Chem Foundation is proud to partner with Miss South Africa (2024), Mia le Roux, and the Miss South Africa Organisation to provide cochlear implants to hearing-impaired individuals who cannot afford this life-changing device. The Gift of Hearing forms part of Le Roux’s campaign, the Mia Le Roux Movement, which advocates for deaf individuals in South Africa and raises awareness about exclusion. 
# The '''National Institute for the Deaf (NID)''' is a registered Non-Profit Company (NPC) – established in 1881, they have been dedicated to the wellbeing of the Deaf community for well over a century.

These organizations play a crucial role in addressing the challenges faced by individuals with hearing loss in South Africa, providing essential services, resources, and advocacy to improve their quality of life.


{{HTitle|Challenges and Opportunities}}Rural South Africa faces a significant gap in audiology services. Limited infrastructure and healthcare resources result in minimal to no access to audiology care in these areas. Additionally, the healthcare workforce ratios remain insufficient to meet the growing demand for audiology services, especially in underserved regions. The National Health Insurance (NHI) bill highlights the need for an additional 608 audiologists by 2030 to address these gaps (Pillay et al., 2020), yet a significant portion of recent graduates face unemployment, partially due to the lack of available positions and other systemic barriers (Hlayisi, 2020). This shortage has been compounded further due to limited resources in public healthcare settings, where hospitals and clinics often struggle with equipment shortages and understaffing, making it difficult to provide comprehensive care (Bhamjee et al., 2022). 

Regardless of these challenges, opportunities exist to improve access to hearing healthcare. South Africa has the potential to improve the accessibility and quality of hearing care across the country. Efforts to address the challenges require collaboration between the government, private sector, and NGOs. These could include:	
* Enhancing training programs to produce more audiologists
* Targeted policies and incentives to attract specialists to rural and underserved areas
* Expanding mobile audiology services to underserved areas
* The formalization and integration of CHWs into hearing healthcare to improve service accessibility


{{HTitle|References}}
# Cooper,B., Rusare,M., Ferreira,M.,Gatwabuyege,F., Hougaard,C. (2020). Identifying regional economic hubs in Africa. Accessed from: https://cenfri.org/wp-content/uploads/Identifying-regional-economic-hubs-in-Africa.pdf
# Saharan Africa. https://cenfri.org/publications/regional-economic-hubs-in-sub-saharan-africa/
# Dixon, E. (2023). We live in a “Rainbow Nation”, but its potential is yet to be unlocked. CommonPurpose.Accessed from:  ttps://commonpurpose.org/resources/blog/unlocking-rainbow-nation
# Bhamjee, A., Le Roux, T., Schlemmer, K., Graham, M. A., &amp; Mahomed-Asmail, F. (2022). Audiologists’ perceptions of hearing healthcare resources and services in South Africa’s public healthcare system. Health Services Insights, 15, 11786329221135424.
# Booth, H. D., Pfeiffer, R. L., &amp; White, D. (2017). The role of community health workers in South African hearing care services. South African Medical Journal, 107(7), 616-620.
# Cruz, A., Maan, S., &amp; Kaur, M. (2016). Prevalence of hearing loss in the Cape Town metropolitan area: A study of the adult population. South African Journal of Communication Disorders, 63(1), 1-9. https://doi.org/10.4102/sajcd.v63i1.182
# Department of Health. (2006). Health on community service by health professionals: Community Service to improve access to quality healthcare to all South Africans. Retrieved from https://www.gov.za/news/health-community-service-health-professionals-05-jan-2006
# Ehlert, K. (2017). Perceptions of public primary school teachers regarding noise-induced hearing loss in South Africa. South African Journal of Communication Disorders64(1), a185. https://doi.org/10.4102/sajcd.v64i1.185
# Ehlert, K., &amp; Coetzer, C. (2020). Maternal knowledge and views regarding early hearing detection and intervention in children aged 0–5 years at a semi-urban primary care clinic in South Africa. South African Journal of Communication Disorders, 67(1), a681. https://doi.org/10.4102/sajcd.v67i1.681
# Frisby, C., Eikelboom, R. H., Mahomed-Asmail, F., Kuper, H., De Kock, T., Manchaiah, V., &amp; Swanepoel, D. W. (2022). Community-based adult hearing care provided by community healthcare workers using mHealth technologies. Global Health Action, 15(1), 2095784.
# Health Professions Council of South Africa. (2004). Health Professions Act No. 56 of 1974. Retrieved from http://www.hpcsa.co.za
# Health Professions Council of South Africa. (2021). Continuing professional development. Retrieved from http://www.hpcsa.co.za/cpd
# Hessel, P. A., &amp; Sluis-Cremer, G. K. (1987). Hearing loss in white South African goldminers. South African medical journal = Suid-Afrikaanse tydskrif vir geneeskunde, 71(6), 364–367.
# Hussein, S. Y., Swanepoel, D., de Jager, L. B., Myburgh, H. C., Eikelboom, R. H., &amp; Hugo, J. (2018). Community-based hearing screening for young children using an automated smartphone application operated by community healthcare workers. International Journal of Audiology, 57(8), 621-629.
# Hlayisi, V. G. 2020. “Scarce Health Human Resource Wastage: No work for South African Audiologists? A descriptive Survey Study.”
# Joubert, K., &amp; Botha, D. (2019). Contributing factors to high prevalence of hearing impairment in the Elias Motsoaledi Local Municipal area, South Africa: A rural perspective. South African Journal of Communication Disorders, 66(1), a611. https://doi.org/10.4102/sajcd.v66i1.611
# Joubert, K., Sebothoma, B., &amp; Kgare, K.S. (2017). Public awareness of audiology, hearing and hearing health inthe Limpopo Province, SouthAfrica. South African Journal of Communication Disorders 64(1), a557. https://doi.org/10.4102/sajcd.v64i1.557
# Kanji, A. (2022). Newborn and infant hearing screening at primary healthcare clinics in South Africa designated as National Health Insurance pilot sites: An exploratory study. South African Journal of Communication Disorders, 69(1), a840. https://doi.org/10.4102/sajcd.v69i1.840
# Kgare, K.S., &amp; Joubert, K. (2024). Community-based infant hearing screening: Outcomes of a rural pilot programme. South African Journal of Communication Disorders, 71(1), a1045. https://doi.org/10.4102/sajcd.v71i1.1045
# Khan, N.B., &amp; Joseph, L. (2024). Risk factors and hearing outcomes in infants and young children in KwaZulu-Natal, South Africa.South African Journal of Communication Disorders, 71(1), a1031. https://doi.org/10.4102/sajcd.v71i1.1031
# Khoza-Shangase, K., &amp; Moroe,N. (2020). South African hearing conservation programmes in the context of tele-audiology: A scoping reviewSouth African Journal of Communication Disorders, 67(2), a670. https://doi.org/10.4102/sajcd.v67i2.670
# Kuschke, S., Rogers, C., &amp; Meyer, E. (2023). Ten years’ experience with bone conduction hearing aids inthe Western Cape, SouthAfrica. South African Journal of Communication Disorders, 70(1), a940. https://doi.org/10.4102/sajcd.v70i1.940
# Louw, C., Swanepoel, W., Eikelboom, R. H., &amp; Hugo, J. (2018). Prevalence of hearing loss at primary health care clinics in South Africa. African health sciences, 18(2), 313–320. https://doi.org/10.4314/ahs.v18i2.16 
# Mahomed, H., &amp; Panday, S. (2024). Awareness, attitudes and perceptions of students towards leisure noise in Durban, South Africa.South African Journal of Communication Disorders, 71(1), a1040. https://doi.org/10.4102/sajcd.v71i1.1040
# Moll, J., Burger, Z., Jacobs, D.M.P., Mothibe, R.P., Swanepoel, D.W., &amp; Mahomed-Asmail, F. (2024). Hearing aid verification: Practices and perceptions of South African audiologists.South African Journal of Communication Disorders, 71(1), a1059. https://doi.org/10.4102/sajcd.v71i1.1059
# Moonsamy, S., A. Mupawose, J. Seedat, M. Mophosho, and D. Pillay. 2017. “Speech-Language Pathology and Audiology in South Africa: Reflections on Transformation in Professional Training and Practice since the End of Apartheid.” Perspectives of the ASHA Special Interest Groups 2 (17): 30–41. https://doi.org/10.1044/persp2.SIG17.30.
# Mothemela, B., Ramma, L., &amp; Swanepoel, D. W. (2024). Update on the state of audiology in South Africa. International Journal of Audiology, 1–4. https://doi.org/10.1080/14992027.2024.2354511
# Mtimkulu, T.K., &amp; Khoza-Shangase, K. (2024). ‘Help-seeking journey to accessing audiology services in a peri-urban community in South Africa’, South African Journal of Communication Disorders,71(1), a1002. https://doi.org/10.4102/sajcd.v71i1.1002
# Naudé, A., Erasmus, L.-M., De Swardt, L., Bornman, J., &amp; Van Marlé-Köster, E. (2024). Brainstem auditory evoked responses: Objective hearing threshold assessment in Holstein cows.South African Journal of Communication Disorders, 71(1), a1047. https://doi.org/10.4102/sajcd.v71i1.1047 
# Petrocchi-Bartal, L., &amp; Khoza-Shangase, K. (2014). Hearing screening procedures and protocols in use at immunisation clinics in South Africa. South African Journal of Communication Disorders, 61(1), Art. #66, 9 pages. http://dx.doi.org/10.4102/sajcd.v61i1.66
# Pillay, M., R. Tiwari, H. Kathard, and U. Chikte. 2020. “Sustainable Workforce: South African Audiologists and Speech Therapists.” Human Resources for Health 18 (1): 47. https://doi.org/10.1186/s12960-020-00488-6.
# Pillay, M., Tiwari, R., Kathard, H., &amp; Chikte, U. (2020). Sustainable workforce: South African audiologists and speech therapists. Human Resources for Health, 18, 1-13.
# Ramma, L., &amp; Sebothoma, B. (2016). The prevalence of hearing impairment within the Cape Town Metropolitan area. South African Journal of Communication Disorders 63(1), a105. http://dx.doi.org/10.4102/sajcd.v63i1.105
# Smith, J., Adams, L., &amp; Peters, B. (2020). The prevalence of hearing loss in preschool children in the Western Cape. Journal of South African Pediatrics, 32(3), 234-240. https://doi.org/10.4314/jsap.v32i3.6
# Statistics South Africa (2024) Mid-year population estimates 2024. Accessed from: https://www.statssa.gov.za/?p=17430  
# South African History online (2022) A history of Apartheid in South Africa. Accessed from: https://www.sahistory.org.za/article/history-apartheid-south-africa 
# Statistics South Africa (2017) Improving lives through data ecosystems. Accessed from: https://www.statssa.gov.za/?p=9720
# Swanepoel, D. W. 2006. Audiology in South Africa. International Journal of Audiology 45 (5): 262–266. https://doi.org/10.1080/14992020500485650.
# Van Zyl, C., Rogers, C., &amp; Kuschke, S. (2024). Outcomes and device use in children with bone-conduction hearing devices in South Africa.South African Journal of Communication Disorders,71(1), a1005. https://doi.org/10.4102/sajcd.v71i1.1005
# World Health Organization (WHO). (2021). World report on hearing. https://www.who.int/publications-detail-redirect/9789241064322


{{:Global Audiology/Authors-5|Faheema Mahomed-Asmail|Alida Naude |Anita Edwards |Katerina Ehlert |Khomotjo Kgare |https://orcid.org/0000-0002-3666-8331}}
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|journal=Wikijournal Preprints
|last=Christie
|first=David Brooks
|abstract=The 24-cell is one of only a few uniform polytopes in which the edge length equals the radius. It is the only one of the six convex regular 4-polytopes which is not the analogue of one of the five Platonic solids. It contains all the convex regular polytopes of four or fewer dimensions made of triangles or squares except the 4-simplex, but it contains no pentagons. It has just four distinct chord lengths, which are the diameters of the hypercubes of dimensions 1 through 4. The 24-cell is the unique construction of these four hypercubic chords and all the regular polytopes that can be built from them. Isoclinic rotations relate the convex regular 4-polytopes to each other, and determine the way they nest inside one another. The 24-cell's characteristic isoclinic rotation takes place in four Clifford parallel great hexagon central planes. It also inherits an isoclinic rotation in six Clifford parallel great square central planes that is characteristic of its three constituent 16-cells. We explore the internal geometry of the 24-cell in detail, as an expression of its rotational symmetries.
|w1=24-cell
}}

== The unique 24-point 24-cell polytope ==

The [[24-cell]] does not have a regular analogue in three dimensions or any other number of dimensions.{{Sfn|Coxeter|1973|p=289|loc=Epilogue|ps=; &quot;Another peculiarity of four-dimensional space is the occurrence of the 24-cell {3,4,3}, which stands quite alone, having no analogue above or below.&quot;}} It is the only one of the six convex regular 4-polytopes which is not the analogue of one of the five Platonic solids. However, it can be seen as the analogue of a pair of irregular solids: the [[W:Cuboctahedron|cuboctahedron]] and its dual the [[W:Rhombic dodecahedron|rhombic dodecahedron]].{{Sfn|Coxeter|1995|loc=(Paper 3) ''Two aspects of the regular 24-cell in four dimensions''|p=25}}

The 24-cell and the [[W:Tesseract|8-cell (tesseract)]] are the only convex regular 4-polytopes in which the edge length equals the radius. The long radius (center to vertex) of each is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including these two four-dimensional polytopes, the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron. These '''radially equilateral polytopes''' are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.

== The 24-cell in the proper sequence of 4-polytopes ==
The 24-cell incorporates the geometries of every convex regular polytope in the first four dimensions, except the 5-cell (4-simplex), those with a 5 in their Schlӓfli symbol,{{Efn|The convex regular polytopes in the first four dimensions with a 5 in their Schlӓfli symbol are the [[W:Pentagon|pentagon]] {5}, the [[W:Icosahedron|icosahedron]] {3, 5}, the [[W:Dodecahedron|dodecahedron]] {5, 3}, the [[600-cell]] {3,3,5} and the [[120-cell]] {5,3,3}. The [[5-cell]] {3, 3, 3} is also pentagonal in the sense that its [[W:Petrie polygon|Petrie polygon]] is the pentagon.|name=pentagonal polytopes|group=}} and the regular polygons with 7 or more sides. In other words, the 24-cell contains ''all'' of the regular polytopes made of triangles and squares that exist in four dimensions except the regular 5-cell, but ''none'' of the pentagonal polytopes. It is especially useful to explore the 24-cell, because one can see the geometric relationships among all of these regular polytopes in a single 24-cell or [[W:24-cell honeycomb|its honeycomb]].

The 24-cell is the fourth in the sequence of six [[W:Convex regular 4-polytope|convex regular 4-polytope]]s in order of size and complexity. These can be ordered by size as a measure of 4-dimensional content (hypervolume) for the same radius. This is their proper order of enumeration: the order in which they nest inside each other as compounds.{{Sfn|Coxeter|1973|loc=§7.8 The enumeration of possible regular figures|p=136}}{{Sfn|Goucher|2020|loc=Subsumptions of regular polytopes}} Each greater polytope in the sequence is ''rounder'' than its predecessor, enclosing more content{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii): The sixteen regular polytopes {''p,q,r''} in four dimensions|ps=; An invaluable table providing all 20 metrics of each 4-polytope in edge length units. They must be algebraically converted to compare polytopes of unit radius.}} within the same radius. The 5-cell (4-simplex) is the limit smallest (and sharpest) case, and the 120-cell is the largest (and roundest). Complexity (as measured by comparing [[24-cell#As a configuration|configuration matrices]] or simply the number of vertices) follows the same ordering. This provides an alternative numerical naming scheme for regular polytopes in which the 24-cell is the 24-point 4-polytope: fourth in the ascending sequence that runs from 5-point (5-cell) 4-polytope to 600-point (120-cell) 4-polytope.

The 24-cell can be deconstructed into 3 overlapping instances of its predecessor the [[W:Tesseract|8-cell (tesseract)]], as the 8-cell can be deconstructed into 2 instances of its predecessor the [[16-cell]].{{Sfn|Coxeter|1973|p=302|pp=|loc=Table VI (ii): 𝐈𝐈 = {3,4,3}|ps=: see Result column}} The reverse procedure to construct each of these from an instance of its predecessor preserves the radius of the predecessor, but generally produces a successor with a smaller edge length. The edge length will always be different unless predecessor and successor are ''both'' radially equilateral, i.e. their edge length is the same as their radius (so both are preserved). Since radially equilateral polytopes are rare, it seems that the only such construction (in any dimension) is from the 8-cell to the 24-cell, making the 24-cell the unique regular polytope (in any dimension) which has the same edge length as its predecessor of the same radius.

{{Regular convex 4-polytopes|wiki=W:|radius={{radic|2}}}}

== Coordinates ==
The 24-cell has two natural systems of Cartesian coordinates, which reveal distinct structure.

=== Great squares ===
The 24-cell is the [[W:Convex hull|convex hull]] of its vertices which can be described as the 24 coordinate [[W:Permutation|permutation]]s of:

&lt;math display=&quot;block&quot;&gt;(\pm1, \pm 1, 0, 0) \in \mathbb{R}^4 .&lt;/math&gt;

Those coordinates{{Sfn|Coxeter|1973|p=156|loc=§8.7. Cartesian Coordinates}} can be constructed as {{Coxeter–Dynkin diagram|node|3|node_1|3|node|4|node}}, [[W:Rectification (geometry)|rectifying]] the [[16-cell]] {{Coxeter–Dynkin diagram|node_1|3|node|3|node|4|node}} with the 8 vertices that are permutations of (±2,0,0,0). The vertex figure of a 16-cell is the [[W:Octahedron|octahedron]]; thus, cutting the vertices of the 16-cell at the midpoint of its incident edges produces 8 octahedral cells. This process{{Sfn|Coxeter|1973|p=|pp=145-146|loc=§8.1 The simple truncations of the general regular polytope}} also rectifies the tetrahedral cells of the 16-cell which become 16 octahedra, giving the 24-cell 24 octahedral cells.

In this frame of reference the 24-cell has edges of length {{sqrt|2}} and is inscribed in a [[W:3-sphere|3-sphere]] of radius {{sqrt|2}}. Remarkably, the edge length equals the circumradius, as in the [[W:Hexagon|hexagon]], or the [[W:Cuboctahedron|cuboctahedron]].

The 24 vertices form 18 great squares{{Efn|The edges of six of the squares are aligned with the grid lines of the ''{{radic|2}} radius coordinate system''. For example:
{{indent|5}}({{spaces|2}}0, −1,{{spaces|2}}1,{{spaces|2}}0){{spaces|3}}({{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}0, −1, −1,{{spaces|2}}0){{spaces|3}}({{spaces|2}}0,{{spaces|2}}1, −1,{{spaces|2}}0)&lt;br&gt;
is the square in the ''xy'' plane. The edges of the squares are not 24-cell edges, they are interior chords joining two vertices 90&lt;sup&gt;o&lt;/sup&gt; distant from each other; so the squares are merely invisible configurations of four of the 24-cell's vertices, not visible 24-cell features.|name=|group=}} (3 sets of 6 orthogonal{{Efn|Up to 6 planes can be mutually orthogonal in 4 dimensions. 3 dimensional space accommodates only 3 perpendicular axes and 3 perpendicular planes through a single point. In 4 dimensional space we may have 4 perpendicular axes and 6 perpendicular planes through a point (for the same reason that the tetrahedron has 6 edges, not 4): there are 6 ways to take 4 dimensions 2 at a time.{{Efn|name=Six orthogonal planes of the Cartesian basis}} Three such perpendicular planes (pairs of axes) meet at each vertex of the 24-cell (for the same reason that three edges meet at each vertex of the tetrahedron). Each of the 6 planes is [[W:Completely orthogonal|completely orthogonal]] to just one of the other planes: the only one with which it does not share a line (for the same reason that each edge of the tetrahedron is orthogonal to just one of the other edges: the only one with which it does not share a point). Two completely orthogonal planes are perpendicular and opposite each other, as two edges of the tetrahedron are perpendicular and opposite.|name=six orthogonal planes tetrahedral symmetry}} central squares), 3 of which intersect at each vertex. By viewing just one square at each vertex, the 24-cell can be seen as the vertices of 3 pairs of [[W:Completely orthogonal|completely orthogonal]]{{Efn|name=Six orthogonal planes of the Cartesian basis}} great squares which intersect{{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} if they are [[W:Completely orthogonal|completely orthogonal]].|name=how planes intersect}} at no vertices.{{Efn|name=three square fibrations}}

=== Great hexagons ===
The 24-cell is [[W:Self-dual|self-dual]], having the same number of vertices (24) as cells and the same number of edges (96) as faces.

If the dual of the above 24-cell of edge length {{sqrt|2}} is taken by reciprocating it about its ''inscribed'' sphere, another 24-cell is found which has edge length and circumradius 1, and its coordinates reveal more structure. In this frame of reference the 24-cell lies vertex-up, and its vertices can be given as follows:

8 vertices obtained by permuting the ''integer'' coordinates:

&lt;math display=&quot;block&quot;&gt;\left( \pm 1, 0, 0, 0 \right)&lt;/math&gt;

and 16 vertices with ''half-integer'' coordinates of the form:

&lt;math display=&quot;block&quot;&gt;\left( \pm \tfrac{1}{2}, \pm \tfrac{1}{2}, \pm \tfrac{1}{2}, \pm \tfrac{1}{2} \right)&lt;/math&gt;

all 24 of which lie at distance 1 from the origin.

[[24-cell#Quaternionic interpretation|Viewed as quaternions]],{{Efn|In [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]], a [[W:Quaternion|quaternion]] is simply a (w, x, y, z) Cartesian coordinate. [[W:William Rowan Hamilton|Hamilton]] did not see them as such when he [[W:History of quaternions|discovered the quaternions]]. [[W:Ludwig Schläfli|Schläfli]] would be the first to consider [[W:4-dimensional space|four-dimensional Euclidean space]], publishing his discovery of the regular [[W:Polyscheme|polyscheme]]s in 1852, but Hamilton would never be influenced by that work, which remained obscure into the 20th century. Hamilton found the quaternions when he realized that a fourth dimension, in some sense, would be necessary in order to model rotations in three-dimensional space.{{Sfn|Stillwell|2001|p=18-21}} Although he described a quaternion as an ''ordered four-element multiple of real numbers'', the quaternions were for him an extension of the complex numbers, not a Euclidean space of four dimensions.|name=quaternions}} these are the unit [[W:Hurwitz quaternions|Hurwitz quaternions]]. These 24 quaternions represent (in antipodal pairs) the 12 rotations of a regular tetrahedron.{{Sfn|Stillwell|2001|p=22}}

The 24-cell has unit radius and unit edge length in this coordinate system. We refer to the system as ''unit radius coordinates'' to distinguish it from others, such as the {{sqrt|2}} radius coordinates used to reveal the [[#Great squares|great squares]] above.{{Efn|The edges of the orthogonal great squares are ''not'' aligned with the grid lines of the ''unit radius coordinate system''. Six of the squares do lie in the 6 orthogonal planes of this coordinate system, but their edges are the {{sqrt|2}} ''diagonals'' of unit edge length squares of the coordinate lattice. For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}0, −1,{{spaces|2}}0,{{spaces|2}}0){{spaces|3}}({{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0,{{spaces|2}}0)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0, −1,{{spaces|2}}0)&lt;br&gt;
is the square in the ''xy'' plane. Notice that the 8 ''integer'' coordinates comprise the vertices of the 6 orthogonal squares.|name=orthogonal squares|group=}}

{{Regular convex 4-polytopes|wiki=W:|radius=1}}

The 24 vertices and 96 edges form 16 non-orthogonal great hexagons,{{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(−&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(−&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0, −1,{{spaces|2}}0)&lt;br&gt;
is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} four of which intersect{{Efn||name=how planes intersect}} at each vertex.{{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:Cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:Cubic pyramid|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} By viewing just one hexagon at each vertex, the 24-cell can be seen as the 24 vertices of 4 non-intersecting hexagonal great circles which are [[W:Clifford parallel|Clifford parallel]] to each other.{{Efn|name=four hexagonal fibrations}}

The 12 axes and 16 hexagons of the 24-cell constitute a [[W:Reye configuration|Reye configuration]], which in the language of [[W:Configuration (geometry)|configurations]] is written as 12&lt;sub&gt;4&lt;/sub&gt;16&lt;sub&gt;3&lt;/sub&gt; to indicate that each axis belongs to 4 hexagons, and each hexagon contains 3 axes.{{Sfn|Waegell|Aravind|2009|loc=§3.4 The 24-cell: points, lines and Reye's configuration|pp=4-5|ps=; In the 24-cell Reye's &quot;points&quot; and &quot;lines&quot; are axes and hexagons, respectively.}}

=== Great triangles ===
The 24 vertices form 32 equilateral great triangles, of edge length {{radic|3}} in the unit-radius 24-cell,{{Efn|These triangles' edges of length {{sqrt|3}} are the diagonals{{Efn|name=missing the nearest vertices}} of cubical cells of unit edge length found within the 24-cell, but those cubical (tesseract){{Efn|name=three 8-cells}} cells are not cells of the unit radius coordinate lattice.|name=cube diagonals}} inscribed in the 16 great hexagons.{{Efn|These triangles lie in the same planes containing the hexagons;{{Efn|name=non-orthogonal hexagons}} two triangles of edge length {{sqrt|3}} are inscribed in each hexagon.  For example, in unit radius coordinates:
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0)
{{indent|5}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}({{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|5}}(−&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;){{spaces|3}}(−&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;, −&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;,{{spaces|2}}&lt;small&gt;{{sfrac|1|2}}&lt;/small&gt;)
{{indent|17}}({{spaces|2}}0,{{spaces|2}}0, −1,{{spaces|2}}0)&lt;br&gt;
are two opposing central triangles on the ''y'' axis, with each triangle formed by the vertices in alternating rows. Unlike the hexagons, the {{sqrt|3}} triangles are not made of actual 24-cell edges, so they are invisible features of the 24-cell, like the {{sqrt|2}} squares.|name=central triangles|group=}} 

Each great triangle is a ring linking three completely disjoint{{Efn|name=completely disjoint}} great squares. The 18 great squares of the 24-cell occur as three sets of 6 orthogonal great squares,{{Efn|name=Six orthogonal planes of the Cartesian basis}} each forming a [[16-cell]].{{Efn|name=three isoclinic 16-cells}} The three 16-cells are completely disjoint (and [[#Clifford parallel polytopes|Clifford parallel]]): each has its own 8 vertices (on 4 orthogonal axes) and its own 24 edges (of length {{radic|2}}). The 18 square great circles are crossed by 16 hexagonal great circles; each hexagon has one axis (2 vertices) in each 16-cell.{{Efn|name=non-orthogonal hexagons}} The two great triangles inscribed in each great hexagon (occupying its alternate vertices, and with edges that are its {{radic|3}} chords) have one vertex in each 16-cell. Thus ''each great triangle is a ring linking the three completely disjoint 16-cells''. There are four different ways (four different ''fibrations'' of the 24-cell) in which the 8 vertices of the 16-cells correspond by being triangles of vertices {{radic|3}} apart: there are 32 distinct linking triangles. Each ''pair'' of 16-cells forms an 8-cell (tesseract).{{Efn|name=three 16-cells form three tesseracts}} Each great triangle has one {{radic|3}} edge in each tesseract, so it is also a ring linking the three tesseracts.

== Hypercubic chords ==
[[File:24-cell vertex geometry.png|thumb|Vertex geometry of the radially equilateral 24-cell, showing the 3 great circle polygons and the 4 vertex-to-vertex chord lengths.|alt=]]
The 24 vertices of the 24-cell are distributed{{Sfn|Coxeter|1973|p=298|loc=Table V: The Distribution of Vertices of Four-Dimensional Polytopes in Parallel Solid Sections (§13.1); (i) Sections of {3,4,3} (edge 2) beginning with a vertex; see column ''a''|5=}} at four different [[W:Chord (geometry)|chord]] lengths from each other: {{sqrt|1}}, {{sqrt|2}},  {{sqrt|3}} and {{sqrt|4}}. The {{sqrt|1}} chords (the 24-cell edges) are the edges of central hexagons, and the {{sqrt|3}} chords are the diagonals of central hexagons. The {{sqrt|2}} chords are the edges of central squares, and the {{sqrt|4}} chords are the diagonals of central squares.

Each vertex is joined to 8 others{{Efn|The 8 nearest neighbor vertices surround the vertex (in the curved 3-dimensional space of the 24-cell's boundary surface) the way a cube's 8 corners surround its center. (The [[W:Vertex figure|vertex figure]] of the 24-cell is a cube.)|name=8 nearest vertices}} by an edge of length 1, spanning 60° = &lt;small&gt;{{sfrac|{{pi}}|3}}&lt;/small&gt; of arc. Next nearest are 6 vertices{{Efn|The 6 second-nearest neighbor vertices surround the vertex in curved 3-dimensional space the way an octahedron's 6 corners surround its center.|name=6 second-nearest vertices}} located 90° = &lt;small&gt;{{sfrac|{{pi}}|2}}&lt;/small&gt; away, along an interior chord of length {{sqrt|2}}. Another 8 vertices lie 120° = &lt;small&gt;{{sfrac|2{{pi}}|3}}&lt;/small&gt; away, along an interior chord of length {{sqrt|3}}.{{Efn|name=nearest isoclinic vertices are {{radic|3}} away in third surrounding shell}} The opposite vertex is 180° = &lt;small&gt;{{pi}}&lt;/small&gt; away along a diameter of length 2. Finally, as the 24-cell is radially equilateral, its center is 1 edge length away from all vertices.

To visualize how the interior polytopes of the 24-cell fit together (as described [[#Constructions|below]]), keep in mind that the four chord lengths ({{sqrt|1}}, {{sqrt|2}}, {{sqrt|3}}, {{sqrt|4}}) are the long diameters of the [[W:Hypercube|hypercube]]s of dimensions 1 through 4: the long diameter of the square is {{sqrt|2}}; the long diameter of the cube is {{sqrt|3}}; and the long diameter of the tesseract is {{sqrt|4}}.{{Efn|Thus ({{sqrt|1}}, {{sqrt|2}}, {{sqrt|3}}, {{sqrt|4}}) are the vertex chord lengths of the tesseract as well as of the 24-cell. They are also the diameters of the tesseract (from short to long), though not of the 24-cell.}} Moreover, the long diameter of the octahedron is {{sqrt|2}} like the square; and the long diameter of the 24-cell itself is {{sqrt|4}} like the tesseract.

== Geodesics ==
The vertex chords of the 24-cell are arranged in [[W:Geodesic|geodesic]] [[W:great circle|great circle]] polygons.{{Efn|A geodesic great circle lies in a 2-dimensional plane which passes through the center of the polytope. Notice that in 4 dimensions this central plane does ''not'' bisect the polytope into two equal-sized parts, as it would in 3 dimensions, just as a diameter (a central line) bisects a circle but does not bisect a sphere. Another difference is that in 4 dimensions not all pairs of great circles intersect at two points, as they do in 3 dimensions; some pairs do, but some pairs of great circles are non-intersecting Clifford parallels.{{Efn|name=Clifford parallels}}}} The [[W:Geodesic distance|geodesic distance]] between two 24-cell vertices along a path of {{sqrt|1}} edges is always 1, 2, or 3, and it is 3 only for opposite vertices.{{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90&lt;sup&gt;o&lt;/sup&gt; bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60&lt;sup&gt;o&lt;/sup&gt; bend, or as a straight line with one 60&lt;sup&gt;o&lt;/sup&gt; bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}}

The {{sqrt|1}} edges occur in 16 [[#Great hexagons|hexagonal great circles]] (in planes inclined at 60 degrees to each other), 4 of which cross{{Efn|name=cuboctahedral hexagons}} at each vertex.{{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:Vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as &quot;the convex hull of the neighbouring vertices of a given vertex&quot;.{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:Cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its &quot;radius&quot; equals its edge length.{{Efn|The cube is not radially equilateral in Euclidean 3-space &lt;math&gt;\mathbb{R}^3&lt;/math&gt;, but a cubic pyramid is radially equilateral in the curved 3-space of the 24-cell's surface, the [[W:3-sphere|3-sphere]] &lt;math&gt;\mathbb{S}^3&lt;/math&gt;. In 4-space the 8 edges radiating from its apex are not actually its radii: the apex of the [[W:Cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices. But in curved 3-space the edges radiating symmetrically from the apex ''are'' radii, so the cube is radially equilateral ''in that curved 3-space'' &lt;math&gt;\mathbb{S}^3&lt;/math&gt;. In Euclidean 4-space &lt;math&gt;\mathbb{R}^4&lt;/math&gt; 24 edges radiating symmetrically from a central point make the radially equilateral 24-cell, and a symmetrical subset of 16 of those edges make the [[W:Tesseract#Radial equilateral symmetry|radially equilateral tesseract]].}}|name=24-cell vertex figure}} The 96 distinct {{sqrt|1}} edges divide the surface into 96 triangular faces and 24 octahedral cells: a 24-cell. The 16 hexagonal great circles can be divided into 4 sets of 4 non-intersecting [[W:Clifford parallel|Clifford parallel]] geodesics, such that only one hexagonal great circle in each set passes through each vertex, and the 4 hexagons in each set reach all 24 vertices.{{Efn|name=hexagonal fibrations}}

The {{sqrt|2}} chords occur in 18 [[#Great squares|square great circles]] (3 sets of 6 orthogonal planes{{Efn|name=Six orthogonal planes of the Cartesian basis}}), 3 of which cross at each vertex.{{Efn|Six {{sqrt|2}} chords converge in 3-space from the face centers of the 24-cell's cubical vertex figure{{Efn|name=full size vertex figure}} and meet at its center (the vertex), where they form 3 straight lines which cross there perpendicularly. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell, and eight {{sqrt|1}} edges converge from there, but let us ignore them now, since 7 straight lines crossing at the center is confusing to visualize all at once. Each of the six {{sqrt|2}} chords runs from this cube's center (the vertex) through a face center to the center of an adjacent (face-bonded) cube, which is another vertex of the 24-cell: not a nearest vertex (at the cube corners), but one located 90° away in a second concentric shell of six {{sqrt|2}}-distant vertices that surrounds the first shell of eight {{sqrt|1}}-distant vertices. The face-center through which the {{sqrt|2}} chord passes is the mid-point of the {{sqrt|2}} chord, so it lies inside the 24-cell.|name=|group=}} The 72 distinct {{sqrt|2}} chords do not run in the same planes as the hexagonal great circles; they do not follow the 24-cell's edges, they pass through its octagonal cell centers.{{Efn|One can cut the 24-cell through 6 vertices (in any hexagonal great circle plane), or through 4 vertices (in any square great circle plane). One can see this in the [[W:Cuboctahedron|cuboctahedron]] (the central [[W:hyperplane|hyperplane]] of the 24-cell), where there are four hexagonal great circles (along the edges) and six square great circles (across the square faces diagonally).}} The 72 {{sqrt|2}} chords are the 3 orthogonal axes of the 24 octahedral cells, joining vertices which are 2 {{radic|1}} edges apart. The 18 square great circles can be divided into 3 sets of 6 non-intersecting Clifford parallel geodesics,{{Efn|[[File:Hopf band wikipedia.png|thumb|Two [[W:Clifford parallel|Clifford parallel]] [[W:Great circle|great circle]]s on the [[W:3-sphere|3-sphere]] spanned by a twisted [[W:Annulus (mathematics)|annulus]]. They have a common center point in [[W:Rotations in 4-dimensional Euclidean space|4-dimensional Euclidean space]], and could lie in [[W:Completely orthogonal|completely orthogonal]] rotation planes.]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point.{{Sfn|Tyrrell|Semple|1971|loc=§3. Clifford's original definition of parallelism|pp=5-6}} A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the 2-sphere will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect; various sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. Perhaps the simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles.{{Efn|name=Six orthogonal planes of the Cartesian basis}} Each completely orthogonal pair is Clifford parallel. The two circles cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 3-sphere.{{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but [[W:Completely orthogonal|completely orthogonal]] to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} Because they are perpendicular and share a common center,{{Efn|In 4-space, two great circles can be perpendicular and share a common center ''which is their only point of intersection'', because there is more than one great [[W:2-sphere|2-sphere]] on the [[W:3-sphere|3-sphere]]. The dimensionally analogous structure to a [[W:Great circle|great circle]] (a great 1-sphere) is a great 2-sphere,{{Sfn|Stillwell|2001|p=24}} which is an ordinary sphere that constitutes an ''equator'' boundary dividing the 3-sphere into two equal halves, just as a great circle divides the 2-sphere. Although two Clifford parallel great circles{{Efn|name=Clifford parallels}} occupy the same 3-sphere, they lie on different great 2-spheres. The great 2-spheres are [[#Clifford parallel polytopes|Clifford parallel 3-dimensional objects]], displaced relative to each other by a fixed distance ''d'' in the fourth dimension. Their corresponding points (on their two surfaces) are ''d'' apart. The 2-spheres (by which we mean their surfaces) do not intersect at all, although they have a common center point in 4-space. The displacement ''d'' between a pair of their corresponding points is the [[#Geodesics|chord of a great circle]] which intersects both 2-spheres, so ''d'' can be represented equivalently as a linear chordal distance, or as an angular distance.|name=great 2-spheres}} the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]].|name=Clifford parallels}} such that only one square great circle in each set passes through each vertex, and the 6 squares in each set reach all 24 vertices.{{Efn|name=square fibrations}}

The {{sqrt|3}} chords occur in 32 [[#Great triangles|triangular great circles]] in 16 planes, 4 of which cross at each vertex.{{Efn|Eight {{sqrt|3}} chords converge from the corners of the 24-cell's cubical vertex figure{{Efn|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. Each of the eight {{sqrt|3}} chords runs from this cube's center to the center of a diagonally adjacent (vertex-bonded) cube,{{Efn|name=missing the nearest vertices}} which is another vertex of the 24-cell: one located 120° away in a third concentric shell of eight {{sqrt|3}}-distant vertices surrounding the second shell of six {{sqrt|2}}-distant vertices that surrounds the first shell of eight {{sqrt|1}}-distant vertices.|name=nearest isoclinic vertices are {{radic|3}} away in third surrounding shell}} The 96 distinct {{sqrt|3}} chords{{Efn|name=cube diagonals}} run vertex-to-every-other-vertex in the same planes as the hexagonal great circles.{{Efn|name=central triangles}} They are the 3 edges of the 32 great triangles inscribed in the 16 great hexagons, joining vertices which are 2 {{sqrt|1}} edges apart on a great circle.{{Efn|name=three 8-cells}}

The {{sqrt|4}} chords occur as 12 vertex-to-vertex diameters (3 sets of 4 orthogonal axes), the 24 radii around the 25th central vertex.

The sum of the squared lengths{{Efn|The sum of 1・96 + 2・72 + 3・96 + 4・12 is 576.}} of all these distinct chords of the 24-cell is 576 = 24&lt;sup&gt;2&lt;/sup&gt;.{{Efn|The sum of the squared lengths of all the distinct chords of any regular convex n-polytope of unit radius is the square of the number of vertices.{{Sfn|Copher|2019|loc=§3.2 Theorem 3.4|p=6}}}} These are all the central polygons through vertices, but in 4-space there are geodesics on the 3-sphere which do not lie in central planes at all. There are geodesic shortest paths between two 24-cell vertices that are helical rather than simply circular; they correspond to diagonal [[#Isoclinic rotations|isoclinic rotations]] rather than [[#Simple rotations|simple rotations]].{{Efn|name=isoclinic geodesic}}

The {{sqrt|1}} edges occur in 48 parallel pairs, {{sqrt|3}} apart. The {{sqrt|2}} chords occur in 36 parallel pairs, {{sqrt|2}} apart. The {{sqrt|3}} chords occur in 48 parallel pairs, {{sqrt|1}} apart.{{Efn|Each pair of parallel {{sqrt|1}} edges joins a pair of parallel {{sqrt|3}} chords to form one of 48 rectangles (inscribed in the 16 central hexagons), and each pair of parallel {{sqrt|2}} chords joins another pair of parallel {{sqrt|2}} chords to form one of the 18 central squares.|name=|group=}}

The central planes of the 24-cell can be divided into 4 orthogonal central hyperplanes (3-spaces) each forming a [[W:Cuboctahedron|cuboctahedron]]. The great hexagons are 60 degrees apart; the great squares are 90 degrees or 60 degrees apart; a great square and a great hexagon are 90 degrees ''and'' 60 degrees apart.{{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; &quot;In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)&quot;.}} Since all planes in the same hyperplane{{Efn|One way to visualize the ''n''-dimensional [[W:Hyperplane|hyperplane]]s is as the ''n''-spaces which can be defined by ''n + 1'' points. A point is the 0-space which is defined by 1 point. A line is the 1-space which is defined by 2 points which are not coincident. A plane is the 2-space which is defined by 3 points which are not colinear (any triangle). In 4-space, a 3-dimensional hyperplane is the 3-space which is defined by 4 points which are not coplanar (any tetrahedron). In 5-space, a 4-dimensional hyperplane is the 4-space which is defined by 5 points which are not cocellular (any 5-cell). These [[W:Simplex|simplex]] figures divide the hyperplane into two parts (inside and outside the figure), but in addition they divide the enclosing space into two parts (above and below the hyperplane). The ''n'' points ''bound'' a finite simplex figure (from the outside), and they ''define'' an infinite hyperplane (from the inside).{{Sfn|Coxeter|1973|loc=§7.2.|p=120|ps=: &quot;... any ''n''+1 points which do not lie in an (''n''-1)-space are the vertices of an ''n''-dimensional ''simplex''.... Thus the general simplex may alternatively be defined as a finite region of ''n''-space enclosed by ''n''+1 ''hyperplanes'' or (''n''-1)-spaces.&quot;}} These two divisions are orthogonal, so the defining simplex divides space into six regions: inside the simplex and in the hyperplane, inside the simplex but above or below the hyperplane, outside the simplex but in the hyperplane, and outside the simplex above or below the hyperplane.|name=hyperplanes|group=}} are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles ([[W:Completely orthogonal|completely orthogonal]]) or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes ''may'' be isoclinic, but often they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} Each set of similar central polygons (squares or hexagons) can be divided into 4 sets of non-intersecting Clifford parallel polygons (of 6 squares or 4 hexagons).{{Efn|Each pair of Clifford parallel polygons lies in two different hyperplanes (cuboctahedrons). The 4 Clifford parallel hexagons lie in 4 different cuboctahedrons.}} Each set of Clifford parallel great circles is a parallel [[W:Hopf fibration|fiber bundle]] which visits all 24 vertices just once.

Each great circle intersects{{Efn|name=how planes intersect}} with the other great circles to which it is not Clifford parallel at one {{sqrt|4}} diameter of the 24-cell.{{Efn|Two intersecting great squares or great hexagons share two opposing vertices, but squares or hexagons on Clifford parallel great circles share no vertices. Two intersecting great triangles share only one vertex, since they lack opposing vertices.|name=how great circle planes intersect|group=}} Great circles which are [[W:Completely orthogonal|completely orthogonal]] or otherwise Clifford parallel{{Efn|name=Clifford parallels}} do not intersect at all: they pass through disjoint sets of vertices.{{Efn|name=pairs of completely orthogonal planes}}

== Constructions ==
Triangles and squares come together uniquely in the 24-cell to generate, as interior features,{{Efn|Interior features are not considered elements of the polytope. For example, the center of a 24-cell is a noteworthy feature (as are its long radii), but these interior features do not count as elements in [[#Configuration|its configuration matrix]], which counts only elementary features (which are not interior to any other feature including the polytope itself). Interior features are not rendered in most of the diagrams and illustrations in this article (they are normally invisible). In illustrations showing interior features, we always draw interior edges as dashed lines, to distinguish them from elementary edges.|name=interior features|group=}} all of the triangle-faced and square-faced regular convex polytopes in the first four dimensions (with caveats for the [[5-cell]] and the [[600-cell]]).{{Efn|The [[600-cell]] is larger than the 24-cell, and contains the 24-cell as an interior feature.{{Sfn|Coxeter|1973|p=153|loc=8.5. Gosset's construction for {3,3,5}|ps=: &quot;In fact, the vertices of {3,3,5}, each taken 5 times, are the vertices of 25 {3,4,3}'s.&quot;}} The regular [[5-cell]] is not found in the interior of any convex regular 4-polytope except the [[120-cell]],{{Sfn|Coxeter|1973|p=304|loc=Table VI(iv) II={5,3,3}|ps=: Faceting {5,3,3}[120𝛼&lt;sub&gt;4&lt;/sub&gt;]{3,3,5} of the 120-cell reveals 120 regular 5-cells.}} though every convex 4-polytope can be [[#Characteristic orthoscheme|deconstructed into irregular 5-cells.]]|name=|group=}} Consequently, there are numerous ways to construct or deconstruct the 24-cell.

==== Reciprocal constructions from 8-cell and 16-cell ====
The 8 integer vertices (±1, 0, 0, 0) are the vertices of a regular [[16-cell]], and the 16 half-integer vertices (±{{sfrac|1|2}}, ±{{sfrac|1|2}}, ±{{sfrac|1|2}}, ±{{sfrac|1|2}}) are the vertices of its dual, the [[W:Tesseract|8-cell (tesseract)]].{{Sfn|Egan|2021|loc=animation of a rotating 24-cell|ps=: {{color|red}} half-integer vertices (tesseract), {{Font color|fg=yellow|bg=black|text=yellow}} and {{color|black}} integer vertices (16-cell).}} The tesseract gives Gosset's construction{{Sfn|Coxeter|1973|p=150|loc=Gosset}} of the 24-cell, equivalent to cutting a tesseract into 8 [[W:Cubic pyramid|cubic pyramid]]s, and then attaching them to the facets of a second tesseract. The analogous construction in 3-space gives the [[W:Rhombic dodecahedron|rhombic dodecahedron]] which, however, is not regular.{{Efn|[[File:R1-cube.gif|thumb|150px|Construction of a [[W:Rhombic dodecahedron|rhombic dodecahedron]] from a cube.]]This animation shows the construction of a [[W:Rhombic dodecahedron|rhombic dodecahedron]] from a cube, by inverting the center-to-face pyramids of a cube. Gosset's construction of a 24-cell from a tesseract is the 4-dimensional analogue of this process, inverting the center-to-cell pyramids of an 8-cell (tesseract).{{Sfn|Coxeter|1973|p=150|loc=Gosset}}|name=rhombic dodecahedron from a cube}} The 16-cell gives the reciprocal construction of the 24-cell, Cesaro's construction,{{Sfn|Coxeter|1973|p=148|loc=§8.2. Cesaro's construction for {3, 4, 3}.}} equivalent to rectifying a 16-cell (truncating its corners at the mid-edges, as described [[#Great squares|above]]). The analogous construction in 3-space gives the [[W:Cuboctahedron|cuboctahedron]] (dual of the rhombic dodecahedron) which, however, is not regular. The tesseract and the 16-cell are the only regular 4-polytopes in the 24-cell.{{Sfn|Coxeter|1973|p=302|loc=Table VI(ii) II={3,4,3}, Result column}}

We can further divide the 16 half-integer vertices into two groups: those whose coordinates contain an even number of minus (−) signs and those with an odd number. Each of these groups of 8 vertices also define a regular 16-cell. This shows that the vertices of the 24-cell can be grouped into three disjoint sets of eight with each set defining a regular 16-cell, and with the complement defining the dual tesseract.{{Sfn|Coxeter|1973|pp=149-150|loc=§8.22. see illustrations Fig. 8.2&lt;small&gt;A&lt;/small&gt; and Fig 8.2&lt;small&gt;B&lt;/small&gt;|p=|ps=}} This also shows that the symmetries of the 16-cell form a subgroup of index 3 of the symmetry group of the 24-cell.{{Efn|name=three 16-cells form three tesseracts}}

==== Diminishings ====
We can [[W:Faceting|facet]] the 24-cell by cutting{{Efn|We can cut a vertex off a polygon with a 0-dimensional cutting instrument (like the point of a knife, or the head of a zipper) by sweeping it along a 1-dimensional line, exposing a new edge. We can cut a vertex off a polyhedron with a 1-dimensional cutting edge (like a knife) by sweeping it through a 2-dimensional face plane, exposing a new face. We can cut a vertex off a polychoron (a 4-polytope) with a 2-dimensional cutting plane (like a snowplow), by sweeping it through a 3-dimensional cell volume, exposing a new cell. Notice that as within the new edge length of the polygon or the new face area of the polyhedron, every point within the new cell volume is now exposed on the surface of the polychoron.}} through interior cells bounded by vertex chords to remove vertices, exposing the [[W:Facet (geometry)|facets]] of interior 4-polytopes [[W:Inscribed figure|inscribed]] in the 24-cell. One can cut a 24-cell through any planar hexagon of 6 vertices, any planar rectangle of 4 vertices, or any triangle of 3 vertices. The great circle central planes ([[#Geodesics|above]]) are only some of those planes. Here we shall expose some of the others: the face planes{{Efn|Each cell face plane intersects with the other face planes of its kind to which it is not completely orthogonal or parallel at their characteristic vertex chord edge. Adjacent face planes of orthogonally-faced cells (such as cubes) intersect at an edge since they are not completely orthogonal.{{Efn|name=how planes intersect}} Although their dihedral angle is 90 degrees in the boundary 3-space, they lie in the same hyperplane{{Efn|name=hyperplanes}} (they are coincident rather than perpendicular in the fourth dimension); thus they intersect in a line, as non-parallel planes do in any 3-space.|name=how face planes intersect}} of interior polytopes.{{Efn|The only planes through exactly 6 vertices of the 24-cell (not counting the central vertex) are the '''16 hexagonal great circles'''. There are no planes through exactly 5 vertices. There are several kinds of planes through exactly 4 vertices: the 18 {{sqrt|2}} square great circles, the '''72 {{sqrt|1}} square (tesseract) faces''', and 144 {{sqrt|1}} by {{sqrt|2}} rectangles. The planes through exactly 3 vertices are the 96 {{sqrt|2}} equilateral triangle (16-cell) faces, and the '''96 {{sqrt|1}} equilateral triangle (24-cell) faces'''. There are an infinite number of central planes through exactly two vertices (great circle [[W:Digon|digon]]s); 16 are distinguished, as each is [[W:Completely orthogonal|completely orthogonal]] to one of the 16 hexagonal great circles. '''Only the polygons composed of 24-cell {{radic|1}} edges are visible''' in the projections and rotating animations illustrating this article; the others contain invisible interior chords.{{Efn|name=interior features}}|name=planes through vertices|group=}}

===== 8-cell =====
Starting with a complete 24-cell, remove 8 orthogonal vertices (4 opposite pairs on 4 perpendicular axes), and the 8 edges which radiate from each, by cutting through 8 cubic cells bounded by {{sqrt|1}} edges to remove 8 [[W:Cubic pyramid|cubic pyramid]]s whose [[W:Apex (geometry)|apexes]] are the vertices to be removed. This removes 4 edges from each hexagonal great circle (retaining just one opposite pair of edges), so no continuous hexagonal great circles remain. Now 3 perpendicular edges meet and form the corner of a cube at each of the 16 remaining vertices,{{Efn|The 24-cell's cubical vertex figure{{Efn|name=full size vertex figure}} has been truncated to a tetrahedral vertex figure (see [[#Relationships among interior polytopes|Kepler's drawing]]). The vertex cube has vanished, and now there are only 4 corners of the vertex figure where before there were 8. Four tesseract edges converge from the tetrahedron vertices and meet at its center, where they do not cross (since the tetrahedron does not have opposing vertices).|name=|group=}} and the 32 remaining edges divide the surface into 24 square faces and 8 cubic cells: a [[W:Tesseract|tesseract]]. There are three ways you can do this (choose a set of 8 orthogonal vertices out of 24), so there are three such tesseracts inscribed in the 24-cell.{{Efn|name=three 8-cells}} They overlap with each other, but most of their element sets are disjoint: they share some vertex count, but no edge length, face area, or cell volume.{{Efn|name=vertex-bonded octahedra}} They do share 4-content, their common core.{{Efn||name=common core|group=}}

===== 16-cell =====
Starting with a complete 24-cell, remove the 16 vertices of a tesseract (retaining the 8 vertices you removed above), by cutting through 16 tetrahedral cells bounded by {{sqrt|2}} chords to remove 16 [[W:Tetrahedral pyramid|tetrahedral pyramid]]s whose apexes are the vertices to be removed. This removes 12 great squares (retaining just one orthogonal set) and all the {{sqrt|1}} edges, exposing {{sqrt|2}} chords as the new edges. Now the remaining 6 great squares cross perpendicularly, 3 at each of 8 remaining vertices,{{Efn|The 24-cell's cubical vertex figure{{Efn|name=full size vertex figure}} has been truncated to an octahedral vertex figure. The vertex cube has vanished, and now there are only 6 corners of the vertex figure where before there were 8. The 6 {{sqrt|2}} chords which formerly converged from cube face centers now converge from octahedron vertices; but just as before, they meet at the center where 3 straight lines cross perpendicularly. The octahedron vertices are located 90° away outside the vanished cube, at the new nearest vertices; before truncation those were 24-cell vertices in the second shell of surrounding vertices.|name=|group=}} and their 24 edges divide the surface into 32 triangular faces and 16 tetrahedral cells: a [[16-cell]]. There are three ways you can do this (remove 1 of 3 sets of tesseract vertices), so there are three such 16-cells inscribed in the 24-cell.{{Efn|name=three isoclinic 16-cells}} They overlap with each other, but all of their element sets are disjoint:{{Efn|name=completely disjoint}} they do not share any vertex count, edge length,{{Efn|name=root 2 chords}} or face area, but they do share cell volume. They also share 4-content, their common core.{{Efn||name=common core|group=}}

==== Tetrahedral constructions ====
The 24-cell can be constructed radially from 96 equilateral triangles of edge length {{sqrt|1}} which meet at the center of the polytope, each contributing two radii and an edge. They form 96 {{sqrt|1}} tetrahedra (each contributing one 24-cell face), all sharing the 25th central apex vertex. These form 24 octahedral pyramids (half-16-cells) with their apexes at the center.

The 24-cell can be constructed from 96 equilateral triangles of edge length {{sqrt|2}}, where the three vertices of each triangle are  located 90° = &lt;small&gt;{{sfrac|{{pi}}|2}}&lt;/small&gt; away from each other on the 3-sphere. They form 48 {{sqrt|2}}-edge tetrahedra (the cells of the [[#16-cell|three 16-cells]]), centered at the 24 mid-edge-radii of the 24-cell.{{Efn|Each of the 72 {{sqrt|2}} chords in the 24-cell is a face diagonal in two distinct cubical cells (of different 8-cells) and an edge of four tetrahedral cells (in just one 16-cell).|name=root 2 chords}}

The 24-cell can be constructed directly from its [[#Characteristic orthoscheme|characteristic simplex]] {{Coxeter–Dynkin diagram|node|3|node|4|node|3|node}}, the [[5-cell#Irregular 5-cells|irregular 5-cell]] which is the [[W:Fundamental region|fundamental region]] of its [[W:Coxeter group|symmetry group]] [[W:F4 polytope|F&lt;sub&gt;4&lt;/sub&gt;]], by reflection of that 4-[[W:Orthoscheme|orthoscheme]] in its own cells (which are 3-orthoschemes).{{Efn|An [[W:Orthoscheme|orthoscheme]] is a [[W:chiral|chiral]] irregular [[W:Simplex|simplex]] with [[W:Right triangle|right triangle]] faces that is characteristic of some polytope if it will exactly fill that polytope with the reflections of itself in its own [[W:Facet (geometry)|facet]]s (its ''mirror walls''). Every regular polytope can be dissected radially into instances of its [[W:Orthoscheme#Characteristic simplex of the general regular polytope|characteristic orthoscheme]] surrounding its center. The characteristic orthoscheme has the shape described by the same [[W:Coxeter-Dynkin diagram|Coxeter-Dynkin diagram]] as the regular polytope without the ''generating point'' ring.|name=characteristic orthoscheme}}

==== Cubic constructions ====
The 24-cell is not only the 24-octahedral-cell, it is also the 24-cubical-cell, although the cubes are cells of the three 8-cells, not cells of the 24-cell, in which they are not volumetrically disjoint.

The 24-cell can be constructed from 24 cubes of its own edge length (three 8-cells).{{Efn|name=three 8-cells}} Each of the cubes is shared by 2 8-cells, each of the cubes' square faces is shared by 4 cubes (in 2 8-cells), each of the 96 edges is shared by 8 square faces (in 4 cubes in 2 8-cells), and each of the 96 vertices is shared by 16 edges (in 8 square faces in 4 cubes in 2 8-cells).

== Relationships among interior polytopes ==
The 24-cell, three tesseracts, and three 16-cells are deeply entwined around their common center, and intersect in a common core.{{Efn|A simple way of stating this relationship is that the common core of the {{radic|2}}-radius 4-polytopes is the unit-radius 24-cell. The common core of the 24-cell and its inscribed 8-cells and 16-cells is the unit-radius 24-cell's insphere-inscribed dual 24-cell of edge length and radius {{radic|1/2}}.{{Sfn|Coxeter|1995|p=29|loc=(Paper 3) ''Two aspects of the regular 24-cell in four dimensions''|ps=; &quot;The common content of the 4-cube and the 16-cell is a smaller {3,4,3} whose vertices are the permutations of [(±{{sfrac|1|2}}, ±{{sfrac|1|2}}, 0, 0)]&quot;.}} Rectifying any of the three 16-cells reveals this smaller 24-cell, which has a 4-content of only 1/2 (1/4 that of the unit-radius 24-cell). Its vertices lie at the centers of the 24-cell's octahedral cells, which are also the centers of the tesseracts' square faces, and are also the centers of the 16-cells' edges.{{Sfn|Coxeter|1973|p=147|loc=§8.1 The simple truncations of the general regular polytope|ps=; &quot;At a point of contact, [elements of a regular polytope and elements of its dual in which it is inscribed in some manner] lie in [[W:completely orthogonal|completely orthogonal]] subspaces of the tangent hyperplane to the sphere [of reciprocation], so their only common point is the point of contact itself....{{Efn|name=how planes intersect}} In fact, the [various] radii &lt;sub&gt;0&lt;/sub&gt;𝑹, &lt;sub&gt;1&lt;/sub&gt;𝑹, &lt;sub&gt;2&lt;/sub&gt;𝑹, ... determine the polytopes ... whose vertices are the centers of elements 𝐈𝐈&lt;sub&gt;0&lt;/sub&gt;, 𝐈𝐈&lt;sub&gt;1&lt;/sub&gt;, 𝐈𝐈&lt;sub&gt;2&lt;/sub&gt;, ... of the original polytope.&quot;}}|name=common core|group=}} The tesseracts and the 16-cells are rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other. This means that the corresponding vertices of two tesseracts or two 16-cells are {{radic|3}} (120°) apart.{{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diameters). The 8-cells are not completely disjoint (they share vertices),{{Efn|name=completely disjoint}} but each {{radic|3}} chord occurs as a cube long diameter in just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell as cube diameters.{{Efn|name=nearest isoclinic vertices are {{radic|3}} away in third surrounding shell}}|name=three 8-cells}}

The tesseracts are inscribed in the 24-cell{{Efn|The 24 vertices of the 24-cell, each used twice, are the vertices of three 16-vertex tesseracts.|name=|group=}} such that their vertices and edges are exterior elements of the 24-cell, but their square faces and cubical cells lie inside the 24-cell (they are not elements of the 24-cell). The 16-cells are inscribed in the 24-cell{{Efn|The 24 vertices of the 24-cell, each used once, are the vertices of three 8-vertex 16-cells.{{Efn|name=three basis 16-cells}}|name=|group=}} such that only their vertices are exterior elements of the 24-cell: their edges, triangular faces, and tetrahedral cells lie inside the 24-cell. The interior{{Efn|The edges of the 16-cells are not shown in any of the renderings in this article; if we wanted to show interior edges, they could be drawn as dashed lines. The edges of the inscribed tesseracts are always visible, because they are also edges of the 24-cell.}} 16-cell edges have length {{sqrt|2}}.[[File:Kepler's tetrahedron in cube.png|thumb|Kepler's drawing of tetrahedra in the cube.{{Sfn|Kepler|1619|p=181}}]]

The 16-cells are also inscribed in the tesseracts: their {{sqrt|2}} edges are the face diagonals of the tesseract, and their 8 vertices occupy every other vertex of the tesseract. Each tesseract has two 16-cells inscribed in it (occupying the opposite vertices and face diagonals), so each 16-cell is inscribed in two of the three 8-cells.{{Sfn|van Ittersum|2020|loc=§4.2|pp=73-79}}{{Efn|name=three 16-cells form three tesseracts}} This is reminiscent of the way, in 3 dimensions, two opposing regular tetrahedra can be inscribed in a cube, as discovered by Kepler.{{Sfn|Kepler|1619|p=181}} In fact it is the exact dimensional analogy (the [[W:Demihypercube|demihypercube]]s), and the 48 tetrahedral cells are inscribed in the 24 cubical cells in just that way.{{Sfn|Coxeter|1973|p=269|loc=§14.32|ps=. &quot;For instance, in the case of &lt;math&gt;\gamma_4[2\beta_4]&lt;/math&gt;....&quot;}}{{Efn|name=root 2 chords}}

The 24-cell encloses the three tesseracts within its envelope of octahedral facets, leaving 4-dimensional space in some places between its envelope and each tesseract's envelope of cubes. Each tesseract encloses two of the three 16-cells, leaving 4-dimensional space in some places between its envelope and each 16-cell's envelope of tetrahedra. Thus there are measurable{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii): The sixteen regular polytopes {''p,q,r''} in four dimensions|ps=; An invaluable table providing all 20 metrics of each 4-polytope in edge length units. They must be algebraically converted to compare polytopes of unit radius.}} 4-dimensional interstices{{Efn|The 4-dimensional content of the unit edge length tesseract is 1 (by definition). The content of the unit edge length 24-cell is 2, so half its content is inside each tesseract, and half is between their envelopes. Each 16-cell (edge length {{sqrt|2}}) encloses a content of 2/3, leaving 1/3 of an enclosing tesseract between their envelopes.|name=|group=}} between the 24-cell, 8-cell and 16-cell envelopes. The shapes filling these gaps are [[W:Hyperpyramid|4-pyramids]], alluded to above.{{Efn|Between the 24-cell envelope and the 8-cell envelope, we have the 8 cubic pyramids of Gosset's construction. Between the 8-cell envelope and the 16-cell envelope, we have 16 right [[5-cell#Irregular 5-cell|tetrahedral pyramids]], with their apexes filling the corners of the tesseract.}}

== Boundary cells ==
Despite the 4-dimensional interstices between 24-cell, 8-cell and 16-cell envelopes, their 3-dimensional volumes overlap. The different envelopes are separated in some places, and in contact in other places (where no 4-pyramid lies between them). Where they are in contact, they merge and share cell volume: they are the same 3-membrane in those places, not two separate but adjacent 3-dimensional layers.{{Efn|Because there are three overlapping tesseracts inscribed in the 24-cell,{{Efn|name=three 8-cells}} each octahedral cell lies ''on'' a cubic cell of one tesseract (in the cubic pyramid based on the cube, but not in the cube's volume), and ''in'' two cubic cells of each of the other two tesseracts (cubic cells which it spans, sharing their volume).{{Efn|name=octahedral diameters}}|name=octahedra both on and in cubes}} Because there are a total of 7 envelopes, there are places where several envelopes come together and merge volume, and also places where envelopes interpenetrate (cross from inside to outside each other).

Some interior features lie within the 3-space of the (outer) boundary envelope of the 24-cell itself: each octahedral cell is bisected by three perpendicular squares (one from each of the tesseracts), and the diagonals of those squares (which cross each other perpendicularly at the center of the octahedron) are 16-cell edges (one from each 16-cell). Each square bisects an octahedron into two square pyramids, and also bonds two adjacent cubic cells of a tesseract together as their common face.{{Efn|Consider the three perpendicular {{sqrt|2}} long diameters of the octahedral cell.{{Sfn|van Ittersum|2020|p=79}} Each of them is an edge of a different 16-cell. Two of them are the face diagonals of the square face between two cubes; each is a {{sqrt|2}} chord that connects two vertices of those 8-cell cubes across a square face, connects two vertices of two 16-cell tetrahedra (inscribed in the cubes), and connects two opposite vertices of a 24-cell octahedron (diagonally across two of the three orthogonal square central sections).{{Efn|name=root 2 chords}} The third perpendicular long diameter of the octahedron does exactly the same (by symmetry); so it also connects two vertices of a pair of cubes across their common square face: but a different pair of cubes, from one of the other tesseracts in the 24-cell.{{Efn|name=vertex-bonded octahedra}}|name=octahedral diameters}}

As we saw [[#Relationships among interior polytopes|above]], 16-cell {{sqrt|2}} tetrahedral cells are inscribed in tesseract {{sqrt|1}} cubic cells, sharing the same volume. 24-cell {{sqrt|1}} octahedral cells overlap their volume with {{sqrt|1}} cubic cells: they are bisected by a square face into two square pyramids,{{sfn|Coxeter|1973|page=150|postscript=: &quot;Thus the 24 cells of the {3, 4, 3} are dipyramids based on the 24 squares of the &lt;math&gt;\gamma_4&lt;/math&gt;. (Their centres are the mid-points of the 24 edges of the &lt;math&gt;\beta_4&lt;/math&gt;.)&quot;}} the apexes of which also lie at a vertex of a cube.{{Efn|This might appear at first to be angularly impossible, and indeed it would be in a flat space of only three dimensions. If two cubes rest face-to-face in an ordinary 3-dimensional space (e.g. on the surface of a table in an ordinary 3-dimensional room), an octahedron will fit inside them such that four of its six vertices are at the four corners of the square face between the two cubes; but then the other two octahedral vertices will not lie at a cube corner (they will fall within the volume of the two cubes, but not at a cube vertex). In four dimensions, this is no less true! The other two octahedral vertices do ''not'' lie at a corner of the adjacent face-bonded cube in the same tesseract. However, in the 24-cell there is not just one inscribed tesseract (of 8 cubes), there are three overlapping tesseracts (of 8 cubes each). The other two octahedral vertices ''do'' lie at the corner of a cube: but a cube in another (overlapping) tesseract.{{Efn|name=octahedra both on and in cubes}}}} The octahedra share volume not only with the cubes, but with the tetrahedra inscribed in them; thus the 24-cell, tesseracts, and 16-cells all share some boundary volume.{{Efn|name=octahedra both on and in cubes}}

== Radially equilateral honeycomb ==
The dual tessellation of the [[W:24-cell honeycomb|24-cell honeycomb {3,4,3,3}]] is the [[W:16-cell honeycomb|16-cell honeycomb {3,3,4,3}]]. The third regular tessellation of four dimensional space is the [[W:Tesseractic honeycomb|tesseractic honeycomb {4,3,3,4}]], whose vertices can be described by 4-integer Cartesian coordinates.{{Efn|name=quaternions}} The congruent relationships among these three tessellations can be helpful in visualizing the 24-cell, in particular the radial equilateral symmetry which it shares with the tesseract.

A honeycomb of unit edge length 24-cells may be overlaid on a honeycomb of unit edge length tesseracts such that every vertex of a tesseract (every 4-integer coordinate) is also the vertex of a 24-cell (and tesseract edges are also 24-cell edges), and every center of a 24-cell is also the center of a tesseract.{{Sfn|Coxeter|1973|p=163|ps=: Coxeter notes that [[W:Thorold Gosset|Thorold Gosset]] was apparently the first to see that the cells of the 24-cell honeycomb {3,4,3,3} are concentric with alternate cells of the tesseractic honeycomb {4,3,3,4}, and that this observation enabled Gosset's method of construction of the complete set of regular polytopes and honeycombs.}} The 24-cells are twice as large as the tesseracts by 4-dimensional content (hypervolume), so overall there are two tesseracts for every 24-cell, only half of which are inscribed in a 24-cell. If those tesseracts are colored black, and their adjacent tesseracts (with which they share a cubical facet) are colored red, a 4-dimensional checkerboard results.{{Sfn|Coxeter|1973|p=156|loc=|ps=: &quot;...the chess-board has an n-dimensional analogue.&quot;}} Of the 24 center-to-vertex radii{{Efn|It is important to visualize the radii only as invisible interior features of the 24-cell (dashed lines), since they are not edges of the honeycomb. Similarly, the center of the 24-cell is empty (not a vertex of the honeycomb).}} of each 24-cell, 16 are also the radii of a black tesseract inscribed in the 24-cell. The other 8 radii extend outside the black tesseract (through the centers of its cubical facets) to the centers of the 8 adjacent red tesseracts. Thus the 24-cell honeycomb and the tesseractic honeycomb coincide in a special way: 8 of the 24 vertices of each 24-cell do not occur at a vertex of a tesseract (they occur at the center of a tesseract instead). Each black tesseract is cut from a 24-cell by truncating it at these 8 vertices, slicing off 8 cubic pyramids (as in reversing Gosset's construction,{{Sfn|Coxeter|1973|p=150|loc=Gosset}} but instead of being removed the pyramids are simply colored red and left in place). Eight 24-cells meet at the center of each red tesseract: each one meets its opposite at that shared vertex, and the six others at a shared octahedral cell. &lt;!-- illustration needed: the red/black checkerboard of the combined 24-cell honeycomb and tesseractic honeycomb; use a vertex-first projection of the 24-cells, and outline the edges of the rhombic dodecahedra as blue lines --&gt;

The red tesseracts are filled cells (they contain a central vertex and radii); the black tesseracts are empty cells. The vertex set of this union of two honeycombs includes the vertices of all the 24-cells and tesseracts, plus the centers of the red tesseracts. Adding the 24-cell centers (which are also the black tesseract centers) to this honeycomb yields a 16-cell honeycomb, the vertex set of which includes all the vertices and centers of all the 24-cells and tesseracts. The formerly empty centers of adjacent 24-cells become the opposite vertices of a unit edge length 16-cell. 24 half-16-cells (octahedral pyramids) meet at each formerly empty center to fill each 24-cell, and their octahedral bases are the 6-vertex octahedral facets of the 24-cell (shared with an adjacent 24-cell).{{Efn|Unlike the 24-cell and the tesseract, the 16-cell is not radially equilateral; therefore 16-cells of two different sizes (unit edge length versus unit radius) occur in the unit edge length honeycomb. The twenty-four 16-cells that meet at the center of each 24-cell have unit edge length, and radius {{sfrac|{{radic|2}}|2}}. The three 16-cells inscribed in each 24-cell have edge length {{radic|2}}, and unit radius.}}

Notice the complete absence of pentagons anywhere in this union of three honeycombs. Like the 24-cell, 4-dimensional Euclidean space itself is entirely filled by a complex of all the polytopes that can be built out of regular triangles and squares (except the 5-cell), but that complex does not require (or permit) any of the pentagonal polytopes.{{Efn|name=pentagonal polytopes}}

== Rotations ==
[[File:24-cell-3CP.gif|thumb|The 24-point 24-cell contains three 8-point 16-cells (red, green, and blue),{{Sfn|Egan|2019|ps=; Double-rotating 24-cell with orthogonal red, green and blue vertices.}} double-rotated by 60 degrees with respect to each other.{{Efn|name=three isoclinic 16-cells}} Each 8-point 16-cell is a coordinate system basis frame of four perpendicular (w,x,y,z) axes.{{Efn|name=three basis 16-cells}} One octahedral cell of the 24 cells is emphasized. Each octahedral cell has two vertices of each color, delimiting an invisible perpendicular axis of the octahedron, which is a {{radic|2}} edge of the red, green, or blue 16-cell.{{Efn|name=octahedral diameters}}]]
The [[#The 24-cell in the proper sequence of 4-polytopes|regular convex 4-polytopes]] are an [[W:Group action|expression]] of their underlying [[W:Symmetry (geometry)|symmetry]] which is known as [[W:SO(4)|SO(4)]],{{Sfn|Goucher|2019|loc=Spin Groups}} the [[W:Orthogonal group|group]] of rotations{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹&lt;sub&gt;4&lt;/sub&gt;.}} about a fixed point in 4-dimensional Euclidean space.{{Efn|[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] may occur around a plane, as when adjacent cells are folded around their plane of intersection (by analogy to the way adjacent faces are folded around their line of intersection).{{Efn|Three dimensional [[W:Rotation (mathematics)#In Euclidean geometry|rotations]] occur around an axis line. [[W:Rotations in 4-dimensional Euclidean space|Four dimensional rotations]] may occur around a plane. So in three dimensions we may fold planes around a common line (as when folding a flat net of 6 squares up into a cube), and in four dimensions we may fold cells around a common plane (as when [[W:Tesseract#Geometry|folding a flat net of 8 cubes up into a tesseract]]). Folding around a square face is just folding around ''two'' of its orthogonal edges ''at the same time''; there is not enough space in three dimensions to do this, just as there is not enough space in two dimensions to fold around a line (only enough to fold around a point).|name=simple rotations|group=}} But in four dimensions there is yet another way in which rotations can occur, called a '''[[W:Rotations in 4-dimensional Euclidean space#Geometry of 4D rotations|double rotation]]'''. Double rotations are an emergent phenomenon in the fourth dimension and have no analogy in three dimensions: folding up square faces and folding up cubical cells are both examples of '''simple rotations''', the only kind that occur in fewer than four dimensions. In 3-dimensional rotations, the points in a line remain fixed during the rotation, while every other point moves. In 4-dimensional simple rotations, the points in a plane remain fixed during the rotation, while every other point moves. ''In 4-dimensional double rotations, a point remains fixed during rotation, and every other point moves'' (as in a 2-dimensional rotation!).{{Efn|There are (at least) two kinds of correct [[W:Four-dimensional space#Dimensional analogy|dimensional analogies]]: the usual kind between dimension ''n'' and dimension ''n'' + 1, and the much rarer and less obvious kind between dimension ''n'' and dimension ''n'' + 2. An example of the latter is that rotations in 4-space may take place around a single point, as do rotations in 2-space. Another is the [[W:n-sphere#Other relations|''n''-sphere rule]] that the ''surface area'' of the sphere embedded in ''n''+2 dimensions is exactly 2''π r'' times the ''volume'' enclosed by the sphere embedded in ''n'' dimensions, the most well-known examples being that the circumference of a circle is 2''π r'' times 1, and the surface area of the ordinary sphere is 2''π r'' times 2''r''. Coxeter cites{{Sfn|Coxeter|1973|p=119|loc=§7.1. Dimensional Analogy|ps=: &quot;For instance, seeing that the circumference of a circle is 2''π r'', while the surface of a sphere is 4''π r ''&lt;sup&gt;2&lt;/sup&gt;, ... it is unlikely that the use of analogy, unaided by computation, would ever lead us to the correct expression [for the hyper-surface of a hyper-sphere], 2''π'' &lt;sup&gt;2&lt;/sup&gt;''r'' &lt;sup&gt;3&lt;/sup&gt;.&quot;}} this as an instance in which dimensional analogy can fail us as a method, but it is really our failure to recognize whether a one- or two-dimensional analogy is the appropriate method.|name=two-dimensional analogy}}|name=double rotations}}

=== The 3 Cartesian bases of the 24-cell ===
There are three distinct orientations of the tesseractic honeycomb which could be made to coincide with the 24-cell [[#Radially equilateral honeycomb|honeycomb]], depending on which of the 24-cell's three disjoint sets of 8 orthogonal vertices (which set of 4 perpendicular axes, or equivalently, which inscribed basis 16-cell){{Efn|name=three basis 16-cells}} was chosen to align it, just as three tesseracts can be inscribed in the 24-cell, rotated with respect to each other.{{Efn|name=three 8-cells}} The distance from one of these orientations to another is an [[#Isoclinic rotations|isoclinic rotation]] through 60 degrees (a [[W:Rotations in 4-dimensional Euclidean space#Double rotations|double rotation]] of 60 degrees in each pair of orthogonal invariant planes, around a single fixed point).{{Efn|name=Clifford displacement}} This rotation can be seen most clearly in the hexagonal central planes, where every hexagon rotates to change which of its three diameters is aligned with a coordinate system axis.{{Efn|name=non-orthogonal hexagons|group=}}

=== Planes of rotation ===
[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes.{{Sfn|Kim|Rote|2016|p=6|loc=§5. Four-Dimensional Rotations}} Thus the general rotation in 4-space is a ''double rotation''.{{Sfn|Perez-Gracia|Thomas|2017|loc=§7. Conclusions|ps=; &quot;Rotations in three dimensions are determined by a rotation axis and the rotation angle about it, where the rotation axis is perpendicular to the plane in which points are being rotated. The situation in four dimensions is more complicated. In this case, rotations are determined by two orthogonal planes
and two angles, one for each plane. Cayley proved that a general 4D rotation can always be decomposed into two 4D rotations, each of them being determined by two equal rotation angles up to a sign change.&quot;}} There are two important special cases, called a ''simple rotation'' and an ''isoclinic rotation''.{{Efn|A [[W:Rotations in 4-dimensional Euclidean space|rotation in 4-space]] is completely characterized by choosing an invariant plane and an angle and direction (left or right) through which it rotates, and another angle and direction through which its one completely orthogonal invariant plane rotates. Two rotational displacements are identical if they have the same pair of invariant planes of rotation, through the same angles in the same directions (and hence also the same chiral pairing of directions). Thus the general rotation in 4-space is a '''double rotation''', characterized by ''two'' angles. A '''simple rotation''' is a special case in which one rotational angle is 0.{{Efn|Any double rotation (including an isoclinic rotation) can be seen as the composition of two simple rotations ''a'' and ''b'': the ''left'' double rotation as ''a'' then ''b'', and the ''right'' double rotation as ''b'' then ''a''. Simple rotations are not commutative; left and right rotations (in general) reach different destinations. The difference between a double rotation and its two composing simple rotations is that the double rotation is 4-dimensionally diagonal: each moving vertex reaches its destination ''directly'' without passing through the intermediate point touched by ''a'' then ''b'', or the other intermediate point touched by ''b'' then ''a'', by rotating on a single helical geodesic (so it is the shortest path).{{Efn|name=helical geodesic}} Conversely, any simple rotation can be seen as the composition of two ''equal-angled'' double rotations (a left isoclinic rotation and a right isoclinic rotation),{{Efn|name=one true circle}} as discovered by [[W:Arthur Cayley|Cayley]]; perhaps surprisingly, this composition ''is'' commutative, and is possible for any double rotation as well.{{Sfn|Perez-Gracia|Thomas|2017}}|name=double rotation}} An '''isoclinic rotation''' is a different special case,{{Efn|name=Clifford displacement}} similar but not identical to two simple rotations through the ''same'' angle.{{Efn|name=plane movement in rotations}}|name=identical rotations}}

==== Simple rotations ====
[[Image:24-cell.gif|thumb|A 3D projection of a 24-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|ps=; Illustration created by Jason Hise with Maya and Macromedia Fireworks.}}]]In 3 dimensions a spinning polyhedron has a single invariant central ''plane of rotation''. The plane is an [[W:Invariant set|invariant set]] because each point in the plane moves in a circle but stays within the plane. Only ''one'' of a polyhedron's central planes can be invariant during a particular rotation; the choice of invariant central plane, and the angular distance and direction it is rotated, completely specifies the rotation. Points outside the invariant plane also move in circles (unless they are on the fixed ''axis of rotation'' perpendicular to the invariant plane), but the circles do not lie within a [[#Geodesics|''central'' plane]].

When a 4-polytope is rotating with only one invariant central plane, the same kind of [[W:Rotations in 4-dimensional Euclidean space#Simple rotations|simple rotation]] is happening that occurs in 3 dimensions. One difference is that instead of a fixed axis of rotation, there is an entire fixed central plane in which the points do not move. The fixed plane is the one central plane that is [[W:Completely orthogonal|completely orthogonal]]{{Efn|name=Six orthogonal planes of the Cartesian basis}} to the invariant plane of rotation. In the 24-cell, there is a simple rotation which will take any vertex ''directly'' to any other vertex, also moving most of the other vertices but leaving at least 2 and at most 6 other vertices fixed (the vertices that the fixed central plane intersects). The vertex moves along a great circle in the invariant plane of rotation between adjacent vertices of a great hexagon, a great square or a great [[W:Digon|digon]], and the completely orthogonal fixed plane is a digon, a square or a hexagon, respectively.{{Efn|In the 24-cell each great square plane is [[W:Completely orthogonal|completely orthogonal]] to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two antipodal vertices: a great [[W:Digon|digon]] plane.|name=pairs of completely orthogonal planes}}

==== Double rotations ====
[[Image:24-cell-orig.gif|thumb|A 3D projection of a 24-cell performing a [[W:SO(4)#Geometry of 4D rotations|double rotation]].{{Sfn|Hise|2007|ps=; Illustration created by Jason Hise with Maya and Macromedia Fireworks.}}]]The points in the completely orthogonal central plane are not ''constrained'' to be fixed. It is also possible for them to be rotating in circles, as a second invariant plane, at a rate independent of the first invariant plane's rotation: a [[W:Rotations in 4-dimensional Euclidean space#Double rotations|double rotation]] in two perpendicular non-intersecting planes{{Efn|name=how planes intersect at a single point}} of rotation at once.{{Efn|name=double rotation}} In a double rotation there is no fixed plane or axis: every point moves except the center point. The angular distance rotated may be different in the two completely orthogonal central planes, but they are always both invariant: their circularly moving points remain within the plane ''as the whole plane tilts sideways'' in the completely orthogonal rotation. A rotation in 4-space always has (at least) ''two'' completely orthogonal invariant planes of rotation, although in a simple rotation the angle of rotation in one of them is 0.

Double rotations come in two [[W:Chiral|chiral]] forms: ''left'' and ''right'' rotations.{{Efn|The adjectives ''left'' and ''right'' are commonly used in two different senses, to distinguish two distinct kinds of pairing. They can refer to alternate directions: the hand on the left side of the body, versus the hand on the right side. Or they can refer to a [[W:Chiral|chiral]] pair of enantiomorphous objects: a left hand is the mirror image of a right hand (like an inside-out glove). In the case of hands the sense intended is rarely ambiguous, because of course the hand on your left side ''is'' the mirror image of the hand on your right side: a hand is either left ''or'' right in both senses. But in the case of double-rotating 4-dimensional objects, only one sense of left versus right properly applies: the enantiomorphous sense, in which the left and right rotation are inside-out mirror images of each other. There ''are'' two directions, which we may call positive and negative, in which moving vertices may be circling on their isoclines, but it would be ambiguous to label those circular directions &quot;right&quot; and &quot;left&quot;, since a rotation's direction and its chirality are independent properties: a right (or left) rotation may be circling in either the positive or negative direction. The left rotation is not rotating &quot;to the left&quot;, the right rotation is not rotating &quot;to the right&quot;, and unlike your left and right hands, double rotations do not lie on the left or right side of the 4-polytope. If double rotations must be analogized to left and right hands, they are better thought of as a pair of clasped hands, centered on the body, because of course they have a common center.|name=clasped hands}} In a double rotation each vertex moves in a spiral along two orthogonal great circles at once.{{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in their places in the plane ''as the plane moves'', rotating ''and'' tilting sideways by the angle that the ''other'' plane rotates.|name=helical geodesic}} Either the path is right-hand [[W:Screw thread#Handedness|threaded]] (like most screws and bolts), moving along the circles in the &quot;same&quot; directions, or it is left-hand threaded (like a reverse-threaded bolt), moving along the circles in what we conventionally say are &quot;opposite&quot; directions (according to the [[W:Right hand rule|right hand rule]] by which we conventionally say which way is &quot;up&quot; on each of the 4 coordinate axes).{{Sfn|Perez-Gracia|Thomas|2017|loc=§5. A useful mapping|pp=12−13}}

In double rotations of the 24-cell that take vertices to vertices, one invariant plane of rotation contains either a great hexagon, a great square, or only an axis (two vertices, a great digon). The completely orthogonal invariant plane of rotation will necessarily contain a great digon, a great square, or a great hexagon, respectively. The selection of an invariant plane of rotation, a rotational direction and angle through which to rotate it, and a rotational direction and angle through which to rotate its completely orthogonal plane, completely determines the nature of the rotational displacement. In the 24-cell there are several noteworthy kinds of double rotation permitted by these parameters.{{Sfn|Coxeter|1995|loc=(Paper 3) ''Two aspects of the regular 24-cell in four dimensions''|pp=30-32|ps=; §3. The Dodecagonal Aspect;{{Efn|name=Petrie dodecagram and Clifford hexagram}} Coxeter considers the 150°/30° double rotation of period 12 which locates 12 of the 225 distinct 24-cells inscribed in the [[120-cell]], a regular 4-polytope with 120 dodecahedral cells that is the convex hull of the compound of 25 disjoint 24-cells.}}

==== Isoclinic rotations ====
When the angles of rotation in the two completely orthogonal invariant planes are exactly the same, a [[W:Rotations in 4-dimensional Euclidean space#Special property of SO(4) among rotation groups in general|remarkably symmetric]] [[W:Geometric transformation|transformation]] occurs:{{Sfn|Perez-Gracia|Thomas|2017|loc=§2. Isoclinic rotations|pp=2−3}} all the great circle planes Clifford parallel{{Efn|name=Clifford parallels}} to the pair of invariant planes become pairs of invariant planes of rotation themselves, through that same angle, and the 4-polytope rotates [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] in many directions at once.{{Sfn|Kim|Rote|2016|loc=§6. Angles between two Planes in 4-Space|pp=7-10}} Each vertex moves an equal distance in four orthogonal directions at the same time.{{Efn|In an [[#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance|Pythagorean distance]] equal to the square root of four times the square of that distance. All vertices are displaced to a vertex at least two edge lengths away.{{Efn|name=missing the nearest vertices}} For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} ≈ 0.866 (half the {{radic|3}} chord length) in four orthogonal directions.{{Efn|{{radic|3/4}} ≈ 0.866 is the long radius of the {{radic|2}}-edge regular tetrahedron (the unit-radius 16-cell's cell). Those four tetrahedron radii are not orthogonal, and they radiate symmetrically compressed into 3 dimensions (not 4). The four orthogonal {{radic|3/4}} ≈ 0.866 displacements summing to a 120° degree displacement in the 24-cell's characteristic isoclinic rotation{{Efn|name=isoclinic 4-dimensional diagonal}} are not as easy to visualize as radii, but they can be imagined as successive orthogonal steps in a path extending in all 4 dimensions, along the orthogonal edges of a [[5-cell#Orthoschemes|4-orthoscheme]]. In an actual left (or right) isoclinic rotation the four orthogonal {{radic|3/4}} ≈ 0.866 steps of each 120° displacement are concurrent, not successive, so they ''are'' actually symmetrical radii in 4 dimensions. In fact they are four orthogonal [[#Characteristic orthoscheme|mid-edge radii of a unit-radius 24-cell]] centered at the rotating vertex. Finally, in 2 dimensional units, {{radic|3/4}} ≈ 0.866 is the area of the equilateral triangle face of the unit-edge, unit-radius 24-cell. The area of the radial equilateral triangles in a unit-radius radially equilateral polytope is {{radic|3/4}} ≈ 0.866.|name=root 3/4}}|name=isoclinic 4-dimensional diagonal}} In the 24-cell any isoclinic rotation through 60 degrees in a hexagonal plane takes each vertex to a vertex two edge lengths away, rotates ''all 16'' hexagons by 60 degrees, and takes ''every'' great circle polygon (square,{{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} hexagon or triangle) to a Clifford parallel great circle polygon of the same kind 120 degrees away. An isoclinic rotation is also called a ''Clifford displacement'', after its [[W:William Kingdon Clifford|discoverer]].{{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle in the completely orthogonal rotation.{{Efn|name=one true circle}} A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways.{{Efn|name=plane movement in rotations}} All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon 120 degrees away. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 120 degrees away.|name=Clifford displacement}}

The 24-cell in the ''double'' rotation animation appears to turn itself inside out.{{Efn|That a double rotation can turn a 4-polytope inside out is even more noticeable in the [[W:Rotations in 4-dimensional Euclidean space#Double rotations|tesseract double rotation]].}} It appears to, because it actually does, reversing the [[W:Chirality|chirality]] of the whole 4-polytope just the way your bathroom mirror reverses the chirality of your image by a 180 degree reflection. Each 360 degree isoclinic rotation is as if the 24-cell surface had been stripped off like a glove and turned inside out, making a right-hand glove into a left-hand glove (or vice versa).{{Sfn|Coxeter|1973|p=141|loc=§7.x. Historical remarks|ps=; &quot;[[W:August Ferdinand Möbius|Möbius]] realized, as early as 1827, that a four-dimensional rotation would be required to bring two enantiomorphous solids into coincidence. This idea was neatly deployed by [[W:H. G. Wells|H. G. Wells]] in ''The Plattner Story''.&quot;}}

In a simple rotation of the 24-cell in a hexagonal plane, each vertex in the plane rotates first along an edge to an adjacent vertex 60 degrees away. But in an isoclinic rotation in ''two'' completely orthogonal planes one of which is a great hexagon,{{Efn|name=pairs of completely orthogonal planes}} each vertex rotates first to a vertex ''two'' edge lengths away ({{radic|3}} and 120° distant). The double 60-degree rotation's helical geodesics pass through every other vertex, missing the vertices in between.{{Efn|In an isoclinic rotation vertices move diagonally, like the [[W:bishop (chess)|bishop]]s in [[W:Chess|chess]]. Vertices in an isoclinic rotation ''cannot'' reach their orthogonally nearest neighbor vertices{{Efn|name=8 nearest vertices}} by double-rotating directly toward them (and also orthogonally to that direction), because that double rotation takes them diagonally between their nearest vertices, missing them, to a vertex farther away in a larger-radius surrounding shell of vertices,{{Efn|name=nearest isoclinic vertices are {{radic|3}} away in third surrounding shell}} the way bishops are confined to the white or black squares of the [[W:Chessboard|chessboard]] and cannot reach squares of the opposite color, even those immediately adjacent.{{Efn|Isoclinic rotations{{Efn|name=isoclinic geodesic}} partition the 24 cells (and the 24 vertices) of the 24-cell into two disjoint subsets of 12 cells (and 12 vertices), even and odd (or black and white), which shift places among themselves, in a manner dimensionally analogous to the way the [[W:Bishop (chess)|bishops]]' diagonal moves{{Efn|name=missing the nearest vertices}} restrict them to the black or white squares of the [[W:Chessboard|chessboard]].{{Efn|Left and right isoclinic rotations partition the 24 cells (and 24 vertices) into black and white in the same way.{{Sfn|Coxeter|1973|p=156|loc=|ps=: &quot;...the chess-board has an n-dimensional analogue.&quot;}} The rotations of all fibrations of the same kind of great polygon use the same chessboard, which is a convention of the coordinate system based on even and odd coordinates. ''Left and right are not colors:'' in either a left (or right) rotation half the moving vertices are black, running along black isoclines through black vertices, and the other half are white vertices, also rotating among themselves.{{Efn|Chirality and even/odd parity are distinct flavors. Things which have even/odd coordinate parity are '''''black or white:''''' the squares of the [[W:Chessboard|chessboard]],{{Efn|Since it is difficult to color points and lines white, we sometimes use black and red instead of black and white. In particular, isocline chords are sometimes shown as black or red ''dashed'' lines.{{Efn|name=interior features}}|name=black and red}} '''cells''', '''vertices''' and the '''isoclines''' which connect them by isoclinic rotation.{{Efn|name=isoclinic geodesic}} Everything else is '''''black and white:''''' e.g. adjacent '''face-bonded cell pairs''', or '''edges''' and '''chords''' which are black at one end and white at the other. Things which have [[W:Chirality|chirality]] come in '''''right or left''''' enantiomorphous forms: '''[[#Isoclinic rotations|isoclinic rotations]]''' and '''chiral objects''' which include '''[[#Characteristic orthoscheme|characteristic orthoscheme]]s''', '''[[#Chiral symmetry operations|sets of Clifford parallel great polygon planes]]''',{{Efn|name=completely orthogonal Clifford parallels are special}} '''[[W:Fiber bundle|fiber bundle]]s''' of Clifford parallel circles (whether or not the circles themselves are chiral), and the chiral cell rings of tetrahedra found in the [[16-cell#Helical construction|16-cell]] and [[600-cell#Boerdijk–Coxeter helix rings|600-cell]]. Things which have '''''neither''''' an even/odd parity nor a chirality include all '''edges''' and '''faces''' (shared by black and white cells), '''[[#Geodesics|great circle polygons]]''' and their '''[[W:Hopf fibration|fibration]]s''', and non-chiral cell rings such as the 24-cell's [[24-cell#Cell rings|cell rings of octahedra]]. Some things are associated with '''''both''''' an even/odd parity and a chirality: '''isoclines''' are black or white because they connect vertices which are all of the same color, and they ''act'' as left or right chiral objects when they are vertex paths in a left or right rotation, although they have no inherent chirality themselves. Each left (or right) rotation traverses an equal number of black and white isoclines.{{Efn|name=Clifford polygon}}|name=left-right versus black-white}}|name=isoclinic chessboard}}|name=black and white}} Things moving diagonally move farther than 1 unit of distance in each movement step ({{radic|2}} on the chessboard, {{radic|3}} in the 24-cell), but at the cost of ''missing'' half the destinations.{{Efn|name=one true circle}} However, in an isoclinic rotation of a rigid body all the vertices rotate at once, so every destination ''will'' be reached by some vertex. Moreover, there is another isoclinic rotation in hexagon invariant planes which does take each vertex to an adjacent (nearest) vertex. A 24-cell can displace each vertex to a vertex 60° away (a nearest vertex) by rotating isoclinically by 30° in two completely orthogonal invariant planes (one of them a hexagon), ''not'' by double-rotating directly toward the nearest vertex (and also orthogonally to that direction), but instead by double-rotating directly toward a more distant vertex (and also orthogonally to that direction). This helical 30° isoclinic rotation takes the vertex 60° to its nearest-neighbor vertex by a ''different path'' than a simple 60° rotation would. The path along the helical isocline and the path along the simple great circle have the same 60° arc-length, but they consist of disjoint sets of points (except for their endpoints, the two vertices). They are both geodesic (shortest) arcs, but on two alternate kinds of geodesic circle. One is doubly curved (through all four dimensions), and one is simply curved (lying in a two-dimensional plane).|name=missing the nearest vertices}} Each {{radic|3}} chord of the helical geodesic{{Efn|Although adjacent vertices on the isoclinic geodesic are a {{radic|3}} chord apart, a point on a rigid body under rotation does not travel along a chord: it moves along an arc between the two endpoints of the chord (a longer distance). In a ''simple'' rotation between two vertices {{radic|3}} apart, the vertex moves along the arc of a hexagonal great circle to a vertex two great hexagon edges away, and passes through the intervening hexagon vertex midway. But in an ''isoclinic'' rotation between two vertices {{radic|3}} apart the vertex moves along a helical arc called an isocline (not a planar great circle),{{Efn|name=isoclinic geodesic}} which does ''not'' pass through an intervening vertex: it misses the vertex nearest to its midpoint.{{Efn|name=missing the nearest vertices}}|name=isocline misses vertex}} crosses between two Clifford parallel hexagon central planes, and lies in another hexagon central plane that intersects them both.{{Efn|Departing from any vertex V&lt;sub&gt;0&lt;/sub&gt; in the original great hexagon plane of isoclinic rotation P&lt;sub&gt;0&lt;/sub&gt;, the first vertex reached V&lt;sub&gt;1&lt;/sub&gt; is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P&lt;sub&gt;1&lt;/sub&gt;. P&lt;sub&gt;1&lt;/sub&gt; is inclined to P&lt;sub&gt;0&lt;/sub&gt; at a 60° angle.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt; lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V&lt;sub&gt;2&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;1&lt;/sub&gt; along a second {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;2&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;0&lt;/sub&gt;.{{Efn|P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''two'' {{radic|3}} chords apart,{{Efn|V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt; are ''one'' {{radic|3}} chord apart on some other isocline, and just {{radic|1}} apart on some great hexagon. Between V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;2&lt;/sub&gt;, the isoclinic rotation has gone the long way around the 24-cell over two {{radic|3}} chords to reach a vertex that was only {{radic|1}} away. More generally, isoclines are geodesics because the distance between their successive vertices is the shortest distance between those two vertices in some rotation connecting them, but on the 3-sphere there may be another rotation which is shorter. A path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}} P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V&lt;sub&gt;1&lt;/sub&gt; lies in both intersecting planes P&lt;sub&gt;1&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt;, as V&lt;sub&gt;0&lt;/sub&gt; lies in both P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;1&lt;/sub&gt;. But P&lt;sub&gt;0&lt;/sub&gt; and P&lt;sub&gt;2&lt;/sub&gt; have ''no'' vertices in common; they do not intersect.) The third vertex reached V&lt;sub&gt;3&lt;/sub&gt; is 120 degrees beyond V&lt;sub&gt;2&lt;/sub&gt; along a third {{radic|3}} chord lying in another hexagonal plane P&lt;sub&gt;3&lt;/sub&gt; that is Clifford parallel to P&lt;sub&gt;1&lt;/sub&gt;. V&lt;sub&gt;0&lt;/sub&gt; and V&lt;sub&gt;3&lt;/sub&gt; are adjacent vertices, {{radic|1}} apart.{{Efn|name=skew hexagram}} The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V&lt;sub&gt;0&lt;/sub&gt; to V&lt;sub&gt;3&lt;/sub&gt; is a 360° isoclinic rotation, and one half of the 24-cell's double-loop hexagram&lt;sub&gt;2&lt;/sub&gt; Clifford polygon.{{Efn|name=Clifford polygon}}|name=360 degree geodesic path visiting 3 hexagonal planes}} The {{radic|3}} chords meet at a 60° angle, but since they lie in different planes they form a [[W:Helix|helix]] not a [[#Great triangles|triangle]]. Three {{radic|3}} chords and 360° of rotation takes the vertex to an adjacent vertex, not back to itself. The helix of {{radic|3}} chords closes into a loop only after six {{radic|3}} chords: a 720° rotation twice around the 24-cell{{Efn|An isoclinic rotation by 60° is two simple rotations by 60° at the same time.{{Efn|The composition of two simple 60° rotations in a pair of completely orthogonal invariant planes is a 60° isoclinic rotation in ''four'' pairs of completely orthogonal invariant planes.{{Efn|name=double rotation}} Thus the isoclinic rotation is the compound of four simple rotations, and all 24 vertices rotate in invariant hexagon planes, versus just 6 vertices in a simple rotation.}} It moves all the vertices 120° at the same time, in various different directions. Six successive diagonal rotational increments, of 60°x60° each, move each vertex through 720° on a Möbius double loop called an ''isocline'', ''twice'' around the 24-cell and back to its point of origin, in the ''same time'' (six rotational units) that it would take a simple rotation to take the vertex ''once'' around the 24-cell on an ordinary great circle.{{Efn|name=double threaded}} The helical double loop 4𝝅 isocline is just another kind of ''single'' full circle, of the same time interval and period (6 chords) as the simple great circle. The isocline is ''one'' true circle,{{Efn|name=4-dimensional great circles}} as perfectly round and geodesic as the simple great circle, even through its chords are {{radic|3}} longer, its circumference is 4𝝅 instead of 2𝝅,{{Efn|All 3-sphere isoclines of the same circumference are directly congruent circles.{{Efn|name=not all isoclines are circles}} An ordinary great circle is an isocline of circumference &lt;math&gt;2\pi r&lt;/math&gt;; simple rotations of unit-radius polytopes take place on 2𝝅 isoclines. Double rotations may have isoclines of other than &lt;math&gt;2\pi r&lt;/math&gt; circumference. The ''characteristic rotation'' of a regular 4-polytope is the isoclinic rotation in which the central planes containing its edges are invariant planes of rotation. The 16-cell and 24-cell edge-rotate on isoclines of 4𝝅 circumference. The 600-cell edge-rotates on isoclines of 5𝝅 circumference.|name=isocline circumference}} it circles through four dimensions instead of two,{{Efn|name=Villarceau circles}} and it acts in two chiral forms (left and right) even though all such circles of the same circumference are directly congruent.{{Efn|name=Clifford polygon}} Nevertheless, to avoid confusion we always refer to it as an ''isocline'' and reserve the term ''great circle'' for an ordinary great circle in the plane.{{Efn|name=isocline}}|name=one true circle}} on a [[W:Skew polygon#Regular skew polygons in four dimensions|skew]] [[W:Hexagram|hexagram]] with {{radic|3}} edges.{{Efn|name=skew hexagram}} Even though all 24 vertices and all the hexagons rotate at once, a 360 degree isoclinic rotation moves each vertex only halfway around its circuit. After 360 degrees each helix has departed from 3 vertices and reached a fourth vertex adjacent to the original vertex, but has ''not'' arrived back exactly at the vertex it departed from. Each central plane (every hexagon or square in the 24-cell) has rotated 360 degrees ''and'' been tilted sideways all the way around 360 degrees back to its original position (like a coin flipping twice), but the 24-cell's [[W:Orientation entanglement|orientation]] in the 4-space in which it is embedded is now different.{{Sfn|Mebius|2015|loc=Motivation|pp=2-3|ps=; &quot;This research originated from ... the desire to construct a computer implementation of a specific motion of the human arm, known among folk dance experts as the ''Philippine wine dance'' or ''Binasuan'' and performed by physicist [[W:Richard P. Feynman|Richard P. Feynman]] during his [[W:Dirac|Dirac]] memorial lecture 1986{{Sfn|Feynman|Weinberg|1987|loc=The reason for antiparticles}} to show that a single rotation (2𝝅) is not equivalent in all respects to no rotation at all, whereas a double rotation (4𝝅) is.&quot;}} Because the 24-cell is now inside-out, if the isoclinic rotation is continued in the ''same'' direction through another 360 degrees, the 24 moving vertices will pass through the other half of the vertices that were missed on the first revolution (the 12 antipodal vertices of the 12 that were hit the first time around), and each isoclinic geodesic ''will'' arrive back at the vertex it departed from, forming a closed six-chord helical loop. It takes a 720 degree isoclinic rotation for each [[#Helical hexagrams and their isoclines|hexagram&lt;sub&gt;2&lt;/sub&gt; geodesic]] to complete a circuit through every ''second'' vertex of its six vertices by [[W:Winding number|winding]] around the 24-cell twice, returning the 24-cell to its original chiral orientation.{{Efn|In a 720° isoclinic rotation of a ''rigid'' 24-cell the 24 vertices rotate along four separate Clifford parallel hexagram&lt;sub&gt;2&lt;/sub&gt; geodesic loops (six vertices circling in each loop) and return to their original positions.{{Efn|name=Villarceau circles}}}}

The hexagonal winding path that each vertex takes as it loops twice around the 24-cell forms a double helix bent into a [[W:Möbius strip|Möbius ring]], so that the two strands of the double helix form a continuous single strand in a closed loop.{{Efn|Because the 24-cell's helical hexagram&lt;sub&gt;2&lt;/sub&gt; geodesic is bent into a twisted ring in the fourth dimension like a [[W:Möbius strip|Möbius strip]], its [[W:Screw thread|screw thread]] doubles back across itself in each revolution, reversing its chirality{{Efn|name=Clifford polygon}} but without ever changing its even/odd parity of rotation (black or white).{{Efn|name=black and white}} The 6-vertex isoclinic path forms a Möbius double loop, like a 3-dimensional double helix with the ends of its two parallel 3-vertex helices cross-connected to each other. This 60° isocline{{Efn|A strip of paper can form a [[W:Möbius strip#Polyhedral surfaces and flat foldings|flattened Möbius strip]] in the plane by folding it at &lt;math&gt;60^\circ&lt;/math&gt; angles so that its center line lies along an equilateral triangle, and attaching the ends. The shortest strip for which this is possible consists of three equilateral paper triangles, folded at the edges where two triangles meet. Since the loop traverses both sides of each paper triangle, it is a hexagonal loop over six equilateral triangles. Its [[W:Aspect ratio|aspect ratio]]{{snd}}the ratio of the strip's length{{efn|The length of a strip can be measured at its centerline, or by cutting the resulting Möbius strip perpendicularly to its boundary so that it forms a rectangle.}} to its width{{snd}}is {{nowrap|&lt;math&gt;\sqrt 3\approx 1.73&lt;/math&gt;.}}}} is a [[W:Skew polygon|skewed]] instance of the [[W:Polygram (geometry)#Regular compound polygons|regular compound polygon]] denoted {6/2}{{=}}2{3} or hexagram&lt;sub&gt;2&lt;/sub&gt;.{{Efn|name=skew hexagram}} Successive {{radic|3}} edges belong to different [[#8-cell|8-cells]], as the 720° isoclinic rotation takes each hexagon through all six hexagons in the [[#6-cell rings|6-cell ring]], and each 8-cell through all three 8-cells twice.{{Efn|name=three 8-cells}}|name=double threaded}} In the first revolution the vertex traverses one 3-chord strand of the double helix; in the second revolution it traverses the second 3-chord strand, moving in the same rotational direction with the same handedness (bending either left or right) throughout. Although this isoclinic Möbius [[#6-cell rings|ring]] is a circular spiral through all 4 dimensions, not a 2-dimensional circle, like a great circle it is a geodesic because it is the shortest path from vertex to vertex.{{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''.{{Efn||name=double rotation}} A '''[[W:Geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:Helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:Screw threads|screw threads]] either, because they form a closed loop like any circle.{{Efn|name=double threaded}} Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in ''two'' orthogonal great circles at once.{{Efn|Isoclinic geodesics or ''isoclines'' are 4-dimensional great circles in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two orthogonal great circles at once.{{Efn|name=not all isoclines are circles}} They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of great circles (great 1-spheres).{{Efn|name=great 2-spheres}} Discrete isoclines are polygons;{{Efn|name=Clifford polygon}} discrete great 2-spheres are polyhedra.|name=4-dimensional great circles}} They are true circles,{{Efn|name=one true circle}} and even form [[W:Hopf fibration|fibrations]] like ordinary 2-dimensional great circles.{{Efn|name=hexagonal fibrations}}{{Efn|name=square fibrations}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are [[W:Geodesics|geodesics]], and isoclines on the [[W:3-sphere|3-sphere]] are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.|name=not all isoclines are circles}} they always occur in pairs{{Efn|Isoclines on the 3-sphere occur in non-intersecting pairs of even/odd coordinate parity.{{Efn|name=black and white}} A single black or white isocline forms a [[W:Möbius loop|Möbius loop]] called the {1,1} torus knot or Villarceau circle{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; &quot;In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot rather than as a planar cut.&quot;}} in which each of two &quot;circles&quot; linked in a Möbius &quot;figure eight&quot; loop traverses through all four dimensions.{{Efn|name=Clifford polygon}} The double loop is a true circle in four dimensions.{{Efn|name=one true circle}} Even and odd isoclines are also linked, not in a Möbius loop but as a [[W:Hopf link|Hopf link]] of two non-intersecting circles,{{Efn|name=Clifford parallels}} as are all the Clifford parallel isoclines of a [[W:Hopf fibration|Hopf fiber bundle]].|name=Villarceau circles}} as [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]], the geodesic paths traversed by vertices in an [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] around the 3-sphere through the non-adjacent vertices{{Efn|name=missing the nearest vertices}} of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew]] '''Clifford polygon'''.{{Efn|name=Clifford polygon}}|name=isoclinic geodesic}}

=== Clifford parallel polytopes ===
Two planes are also called ''isoclinic'' if an isoclinic rotation will bring them together.{{Efn|name=two angles between central planes}} The isoclinic planes are precisely those central planes with Clifford parallel geodesic great circles.{{Sfn|Kim|Rote|2016|loc=Relations to Clifford parallelism|pp=8-9}} Clifford parallel great circles do not intersect,{{Efn|name=Clifford parallels}} so isoclinic great circle polygons have disjoint vertices. In the 24-cell every hexagonal central plane is isoclinic to three others, and every square central plane is isoclinic to five others. We can pick out 4 mutually isoclinic (Clifford parallel) great hexagons (four different ways) covering all 24 vertices of the 24-cell just once (a hexagonal fibration).{{Efn|The 24-cell has four sets of 4 non-intersecting [[W:Clifford parallel|Clifford parallel]]{{Efn|name=Clifford parallels}} great circles each passing through 6 vertices (a great hexagon), with only one great hexagon in each set passing through each vertex, and the 4 hexagons in each set reaching all 24 vertices.{{Efn|name=four hexagonal fibrations}} Each set constitutes a discrete [[W:Hopf fibration|Hopf fibration]] of interlocking great circles. The 24-cell can also be divided (eight different ways) into 4 disjoint subsets of 6 vertices (hexagrams) that do ''not'' lie in a hexagonal central plane, each skew [[#Helical hexagrams and their  isoclines|hexagram forming an isoclinic geodesic or ''isocline'']] that is the rotational circle traversed by those 6 vertices in one particular left or right [[#Isoclinic rotations|isoclinic rotation]]. Each of these sets of four Clifford parallel isoclines belongs to one of the four discrete Hopf fibrations of hexagonal great circles.{{Efn|Each set of [[W:Clifford parallel|Clifford parallel]] [[#Geodesics|great circle]] polygons is a different bundle of fibers than the corresponding set of Clifford parallel isocline{{Efn|name=isoclinic geodesic}} polygrams, but the two [[W:Fiber bundles|fiber bundles]] together constitute the ''same'' discrete [[W:Hopf fibration|Hopf fibration]], because they enumerate the 24 vertices together by their intersection in the same distinct (left or right) isoclinic rotation. They are the [[W:Warp and woof|warp and woof]] of the same woven fabric that is the fibration.|name=great circles and isoclines are same fibration|name=warp and woof}}|name=hexagonal fibrations}} We can pick out 6 mutually isoclinic (Clifford parallel) great squares{{Efn|Each great square plane is isoclinic (Clifford parallel) to five other square planes but [[W:Completely orthogonal|completely orthogonal]] to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal). There is also another way in which completely orthogonal planes are in a distinguished category of Clifford parallel planes: they are not [[W:Chiral|chiral]], or strictly speaking they possess both chiralities. A pair of isoclinic (Clifford parallel) planes is either a ''left pair'' or a ''right pair'', unless they are separated by two angles of 90° (completely orthogonal planes) or 0° (coincident planes).{{Sfn|Kim|Rote|2016|p=8|loc=Left and Right Pairs of Isoclinic Planes}} Most isoclinic planes are brought together only by a left isoclinic rotation or a right isoclinic rotation, respectively. Completely orthogonal planes are special: the pair of planes is both a left and a right pair, so either a left or a right isoclinic rotation will bring them together. This occurs because isoclinic square planes are 180° apart at all vertex pairs: not just Clifford parallel but completely orthogonal. The isoclines (chiral vertex paths){{Efn|name=isoclinic geodesic}} of 90° isoclinic rotations are special for the same reason. Left and right isoclines loop through the same set of antipodal vertices (hitting both ends of each [[16-cell#Helical construction|16-cell axis]]), instead of looping through disjoint left and right subsets of black or white antipodal vertices (hitting just one end of each axis), as the left and right isoclines of all other fibrations do.|name=completely orthogonal Clifford parallels are special}} (three different ways) covering all 24 vertices of the 24-cell just once (a square fibration).{{Efn|The 24-cell has three sets of 6 non-intersecting Clifford parallel great circles each passing through 4 vertices (a great square), with only one great square in each set passing through each vertex, and the 6 squares in each set reaching all 24 vertices.{{Efn|name=three square fibrations}} Each set constitutes a discrete [[W:Hopf fibration|Hopf fibration]] of 6 interlocking great squares, which is simply the compound of the three inscribed 16-cell's discrete Hopf fibrations of 2 interlocking great squares. The 24-cell can also be divided (six different ways) into 3 disjoint subsets of 8 vertices (octagrams) that do ''not'' lie in a square central plane, but comprise a 16-cell and lie on a skew [[#Helical octagrams and thei isoclines|octagram&lt;sub&gt;3&lt;/sub&gt; forming an isoclinic geodesic or ''isocline'']] that is the rotational cirle traversed by those 8 vertices in one particular left or right [[16-cell#Rotations|isoclinic rotation]] as they rotate positions within the 16-cell.{{Efn|name=warp and woof}}|name=square fibrations}} Every isoclinic rotation taking vertices to vertices corresponds to a discrete fibration.{{Efn|name=fibrations are distinguished only by rotations}}

Two dimensional great circle polygons are not the only polytopes in the 24-cell which are parallel in the Clifford sense.{{Sfn|Tyrrell|Semple|1971|pp=1-9|loc=§1. Introduction}} Congruent polytopes of 2, 3 or 4 dimensions can be said to be Clifford parallel in 4 dimensions if their corresponding vertices are all the same distance apart. The three 16-cells inscribed in the 24-cell are Clifford parallels. Clifford parallel polytopes are ''completely disjoint'' polytopes.{{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or linage.|name=completely disjoint}} A 60 degree isoclinic rotation in hexagonal planes takes each 16-cell to a disjoint 16-cell. Like all [[#Double rotations|double rotations]], isoclinic rotations come in two [[W:Chiral|chiral]] forms: there is a disjoint 16-cell to the ''left'' of each 16-cell, and another to its ''right''.{{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=Six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[#Great hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[#Great squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:Tesseract|hypercube (a tesseract or 8-cell)]], in [[#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells (as in [[#Reciprocal constructions from 8-cell and 16-cell|Gosset's construction of the 24-cell]]). The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[W:3-sphere|3-sphere]] symmetric: four [[#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60°  rotation is a ''diagonal'' rotation by 60° in ''two'' orthogonal great circles at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:Chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell (whose vertices are one {{radic|1}} edge away) by rotating toward it;{{Efn|name=missing the nearest vertices}} it can only reach the 16-cell ''beyond'' it (120° away). But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic  rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the &quot;left&quot; is in fact the one reached by the left isoclinic rotation, as that is the only [[#Double rotations|sense in which the two 16-cells are left or right]] of each other.){{Efn|name=clasped hands}}|name=three isoclinic 16-cells}}

All Clifford parallel 4-polytopes are related by an isoclinic rotation,{{Efn|name=Clifford displacement}} but not all isoclinic polytopes are Clifford parallels (completely disjoint).{{Efn|All isoclinic ''planes'' are Clifford parallels (completely disjoint).{{Efn|name=completely disjoint}} Three and four dimensional cocentric objects may intersect (sharing elements) but still be related by an isoclinic rotation. Polyhedra and 4-polytopes may be isoclinic and ''not'' disjoint, if all of their corresponding planes are either Clifford parallel, or cocellular (in the same hyperplane) or coincident (the same plane).}} The three 8-cells in the 24-cell are isoclinic but not Clifford parallel. Like the 16-cells, they are rotated 60 degrees isoclinically with respect to each other, but their vertices are not all disjoint (and therefore not all equidistant). Each vertex occurs in two of the three 8-cells (as each 16-cell occurs in two of the three 8-cells).{{Efn|name=three 8-cells}}

Isoclinic rotations relate the convex regular 4-polytopes to each other. An isoclinic rotation of a single 16-cell will generate{{Efn|By ''generate'' we mean simply that some vertex of the first polytope will visit each vertex of the generated polytope in the course of the rotation.}} a 24-cell. A simple rotation of a single 16-cell will not, because its vertices will not reach either of the other two 16-cells' vertices in the course of the rotation. An isoclinic rotation of the 24-cell will generate the 600-cell, and an isoclinic rotation of the 600-cell will generate the 120-cell. (Or they can all be generated directly by an isoclinic rotation of the 16-cell, generating isoclinic copies of itself.) The different convex regular 4-polytopes nest inside each other, and multiple instances of the same 4-polytope hide next to each other in the Clifford parallel spaces that comprise the 3-sphere.{{Sfn|Tyrrell|Semple|1971|loc=Clifford Parallel Spaces and Clifford Reguli|pp=20-33}} For an object of more than one dimension, the only way to reach these parallel subspaces directly is by isoclinic rotation. Like a key operating a four-dimensional lock, an object must twist in two completely perpendicular tumbler cylinders at once in order to move the short distance between Clifford parallel subspaces.

=== Rings ===
In the 24-cell there are sets of rings of six different kinds, described separately in detail in other sections of [[24-cell|this article]]. This section describes how the different kinds of rings are [[#Relationships among interior polytopes|intertwined]].

The 24-cell contains four kinds of [[#Geodesics|geodesic fibers]] (polygonal rings running through vertices): [[#Great squares|great circle squares]] and their [[16-cell#Helical construction|isoclinic helix octagrams]],{{Efn|name=square fibrations}} and [[#Great hexagons|great circle hexagons]] and their [[#Isoclinic rotations|isoclinic helix hexagrams]].{{Efn|name=hexagonal fibrations}} It also contains two kinds of [[24-cell#Cell rings|cell rings]] (chains of octahedra bent into a ring in the fourth dimension): four octahedra connected vertex-to-vertex and bent into a square, and six octahedra connected face-to-face and bent into a hexagon.{{Sfn|Coxeter|1970|loc=§8. The simplex, cube, cross-polytope and 24-cell|p=18|ps=; Coxeter studied cell rings in the general case of their geometry and [[W:Group theory|group theory]], identifying each cell ring as a [[W:Polytope|polytope]] in its own right which fills a three-dimensional manifold (such as the [[W:3-sphere|3-sphere]]) with its corresponding [[W:Honeycomb (geometry)|honeycomb]]. He found that cell rings follow [[W:Petrie polygon|Petrie polygon]]s{{Efn|name=Petrie dodecagram and Clifford hexagram}} and some (but not all) cell rings and their honeycombs are ''twisted'', occurring in left- and right-handed [[chiral]] forms. Specifically, he found that since the 24-cell's octahedral cells have opposing faces, the cell rings in the 24-cell are of the non-chiral (directly congruent) kind.{{Efn|name=6-cell ring is not chiral}} Each of the 24-cell's cell rings has its corresponding honeycomb in Euclidean (rather than hyperbolic) space, so the 24-cell tiles 4-dimensional Euclidean space by translation to form the [[W:24-cell honeycomb|24-cell honeycomb]].}}{{Sfn|Banchoff|2013|ps=, studied the decomposition of regular 4-polytopes into honeycombs of tori tiling the [[W:Clifford torus|Clifford torus]], showed how the honeycombs correspond to [[W:Hopf fibration|Hopf fibration]]s, and made a particular study of the [[#6-cell rings|24-cell's 4 rings of 6 octahedral cells]] with illustrations.}}

==== 4-cell rings ====
Four unit-edge-length octahedra can be connected vertex-to-vertex along a common axis of length 4{{radic|2}}. The axis can then be bent into a square of edge length {{radic|2}}. Although it is possible to do this in a space of only three dimensions, that is not how it occurs in the 24-cell. Although the {{radic|2}} axes of the four octahedra occupy the same plane, forming one of the 18 {{radic|2}} great squares of the 24-cell, each octahedron occupies a different 3-dimensional hyperplane,{{Efn|Just as each face of a [[W:Polyhedron|polyhedron]] occupies a different (2-dimensional) face plane, each cell of a [[W:Polychoron|polychoron]] occupies a different (3-dimensional) cell [[W:Hyperplane|hyperplane]].{{Efn|name=hyperplanes}}}} and all four dimensions are utilized. The 24-cell can be partitioned into 6 such 4-cell rings (three different ways), mutually interlinked like adjacent links in a chain (but these [[W:Link (knot theory)|links]] all have a common center). An [[#Isoclinic rotations|isoclinic rotation]] in a great square plane by a multiple of 90° takes each octahedron in the ring to an octahedron in the ring.

==== 6-cell rings ====
[[File:Six face-bonded octahedra.jpg|thumb|400px|A 4-dimensional ring of 6 face-bonded octahedra, bounded by two intersecting sets of three Clifford parallel great hexagons of different colors, cut and laid out flat in 3 dimensional space.{{Efn|name=6-cell ring}}]]Six regular octahedra can be connected face-to-face along a common axis that passes through their centers of volume, forming a stack or column with only triangular faces. In a space of four dimensions, the axis can then be bent 60° in the fourth dimension at each of the six octahedron centers, in a plane orthogonal to all three orthogonal central planes of each octahedron, such that the top and bottom triangular faces of the column become coincident. The column becomes a ring around a hexagonal axis. The 24-cell can be partitioned into 4 such rings (four different ways), mutually interlinked. Because the hexagonal axis joins cell centers (not vertices), it is not a great hexagon of the 24-cell.{{Efn|The axial hexagon of the 6-octahedron ring does not intersect any vertices or edges of the 24-cell, but it does hit faces. In a unit-edge-length 24-cell, it has edges of length 1/2.{{Efn|When unit-edge octahedra are placed face-to-face the distance between their centers of volume is {{radic|2/3}} ≈ 0.816.{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(i): Octahedron}} When 24 face-bonded octahedra are bent into a 24-cell lying on the 3-sphere, the centers of the octahedra are closer together in 4-space. Within the curved 3-dimensional surface space filled by the 24 cells, the cell centers are still {{radic|2/3}} apart along the curved geodesics that join them. But on the straight chords that join them, which dip inside the 3-sphere, they are only 1/2 edge length apart.}} Because it joins six cell centers, the axial hexagon is a great hexagon of the smaller dual 24-cell that is formed by joining the 24 cell centers.{{Efn|name=common core}}}} However, six great hexagons can be found in the ring of six octahedra, running along the edges of the octahedra. In the column of six octahedra (before it is bent into a ring) there are six spiral paths along edges running up the column: three parallel helices spiraling clockwise, and three parallel helices spiraling counterclockwise. Each clockwise helix intersects each counterclockwise helix at two vertices three edge lengths apart. Bending the column into a ring changes these helices into great circle hexagons.{{Efn|There is a choice of planes in which to fold the column into a ring, but they are equivalent in that they produce congruent rings. Whichever folding planes are chosen, each of the six helices joins its own two ends and forms a simple great circle hexagon. These hexagons are ''not'' helices: they lie on ordinary flat great circles. Three of them are Clifford parallel{{Efn|name=Clifford parallels}} and belong to one [[#Great hexagons|hexagonal]] fibration. They intersect the other three, which belong to another hexagonal fibration. The three parallel great circles of each fibration spiral around each other in the sense that they form a [[W:Link (knot theory)|link]] of three ordinary circles, but they are not twisted: the 6-cell ring has no [[W:Torsion of a curve|torsion]], either clockwise or counterclockwise.{{Efn|name=6-cell ring is not chiral}}|name=6-cell ring}} The ring has two sets of three great hexagons, each on three Clifford parallel great circles.{{Efn|The three great hexagons are Clifford parallel, which is different than ordinary parallelism.{{Efn|name=Clifford parallels}} Clifford parallel great hexagons pass through each other like adjacent links of a chain, forming a [[W:Hopf link|Hopf link]]. Unlike links in a 3-dimensional chain, they share the same center point. In the 24-cell, Clifford parallel great hexagons occur in sets of four, not three. The fourth parallel hexagon lies completely outside the 6-cell ring; its 6 vertices are completely disjoint from the ring's 18 vertices.}} The great hexagons in each parallel set of three do not intersect, but each intersects the other three great hexagons (to which it is not Clifford parallel) at two antipodal vertices.

A [[#Simple rotations|simple rotation]] in any of the great hexagon planes by a multiple of 60° rotates only that hexagon invariantly, taking each vertex in that hexagon to a vertex in the same hexagon. An [[#Isoclinic rotations|isoclinic rotation]] by 60° in any of the six great hexagon planes rotates all three Clifford parallel great hexagons invariantly, and takes each octahedron in the ring to a ''non-adjacent'' octahedron in the ring.{{Efn|An isoclinic rotation by a multiple of 60° takes even-numbered octahedra in the ring to even-numbered octahedra, and odd-numbered octahedra to odd-numbered octahedra.{{Efn|In the column of 6 octahedral cells, we number the cells 0-5 going up the column. We also label each vertex with an integer 0-5 based on how many edge lengths it is up the column.}} It is impossible for an even-numbered octahedron to reach an odd-numbered octahedron, or vice versa, by a left or a right isoclinic rotation alone.{{Efn|name=black and white}}|name=black and white octahedra}}

Each isoclinically displaced octahedron is also rotated itself. After a 360° isoclinic rotation each octahedron is back in the same position, but in a different orientation. In a 720° isoclinic rotation, its vertices are returned to their original [[W:Orientation entanglement|orientation]].

Four Clifford parallel great hexagons comprise a discrete fiber bundle covering all 24 vertices in a [[W:Hopf fibration|Hopf fibration]]. The 24-cell has four such [[#Great hexagons|discrete hexagonal fibrations]] &lt;math&gt;F_a, F_b, F_c, F_d&lt;/math&gt;. Each great hexagon belongs to just one fibration, and the four fibrations are defined by disjoint sets of four great hexagons each.{{Sfn|Kim|Rote|2016|loc=§8.3 Properties of the Hopf Fibration|pp=14-16|ps=; Corollary 9. Every great circle belongs to a unique right [(and left)] Hopf bundle.}} Each fibration is the domain (container) of a unique left-right pair of isoclinic rotations (left and right Hopf fiber bundles).{{Efn|The choice of a partitioning of a regular 4-polytope into cell rings (a fibration) is arbitrary, because all of its cells are identical. No particular fibration is distinguished, ''unless'' the 4-polytope is rotating. Each fibration corresponds to a left-right pair of isoclinic rotations in a particular set of Clifford parallel invariant central planes of rotation. In the 24-cell, distinguishing a hexagonal fibration{{Efn|name=hexagonal fibrations}} means choosing a cell-disjoint set of four 6-cell rings that is the unique container of a left-right pair of isoclinic rotations in four Clifford parallel hexagonal invariant planes. The left and right rotations take place in chiral subspaces of that container,{{Sfn|Kim|Rote|2016|p=12|loc=§8 The Construction of Hopf Fibrations; 3}} but the fibration and the octahedral cell rings themselves are not chiral objects.{{Efn|name=6-cell ring is not chiral}}|name=fibrations are distinguished only by rotations}}

Four cell-disjoint 6-cell rings also comprise each discrete fibration defined by four Clifford parallel great hexagons. Each 6-cell ring contains only 18 of the 24 vertices, and only 6 of the 16 great hexagons, which we see illustrated above running along the cell ring's edges: 3 spiraling clockwise and 3 counterclockwise. Those 6 hexagons running along the cell ring's edges are not among the set of four parallel hexagons which define the fibration. For example, one of the four 6-cell rings in fibration &lt;math&gt;F_a&lt;/math&gt; contains 3 parallel hexagons running clockwise along the cell ring's edges from fibration &lt;math&gt;F_b&lt;/math&gt;, and 3 parallel hexagons running counterclockwise along the cell ring's edges from fibration &lt;math&gt;F_c&lt;/math&gt;, but that cell ring contains no great hexagons from fibration &lt;math&gt;F_a&lt;/math&gt; or fibration &lt;math&gt;F_d&lt;/math&gt;.

The 24-cell contains 16 great hexagons, divided into four disjoint sets of four hexagons, each disjoint set uniquely defining a fibration. Each fibration is also a distinct set of four cell-disjoint 6-cell rings. The 24-cell has exactly 16 distinct 6-cell rings. Each 6-cell ring belongs to just one of the four fibrations.{{Efn|The dual polytope of the 24-cell is another 24-cell. It can be constructed by placing vertices at the 24 cell centers. Each 6-cell ring corresponds to a great hexagon in the dual 24-cell, so there are 16 distinct 6-cell rings, as there are 16 distinct great hexagons, each belonging to just one fibration.}}

==== Helical hexagrams and their isoclines ====
Another kind of geodesic fiber, the [[#Isoclinic rotations|helical hexagram isoclines]], can be found within a 6-cell ring of octahedra. Each of these geodesics runs through every ''second'' vertex of a skew [[W:Hexagram|hexagram]]&lt;sub&gt;2&lt;/sub&gt;, which in the unit-radius, unit-edge-length 24-cell has six {{radic|3}} edges. The hexagram does not lie in a single central plane, but is composed of six linked {{radic|3}} chords from the six different hexagon great circles in the 6-cell ring. The isocline geodesic fiber is the path of an isoclinic rotation,{{Efn|name=isoclinic geodesic}} a helical rather than simply circular path around the 24-cell which links vertices two edge lengths apart and consequently must wrap twice around the 24-cell before completing its six-vertex loop.{{Efn|The chord-path of an isocline (the geodesic along which a vertex moves under isoclinic rotation) may be called the 4-polytope's '''Clifford polygon''', as it is the skew polygonal shape of the rotational circles traversed by the 4-polytope's vertices in its characteristic [[W:Clifford displacement|Clifford displacement]].{{Sfn|Tyrrell|Semple|1971|loc=Linear Systems of Clifford Parallels|pp=34-57}} The isocline is a helical Möbius double loop which reverses its chirality twice in the course of a full double circuit. The double loop is entirely contained within a single [[24-cell#Cell rings|cell ring]], where it follows chords connecting even (odd) vertices: typically opposite vertices of adjacent cells, two edge lengths apart.{{Efn|name=black and white}} Both &quot;halves&quot; of the double loop pass through each cell in the cell ring, but intersect only two even (odd) vertices in each even (odd) cell. Each pair of intersected vertices in an even (odd) cell lie opposite each other on the [[W:Möbius strip|Möbius strip]], exactly one edge length apart. Thus each cell has both helices passing through it, which are Clifford parallels{{Efn|name=Clifford parallels}} of opposite chirality at each pair of parallel points. Globally these two helices are a single connected circle of ''both'' chiralities, with no net [[W:Torsion of a curve|torsion]]. An isocline acts as a left (or right) isocline when traversed by a left (or right) rotation (of different fibrations).{{Efn|name=one true circle}}|name=Clifford polygon}} Rather than a flat hexagon, it forms a [[W:Skew polygon|skew]] hexagram out of two three-sided 360 degree half-loops: open triangles joined end-to-end to each other in a six-sided Möbius loop.{{Efn|name=double threaded}}

Each 6-cell ring contains six such hexagram isoclines, three black and three white, that connect even and odd vertices respectively.{{Efn|Only one kind of 6-cell ring exists, not two different chiral kinds (right-handed and left-handed), because octahedra have opposing faces and form untwisted cell rings. In addition to two sets of three Clifford parallel{{Efn|name=Clifford parallels}} [[#Great hexagons|great hexagons]], three black and three white [[#Isoclinic rotations|isoclinic hexagram geodesics]] run through the [[#6-cell rings|6-cell ring]].{{Efn|name=hexagonal fibrations}} Each of these chiral skew [[W:Hexagram|hexagram]]s lies on a different kind of circle called an ''isocline'',{{Efn|name=not all isoclines are circles}} a helical circle [[W:Winding number|winding]] through all four dimensions instead of lying in a single plane.{{Efn|name=isoclinic geodesic}} These helical great circles occur in Clifford parallel [[W:Hopf fibration|fiber bundles]] just as ordinary planar great circles do. In the 6-cell ring, black and white hexagrams pass through even and odd vertices respectively, and miss the vertices in between, so the isoclines are disjoint.{{Efn|name=black and white}}|name=6-cell ring is not chiral}} Each of the three black-white pairs of isoclines belongs to one of the three fibrations in which the 6-cell ring occurs. Each fibration's right (or left) rotation traverses two black isoclines and two white isoclines in parallel, rotating all 24 vertices.{{Efn|name=missing the nearest vertices}}

Beginning at any vertex at one end of the column of six octahedra, we can follow an isoclinic path of {{radic|3}} chords of an isocline from octahedron to octahedron. In the 24-cell the {{radic|1}} edges are [[#Great hexagons|great hexagon]] edges (and octahedron edges); in the column of six octahedra we see six great hexagons running along the octahedra's edges. The {{radic|3}} chords are great hexagon diagonals, joining great hexagon vertices two {{radic|1}} edges apart. We find them in the ring of six octahedra running from a vertex in one octahedron to a vertex in the next octahedron, passing through the face shared by the two octahedra (but not touching any of the face's 3 vertices). Each {{radic|3}} chord is a chord of just one great hexagon (an edge of a [[#Great triangles|great triangle]] inscribed in that great hexagon), but successive {{radic|3}} chords belong to different great hexagons.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} At each vertex the isoclinic path of {{radic|3}} chords bends 60 degrees in two central planes{{Efn|Two central planes in which the path bends 60° at the vertex are (a) the great hexagon plane that the chord ''before'' the vertex belongs to, and (b) the great hexagon plane that the chord ''after'' the vertex belongs to. Plane (b) contains the 120° isocline chord joining the original vertex to a vertex in great hexagon plane (c), Clifford parallel to (a); the vertex moves over this chord to this next vertex. The angle of inclination between the Clifford parallel (isoclinic) great hexagon planes (a) and (c) is also 60°. In this 60° interval of the isoclinic rotation, great hexagon plane (a) rotates 60° within itself ''and'' tilts 60° in an orthogonal plane (not plane (b)) to become great hexagon plane (c). The three great hexagon planes (a), (b) and (c) are not orthogonal (they are inclined at 60° to each other), but (a) and (b) are two central hexagons in the same cuboctahedron, and (b) and (c) likewise in an orthogonal cuboctahedron.{{Efn|name=cuboctahedral hexagons}}}} at once: 60 degrees around the great hexagon that the chord before the vertex belongs to, and 60 degrees into the plane of a different great hexagon entirely, that the chord after the vertex belongs to.{{Efn|At each vertex there is only one adjacent great hexagon plane that the isocline can bend 60 degrees into: the isoclinic path is ''deterministic'' in the sense that it is linear, not branching, because each vertex in the cell ring is a place where just two of the six great hexagons contained in the cell ring cross. If each great hexagon is given edges and chords of a particular color (as in the 6-cell ring illustration), we can name each great hexagon by its color, and each kind of vertex by a hyphenated two-color name. The cell ring contains 18 vertices named by the 9 unique two-color combinations; each vertex and its antipodal vertex have the same two colors in their name, since when two great hexagons intersect they do so at antipodal vertices. Each isoclinic skew hexagram{{Efn|Each half of a skew hexagram is an open triangle of three {{radic|3}} chords, the two open ends of which are one {{radic|1}} edge length apart. The two halves, like the whole isocline, have no inherent chirality but the same parity-color (black or white). The halves are the two opposite &quot;edges&quot; of a [[W:Möbius strip|Möbius strip]] that is {{radic|1}} wide; it actually has only one edge, which is a single continuous circle with 6 chords.|name=skew hexagram}} contains one {{radic|3}} chord of each color, and visits 6 of the 9 different color-pairs of vertex.{{Efn|Each vertex of the 6-cell ring is intersected by two skew hexagrams of the same parity (black or white) belonging to different fibrations.{{Efn|name=6-cell ring is not chiral}}|name=hexagrams hitting vertex of 6-cell ring}} Each 6-cell ring contains six such isoclinic skew hexagrams, three black and three white.{{Efn|name=hexagrams missing vertex of 6-cell ring}}|name=Möbius double loop hexagram}} Thus the path follows one great hexagon from each octahedron to the next, but switches to another of the six great hexagons in the next link of the hexagram&lt;sub&gt;2&lt;/sub&gt; path. Followed along the column of six octahedra (and &quot;around the end&quot; where the column is bent into a ring) the path may at first appear to be zig-zagging between three adjacent parallel hexagonal central planes (like a [[W:Petrie polygon|Petrie polygon]]), but it is not: any isoclinic path we can pick out always zig-zags between ''two sets'' of three adjacent parallel hexagonal central planes, intersecting only every even (or odd) vertex and never changing its inherent even/odd parity, as it visits all six of the great hexagons in the 6-cell ring in rotation.{{Efn|The 24-cell's [[W:Petrie polygon#The Petrie polygon of regular polychora (4-polytopes)|Petrie polygon]] is a skew [[W:Skew polygon#Regular skew polygons in four dimensions|dodecagon]] {12} and also (orthogonally) a skew [[W:Dodecagram|dodecagram]] {12/5} which zig-zags 90° left and right like the edges dividing the black and white squares on the [[W:Chessboard|chessboard]].{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii); 24-cell ''h&lt;sub&gt;1&lt;/sub&gt; is {12}, h&lt;sub&gt;2&lt;/sub&gt; is {12/5}''}} In contrast, the skew hexagram&lt;sub&gt;2&lt;/sub&gt; isocline does not zig-zag, and stays on one side or the other of the dividing line between black and white, like the [[W:Bishop (chess)|bishop]]s' paths along the diagonals of either the black or white squares of the chessboard.{{Efn|name=missing the nearest vertices}} The Petrie dodecagon is a circular helix of {{radic|1}} edges that zig-zag 90° left and right along 12 edges of 6 different octahedra (with 3 consecutive edges in each octahedron) in a 360° rotation. In contrast, the isoclinic hexagram&lt;sub&gt;2&lt;/sub&gt; has {{radic|3}} edges which all bend either left or right at every ''second'' vertex along a geodesic spiral of ''both'' chiralities (left and right){{Efn|name=Clifford polygon}} but only one color (black or white),{{Efn|name=black and white}} visiting one vertex of each of those same 6 octahedra in a 720° rotation.|name=Petrie dodecagram and Clifford hexagram}} When it has traversed one chord from each of the six great hexagons, after 720 degrees of isoclinic rotation (either left or right), it closes its skew hexagram and begins to repeat itself, circling again through the black (or white) vertices and cells.

At each vertex, there are four great hexagons{{Efn|Each pair of adjacent edges of a great hexagon has just one isocline curving alongside it,{{Efn|Each vertex of a 6-cell ring is missed by the two halves of the same Möbius double loop hexagram,{{Efn|name=Möbius double loop hexagram}} which curve past it on either side.|name=hexagrams missing vertex of 6-cell ring}} missing the vertex between the two edges (but not the way the {{radic|3}} edge of the great triangle inscribed in the great hexagon misses the vertex,{{Efn|The {{radic|3}} chord passes through the mid-edge of one of the 24-cell's {{radic|1}} radii. Since the 24-cell can be constructed, with its long radii, from {{radic|1}} triangles which meet at its center, this is a mid-edge of one of the six {{radic|1}} triangles in a great hexagon, as seen in the [[#Hypercubic chords|chord diagram]].|name=root 3 chord hits a mid-radius}} because the isocline is an arc on the surface not a chord). If we number the vertices around the hexagon 0-5, the hexagon has three pairs of adjacent edges connecting even vertices (one inscribed great triangle), and three pairs connecting odd vertices (the other inscribed great triangle). Even and odd pairs of edges have the arc of a black and a white isocline respectively curving alongside.{{Efn|name=black and white}} The three black and three white isoclines belong to the same 6-cell ring of the same fibration.{{Efn|name=Möbius double loop hexagram}}|name=isoclines at hexagons}} and four hexagram isoclines (all black or all white) that cross at the vertex.{{Efn|Each hexagram isocline hits only one end of an axis, unlike a great circle which hits both ends. Clifford parallel pairs of black and white isoclines from the same left-right pair of isoclinic rotations (the same fibration) do not intersect, but they hit opposite (antipodal) vertices of ''one'' of the 24-cell's 12 axes.|name=hexagram isoclines at an axis}} Four hexagram isoclines (two black and two white) comprise a unique (left or right) fiber bundle of isoclines covering all 24 vertices in each distinct (left or right) isoclinic rotation. Each fibration has a unique left and right isoclinic rotation, and corresponding unique left and right fiber bundles of isoclines.{{Efn|The isoclines themselves are not left or right, only the bundles are. Each isocline is left ''and'' right.{{Efn|name=Clifford polygon}}}} There are 16 distinct hexagram isoclines in the 24-cell (8 black and 8 white).{{Efn|The 12 black-white pairs of hexagram isoclines in each fibration{{Efn|name=hexagram isoclines at an axis}} and the 16 distinct hexagram isoclines in the 24-cell form a [[W:Reye configuration|Reye configuration]] 12&lt;sub&gt;4&lt;/sub&gt;16&lt;sub&gt;3&lt;/sub&gt;, just the way the 24-cell's 12 axes and [[#Great hexagons|16 hexagons]] do. Each of the 12 black-white pairs occurs in one cell ring of each fibration of 4 hexagram isoclines, and each cell ring contains 3 black-white pairs of the 16 hexagram isoclines.|name=a right (left) isoclinic rotation is a Reye configuration}} Each isocline is a skew ''Clifford polygon'' of no inherent chirality, but acts as a left (or right) isocline when traversed by a left (or right) rotation in different fibrations.{{Efn|name=Clifford polygon}}

==== Helical octagrams and their isoclines ====
The 24-cell contains 18 helical [[W:Octagram|octagram]] isoclines (9 black and 9 white). Three pairs of octagram edge-helices are found in each of the three inscribed 16-cells, described elsewhere as the [[16-cell#Helical construction|helical construction of the 16-cell]]. In summary, each 16-cell can be decomposed (three different ways) into a left-right pair of 8-cell rings of {{radic|2}}-edged tetrahedral cells. Each 8-cell ring twists either left or right around an axial octagram helix of eight chords. In each 16-cell there are exactly 6 distinct helices, identical octagrams which each circle through all eight vertices. Each acts as either a left helix or a right helix or a Petrie polygon in each of the six distinct isoclinic rotations (three left and three right), and has no inherent chirality except in respect to a particular rotation. Adjacent vertices on the octagram isoclines are {{radic|2}} = 90° apart, so the circumference of the isocline is 4𝝅. An ''isoclinic'' rotation by 90° in great square invariant planes takes each vertex to its antipodal vertex, four vertices away in either direction along the isocline, and {{radic|4}} = 180° distant across the diameter of the isocline.

Each of the 3 fibrations of the 24-cell's 18 great squares corresponds to a distinct left (and right) isoclinic rotation in great square invariant planes. Each 60° step of the rotation takes 6 disjoint great squares (2 from each 16-cell) to great squares in a neighboring 16-cell, on [[16-cell#Helical construction|8-chord helical isoclines characteristic of the 16-cell]].{{Efn|As [[16-cell#Helical construction|in the 16-cell, the isocline is an octagram]] which intersects only 8 vertices, even though the 24-cell has more vertices closer together than the 16-cell. The isocline curve misses the additional vertices in between. As in the 16-cell, the first vertex it intersects is {{radic|2}} away. The 24-cell employs more octagram isoclines (3 in parallel in each rotation) than the 16-cell does (1 in each rotation). The 3 helical isoclines are Clifford parallel;{{Efn|name=Clifford parallels}} they spiral around each other in a triple helix, with the disjoint helices' corresponding vertex pairs joined by {{radic|1}} {{=}} 60° chords. The triple helix of 3 isoclines contains 24 disjoint {{radic|2}} edges (6 disjoint great squares) and 24 vertices, and constitutes a discrete fibration of the 24-cell, just as the 4-cell ring does.|name=octagram isoclines}}

In the 24-cell, these 18 helical octagram isoclines can be found within the six orthogonal [[#4-cell rings|4-cell rings]] of octahedra. Each 4-cell ring has cells bonded vertex-to-vertex around a great square axis, and we find antipodal vertices at opposite vertices of the great square. A {{radic|4}} chord (the diameter of the great square and of the isocline) connects them. [[#Boundary cells|Boundary cells]] describes how the {{radic|2}} axes of the 24-cell's octahedral cells are the edges of the 16-cell's tetrahedral cells, each tetrahedron is inscribed in a (tesseract) cube, and each octahedron is inscribed in a pair of cubes (from different tesseracts), bridging them.{{Efn|name=octahedral diameters}} The vertex-bonded octahedra of the 4-cell ring also lie in different tesseracts.{{Efn|Two tesseracts share only vertices, not any edges, faces, cubes (with inscribed tetrahedra), or octahedra (whose central square planes are square faces of cubes). An octahedron that touches another octahedron at a vertex (but not at an edge or a face) is touching an octahedron in another tesseract, and a pair of adjacent cubes in the other tesseract whose common square face the octahedron spans, and a tetrahedron inscribed in each of those cubes.|name=vertex-bonded octahedra}} The isocline's four {{radic|4}} diameter chords form an [[W:Octagram#Star polygon compounds|octagram&lt;sub&gt;8{4}=4{2}&lt;/sub&gt;]] with {{radic|4}} edges that each run from the vertex of one cube and octahedron and tetrahedron, to the vertex of another cube and octahedron and tetrahedron (in a different tesseract), straight through the center of the 24-cell on one of the 12 {{radic|4}} axes.

The octahedra in the 4-cell rings are vertex-bonded to more than two other octahedra, because three 4-cell rings (and their three axial great squares, which belong to different 16-cells) cross at 90° at each bonding vertex. At that vertex the octagram makes two right-angled turns at once: 90° around the great square, and 90° orthogonally into a different 4-cell ring entirely. The 180° four-edge arc joining two ends of each {{radic|4}} diameter chord of the octagram runs through the volumes and opposite vertices of two face-bonded {{radic|2}} tetrahedra (in the same 16-cell), which are also the opposite vertices of two vertex-bonded octahedra in different 4-cell rings (and different tesseracts). The [[W:Octagram|720° octagram]] isocline runs through 8 vertices of the four-cell ring and through the volumes of 16 tetrahedra. At each vertex, there are three great squares and six octagram isoclines (three black-white pairs) that cross at the vertex.{{Efn|name=completely orthogonal Clifford parallels are special}}

This is the characteristic rotation of the 16-cell, ''not'' the 24-cell's characteristic rotation, and it does not take whole 16-cells ''of the 24-cell'' to each other the way the [[#Helical hexagrams and their isoclines|24-cell's rotation in great hexagon planes]] does.{{Efn|The [[600-cell#Squares and 4𝝅 octagrams|600-cell's isoclinic rotation in great square planes]] takes whole 16-cells to other 16-cells in different 24-cells.}}

{| class=&quot;wikitable&quot; width=610
!colspan=5|Five ways of looking at a [[W:Skew polygon|skew]] [[W:24-gon#Related polygons|24-gram]]
|-
![[16-cell#Rotations|Edge path]]
![[W:Petrie polygon|Petrie polygon]]s
![[600-cell#Squares and 4𝝅 octagrams|In a 600-cell]]
![[#Great squares|Discrete fibration]]
![[16-cell#Helical construction|Diameter chords]]
|-
![[16-cell#Helical construction|16-cells]]&lt;sub&gt;3{3/8}&lt;/sub&gt;
![[W:Petrie polygon#The Petrie polygon of regular polychora (4-polytopes)|Dodecagons]]&lt;sub&gt;2{12}&lt;/sub&gt;
![[W:24-gon#Related polygons|24-gram]]&lt;sub&gt;{24/5}&lt;/sub&gt;
![[#Great squares|Squares]]&lt;sub&gt;6{4}&lt;/sub&gt;
![[W:24-gon#Related polygons|&lt;sub&gt;{24/12}={12/2}&lt;/sub&gt;]]
|-
|align=center|[[File:Regular_star_figure_3(8,3).svg|120px]]
|align=center|[[File:Regular_star_figure_2(12,1).svg|120px]]
|align=center|[[File:Regular_star_polygon_24-5.svg|120px]]
|align=center|[[File:Regular_star_figure_6(4,1).svg|120px]]
|align=center|[[File:Regular_star_figure_12(2,1).svg|120px]]
|-
|The 24-cell's three inscribed Clifford parallel 16-cells revealed as disjoint 8-point 4-polytopes with {{radic|2}} edges.{{Efn|name=octagram isoclines}}
|2 [[W:Skew polygon|skew polygon]]s of 12 {{radic|1}} edges each. The 24-cell can be decomposed into 2 disjoint zig-zag [[W:Dodecagon|dodecagon]]s (4 different ways).{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii); 24-cell Petrie polygon ''h&lt;sub&gt;1&lt;/sub&gt;'' is {12} }}
|In [[600-cell#Hexagons|compounds of 5 24-cells]], isoclines with [[600-cell#Golden chords|golden chords]] of length &lt;big&gt;φ&lt;/big&gt; {{=}} {{radic|2.𝚽}} connect all 24-cells in [[600-cell#Squares and 4𝝅 octagrams|24-chord circuits]].{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii); 24-cell Petrie polygon orthogonal ''h&lt;sub&gt;2&lt;/sub&gt;'' is [[W:Dodecagon#Related figures|{12/5}]], half of [[W:24-gon#Related polygons|{24/5}]] as each Petrie polygon is half the 24-cell}}
|Their isoclinic rotation takes 6 Clifford parallel (disjoint) great squares with {{radic|2}} edges to each other.
|Two vertices four {{radic|2}} chords apart on the circular isocline are antipodal vertices joined by a {{radic|4}} axis.
|}

===Characteristic orthoscheme===
{| class=&quot;wikitable floatright&quot;
!colspan=6|Characteristics of the 24-cell{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii); &quot;24-cell&quot;}}
|-
!align=right|
!align=center|edge{{Sfn|Coxeter|1973|p=139|loc=§7.9 The characteristic simplex}}
!colspan=2 align=center|arc
!colspan=2 align=center|dihedral{{Sfn|Coxeter|1973|p=290|loc=Table I(ii); &quot;dihedral angles&quot;}}
|-
!align=right|𝒍
|align=center|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;60°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{3}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;120°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{2\pi}{3}&lt;/math&gt;&lt;/small&gt;
|-
|
|
|
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|-
!align=right|𝟀
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{3}} \approx 0.577&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;45°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{4}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;45°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{4}&lt;/math&gt;&lt;/small&gt;
|-
!align=right|𝝉{{Efn|{{Harv|Coxeter|1973}} uses the greek letter 𝝓 (phi) to represent one of the three ''characteristic angles'' 𝟀, 𝝓, 𝟁 of a regular polytope. Because 𝝓 is commonly used to represent the [[W:Golden ratio|golden ratio]] constant ≈ 1.618, for which Coxeter uses 𝝉 (tau), we reverse Coxeter's conventions, and use 𝝉 to represent the characteristic angle.|name=reversed greek symbols}}
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{4}} = 0.5&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;30°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{6}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;60°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{3}&lt;/math&gt;&lt;/small&gt;
|-
!align=right|𝟁
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{12}} \approx 0.289&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;30°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{6}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;60°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{3}&lt;/math&gt;&lt;/small&gt;
|-
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|-
!align=right|&lt;small&gt;&lt;math&gt;_0R^3/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{2}} \approx 0.707&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;45°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{4}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;90°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{2}&lt;/math&gt;&lt;/small&gt;
|-
!align=right|&lt;small&gt;&lt;math&gt;_1R^3/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{4}} = 0.5&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;30°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{6}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;90°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{2}&lt;/math&gt;&lt;/small&gt;
|-
!align=right|&lt;small&gt;&lt;math&gt;_2R^3/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{6}} \approx 0.408&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;30°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{6}&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;90°&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\tfrac{\pi}{2}&lt;/math&gt;&lt;/small&gt;
|-
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|-
!align=right|&lt;small&gt;&lt;math&gt;_0R^4/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|align=center|
|align=center|
|align=center|
|align=center|
|-
!align=right|&lt;small&gt;&lt;math&gt;_1R^4/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{3}{4}} \approx 0.866&lt;/math&gt;&lt;/small&gt;{{Efn|name=root 3/4}}
|align=center|
|align=center|
|align=center|
|align=center|
|-
!align=right|&lt;small&gt;&lt;math&gt;_2R^4/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{2}{3}} \approx 0.816&lt;/math&gt;&lt;/small&gt;
|align=center|
|align=center|
|align=center|
|align=center|
|-
!align=right|&lt;small&gt;&lt;math&gt;_3R^4/l&lt;/math&gt;&lt;/small&gt;
|align=center|&lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{2}} \approx 0.707&lt;/math&gt;&lt;/small&gt;
|align=center|
|align=center|
|align=center|
|align=center|
|}
Every regular 4-polytope has its [[W:Orthoscheme#Characteristic simplex of the general regular polytope|characteristic 4-orthoscheme]], an [[5-cell#Irregular 5-cells|irregular 5-cell]].{{Efn|name=characteristic orthoscheme}} The '''characteristic 5-cell of the regular 24-cell''' is represented by the [[W:Coxeter-Dynkin diagram|Coxeter-Dynkin diagram]] {{Coxeter–Dynkin diagram|node|3|node|4|node|3|node}}, which can be read as a list of the dihedral angles between its mirror facets.{{Efn|For a regular ''k''-polytope, the [[W:Coxeter-Dynkin diagram|Coxeter-Dynkin diagram]] of the characteristic ''k-''orthoscheme is the ''k''-polytope's diagram without the [[W:Coxeter-Dynkin diagram#Application with uniform polytopes|generating point ring]]. The regular ''k-''polytope is subdivided by its symmetry (''k''-1)-elements into ''g'' instances of its characteristic ''k''-orthoscheme that surround its center, where ''g'' is the ''order'' of the ''k''-polytope's [[W:Coxeter group|symmetry group]].{{Sfn|Coxeter|1973|pp=130-133|loc=§7.6 The symmetry group of the general regular polytope}}}} It is an irregular [[W:Hyperpyramid|tetrahedral pyramid]] based on the [[W:Octahedron#Characteristic orthoscheme|characteristic tetrahedron of the regular octahedron]]. The regular 24-cell is subdivided by its symmetry hyperplanes into 1152 instances of its characteristic 5-cell that all meet at its center.{{Sfn|Kim|Rote|2016|pp=17-20|loc=§10 The Coxeter Classification of Four-Dimensional Point Groups}}

The characteristic 5-cell (4-orthoscheme) has four more edges than its base characteristic tetrahedron (3-orthoscheme), joining the four vertices of the base to its apex (the fifth vertex of the 4-orthoscheme, at the center of the regular 24-cell).{{Efn|The four edges of each 4-orthoscheme which meet at the center of the regular 4-polytope are of unequal length, because they are the four characteristic radii of the regular 4-polytope: a vertex radius, an edge center radius, a face center radius, and a cell center radius. The five vertices of the 4-orthoscheme always include one regular 4-polytope vertex, one regular 4-polytope edge center, one regular 4-polytope face center, one regular 4-polytope cell center, and the regular 4-polytope center. Those five vertices (in that order) comprise a path along four mutually perpendicular edges (that makes three right angle turns), the characteristic feature of a 4-orthoscheme. The 4-orthoscheme has five dissimilar 3-orthoscheme facets.|name=characteristic radii}} If the regular 24-cell has radius and edge length 𝒍 = 1, its characteristic 5-cell's ten edges have lengths &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{3}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{4}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{12}}&lt;/math&gt;&lt;/small&gt; around its exterior right-triangle face (the edges opposite the ''characteristic angles'' 𝟀, 𝝉, 𝟁),{{Efn|name=reversed greek symbols}} plus &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{2}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{4}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{6}}&lt;/math&gt;&lt;/small&gt; (the other three edges of the exterior 3-orthoscheme facet the characteristic tetrahedron, which are the ''characteristic radii'' of the octahedron), plus &lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{3}{4}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{2}{3}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{2}}&lt;/math&gt;&lt;/small&gt; (edges which are the characteristic radii of the 24-cell). The 4-edge path along orthogonal edges of the orthoscheme is &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{4}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{12}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{6}}&lt;/math&gt;&lt;/small&gt;, &lt;small&gt;&lt;math&gt;\sqrt{\tfrac{1}{2}}&lt;/math&gt;&lt;/small&gt;, first from a 24-cell vertex to a 24-cell edge center, then turning 90° to a 24-cell face center, then turning 90° to a 24-cell octahedral cell center, then turning 90° to the 24-cell center.

=== Reflections ===
The 24-cell can be [[#Tetrahedral constructions|constructed by the reflections of its characteristic 5-cell]] in its own facets (its tetrahedral mirror walls).{{Efn|The reflecting surface of a (3-dimensional) polyhedron consists of 2-dimensional faces; the reflecting surface of a (4-dimensional) [[W:Polychoron|polychoron]] consists of 3-dimensional cells.}} Reflections and rotations are related: a reflection in an ''even'' number of ''intersecting'' mirrors is a rotation.{{Sfn|Coxeter|1973|pp=33-38|loc=§3.1 Congruent transformations}} Consequently, regular polytopes can be generated by reflections or by rotations. For example, any [[#Isoclinic rotations|720° isoclinic rotation]] of the 24-cell in a hexagonal invariant plane takes ''each'' of the 24 vertices to and through 5 other vertices and back to itself, on a skew [[#Helical hexagrams and their isoclines|hexagram&lt;sub&gt;2&lt;/sub&gt; geodesic isocline]] that winds twice around the 3-sphere on every ''second'' vertex of the hexagram. Any set of [[#The 3 Cartesian bases of the 24-cell|four orthogonal pairs of antipodal vertices]] (the 8 vertices of one of the [[#Relationships among interior polytopes|three inscribed 16-cells]]) performing ''half'' such an orbit visits 3 * 8 = 24 distinct vertices and [[#Clifford parallel polytopes|generates the 24-cell]] sequentially in 3 steps of a single 360° isoclinic rotation, just as any single characteristic 5-cell reflecting itself in its own mirror walls generates the 24 vertices simultaneously by reflection.

Tracing the orbit of ''one'' such 16-cell vertex during the 360° isoclinic rotation reveals more about the relationship between reflections and rotations as generative operations.{{Efn|&lt;blockquote&gt;Let Q denote a rotation, R a reflection, T a translation, and let Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T denote a product of several such transformations, all commutative with one another. Then RT is a glide-reflection (in two or three dimensions), QR is a rotary-reflection, QT is a screw-displacement, and Q&lt;sup&gt;2&lt;/sup&gt; is a double rotation (in four dimensions).&lt;br&gt;&lt;br&gt;Every orthogonal transformation is expressible as{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt;&lt;br&gt;where 2''q'' + ''r'' ≤ ''n'', the number of dimensions. Transformations involving a translation are expressible as{{indent|12}}Q&lt;sup&gt;''q''&lt;/sup&gt; R&lt;sup&gt;''r''&lt;/sup&gt; T&lt;br&gt;where 2''q'' + ''r'' + 1 ≤ ''n''.&lt;br&gt;&lt;br&gt;For ''n'' {{=}} 4 in particular, every displacement is either a double rotation Q&lt;sup&gt;2&lt;/sup&gt;, or a screw-displacement QT (where the rotation component Q is a simple rotation). Every enantiomorphous transformation in 4-space (reversing chirality) is a QRT.{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}}&lt;/blockquote&gt;|name=transformations}} The vertex follows an [[#Helical hexagrams and their isoclines|isocline]] (a doubly curved geodesic circle) rather than an ordinary great circle.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} The isocline connects vertices two edge lengths apart, but curves away from the great circle path over the two edges connecting those vertices, missing the vertex in between.{{Efn|name=isocline misses vertex}} Although the isocline does not follow any one great circle, it is contained within a ring of another kind: in the 24-cell it stays within a [[#6-cell rings|6-cell ring]] of spherical{{Sfn|Coxeter|1973|p=138|ps=; &quot;We allow the Schläfli symbol {p,..., v} to have three different meanings: a Euclidean polytope, a spherical polytope, and a spherical honeycomb. This need not cause any confusion, so long as the situation is frankly recognized. The differences are clearly seen in the concept of dihedral angle.&quot;}} octahedral cells, intersecting one vertex in each cell, and passing through the volume of two adjacent cells near the missed vertex.

=== Chiral symmetry operations ===

A [[W:Symmetry operation|symmetry operation]] is a rotation or reflection which leaves the object indistinguishable from itself before the transformation. The 24-cell has 1152 distinct symmetry operations (576 rotations and 576 reflections). Each rotation is equivalent to two [[#Reflections|reflections]], in a distinct pair of non-parallel mirror planes.{{Efn|name=transformations}}

Pictured are sets of disjoint [[#Geodesics|great circle polygons]], each in a distinct central plane of the 24-cell. For example, {24/4}=4{6} is an orthogonal projection of the 24-cell picturing 4 of its [16] great hexagon planes.{{Efn|name=four hexagonal fibrations}} The 4 planes lie Clifford parallel to the projection plane and to each other, and their great polygons collectively constitute a discrete [[W:Hopf fibration|Hopf fibration]] of 4 non-intersecting great circles which visit all 24 vertices just once.

Each row of the table describes a class of distinct rotations. Each '''rotation class''' takes the '''left planes''' pictured to the corresponding '''right planes''' pictured.{{Efn|The left planes are Clifford parallel, and the right planes are Clifford parallel; each set of planes is a fibration. Each left plane is Clifford parallel to its corresponding right plane in an isoclinic rotation,{{Efn|In an ''isoclinic'' rotation each invariant plane is Clifford parallel to the plane it moves to, and they do not intersect at any time (except at the central point). In a ''simple'' rotation the invariant plane intersects the plane it moves to in a line, and moves to it by rotating around that line.|name=plane movement in rotations}} but the two sets of planes are not all mutually Clifford parallel; they are different fibrations, except in table rows where the left and right planes are the same set.}} The vertices of the moving planes move in parallel along the polygonal '''isocline''' paths pictured. For example, the &lt;math&gt;[32]R_{q7,q8}&lt;/math&gt; rotation class consists of [32] distinct rotational displacements by an arc-distance of {{sfrac|2𝝅|3}} = 120° between 16 great hexagon planes represented by quaternion group &lt;math&gt;q7&lt;/math&gt; and a corresponding set of 16 great hexagon planes represented by quaternion group &lt;math&gt;q8&lt;/math&gt;.{{Efn|A quaternion group &lt;math&gt;\pm{q_n}&lt;/math&gt; corresponds to a distinct set of Clifford parallel great circle polygons, e.g. &lt;math&gt;q7&lt;/math&gt; corresponds to a set of four disjoint great hexagons.{{Efn|[[File:Regular_star_figure_4(6,1).svg|thumb|200px|The 24-cell as a compound of four non-intersecting great hexagons {24/4}=4{6}.]]There are 4 sets of 4 disjoint great hexagons in the 24-cell (of a total of [16] distinct great hexagons), designated &lt;math&gt;q7&lt;/math&gt;, &lt;math&gt;-q7&lt;/math&gt;, &lt;math&gt;q8&lt;/math&gt; and &lt;math&gt;-q8&lt;/math&gt;.{{Efn|name=union of q7 and q8}} Each named set of 4 Clifford parallel{{Efn|name=Clifford parallels}} hexagons comprises a [[#Chiral symmetry operations|discrete fibration]] covering all 24 vertices.|name=four hexagonal fibrations}} Note that &lt;math&gt;q_n&lt;/math&gt; and &lt;math&gt;-{q_n}&lt;/math&gt; generally are distinct sets. The corresponding vertices of the &lt;math&gt;q_n&lt;/math&gt; planes and the &lt;math&gt;-{q_n}&lt;/math&gt; planes are 180° apart.{{Efn|name=two angles between central planes}}|name=quaternion group}} One of the [32] distinct rotations of this class moves the representative [[#Great hexagons|vertex coordinate]] &lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt; to the vertex coordinate &lt;math&gt;(\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2})&lt;/math&gt;.{{Efn|A quaternion Cartesian coordinate designates a vertex joined to a ''top vertex'' by one instance of a [[#Hypercubic chords|distinct chord]]. The conventional top vertex of a [[#Great hexagons|unit radius 4-polytope]] in standard (vertex-up) orientation is &lt;math&gt;(0,0,1,0)&lt;/math&gt;, the Cartesian &quot;north pole&quot;. Thus e.g. &lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt; designates a {{radic|1}} chord of 60° arc-length. Each such distinct chord is an edge of a distinct [[#Geodesics|great circle polygon]], in this example a [[#Great hexagons|great hexagon]], intersecting the north and south poles. Great circle polygons occur in sets of Clifford parallel central planes, each set of disjoint great circles comprising a discrete [[W:Hopf fibration|Hopf fibration]] that intersects every vertex just once. One great circle polygon in each set intersects the north and south poles. This quaternion coordinate &lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt; is thus representative of the 4 disjoint great hexagons pictured, a quaternion group{{Efn|name=quaternion group}} which comprise one distinct fibration of the [16] great hexagons (four fibrations of great hexagons) that occur in the 24-cell.{{Efn|name=four hexagonal fibrations}}|name=north pole relative coordinate}}

{| class=wikitable style=&quot;white-space:nowrap;text-align:center&quot;
!colspan=15|Proper [[W:SO(4)|rotations]] of the 24-cell [[W:F4 (mathematics)|symmetry group ''F&lt;sub&gt;4&lt;/sub&gt;'']]{{Sfn|Mamone|Pileio|Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes, Table 2, Symmetry operations|pp=1438-1439}}
|-
!Isocline{{Efn|An ''isocline'' is the circular geodesic path taken by a vertex that lies in an invariant plane of rotation, during a complete revolution. In an [[#Isoclinic rotations|isoclinic rotation]] every vertex lies in an invariant plane of rotation, and the isocline it rotates on is a helical geodesic circle that winds through all four dimensions, not a simple geodesic great circle in the plane. In a [[#Simple rotations|simple rotation]] there is only one invariant plane of rotation, and each vertex that lies in it rotates on a simple geodesic great circle in the plane. Both the helical geodesic isocline of an isoclinic rotation and the simple geodesic isocline of a simple rotation are great circles, but to avoid confusion between them we generally reserve the term ''isocline'' for the former, and reserve the term ''great circle'' for the latter, an ordinary great circle in the plane. Strictly, however, the latter is an isocline of circumference &lt;math&gt;2\pi r&lt;/math&gt;, and the former is an isocline of circumference greater than &lt;math&gt;2\pi r&lt;/math&gt;.{{Efn|name=isoclinic geodesic}}|name=isocline}}
!colspan=4|Rotation class{{Efn|Each class of rotational displacements (each table row) corresponds to a distinct rigid left (and right) [[#Isoclinic rotations|isoclinic rotation]] in multiple invariant planes concurrently.{{Efn|name=invariant planes of an isoclinic rotation}} The '''Isocline''' is the path followed by a vertex,{{Efn|name=isocline}} which is a helical geodesic circle that does not lie in any one central plane. Each rotational displacement takes one invariant '''Left plane''' to the corresponding invariant '''Right plane''', with all the left (or right) displacements taking place concurrently.{{Efn|name=plane movement in rotations}} Each left plane is separated from the corresponding right plane by two equal angles,{{Efn|name=two angles between central planes}} each equal to one half of the arc-angle by which each vertex is displaced (the angle and distance that appears in the '''Rotation class''' column).|name=isoclinic rotation}}
!colspan=5|Left planes &lt;math&gt;ql&lt;/math&gt;{{Efn|In an [[#Isoclinic rotations|isoclinic rotation]], all the '''Left planes''' move together, remain Clifford parallel while moving, and carry all their points with them to the '''Right planes''' as they move: they are invariant planes.{{Efn|name=plane movement in rotations}} Because the left (and right) set of central polygons are a fibration covering all the vertices, every vertex is a point carried along in an invariant plane.|name=invariant planes of an isoclinic rotation}}
!colspan=5|Right planes &lt;math&gt;qr&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/8}=4{6/2}]]{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/4}=4{3} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|3}} chords. Each disjoint triangle can be seen as a skew {6/2} [[W:Hexagram|hexagram]] with {{radic|3}} edges: two open skew triangles with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅. The hexagram projects to a single triangle in two dimensions because it skews through all four dimensions. Those 4 disjoint skew [[#Helical hexagrams and their isoclines|hexagram isoclines]] are the Clifford parallel circular vertex paths of the fibration's characteristic left (and right) [[#Isoclinic rotations|isoclinic rotation]].{{Efn|name=isoclinic geodesic}} The 4 Clifford parallel great hexagons of the fibration are invariant planes of this rotation. The great hexagons rotate in incremental displacements of 60° like wheels ''and'' 60° orthogonally like coins flipping, displacing each vertex by 120°, as their vertices move along parallel helical isocline paths through successive Clifford parallel hexagon planes.{{Efn|Each hexagon rides on only three skew hexagram isoclines, not six, because opposite vertices of each hexagon ride on opposing rails of the same Clifford hexagram, in the same (not opposite) rotational direction.{{Efn|name=Clifford polygon}}}} Alternatively, the 4 triangles can be seen as 8 disjoint triangles: 4 pairs of Clifford parallel [[#Great triangles|great triangles]], where two opposing great triangles lie in the same [[#Great hexagons|great hexagon central plane]], so a fibration of 4 Clifford parallel great hexagon planes is represented.{{Efn|name=four hexagonal fibrations}} This illustrates that the 4 hexagram isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 4 great hexagons.|name=hexagram}}&lt;br&gt;[[File:Regular_star_figure_4(3,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,q8}&lt;/math&gt;&lt;br&gt;[16] 4𝝅 {6/2}
|colspan=4|&lt;math&gt;[32]R_{q7,q8}&lt;/math&gt;{{Efn|The &lt;math&gt;[32]R_{q7,q8}&lt;/math&gt; isoclinic rotation in great hexagon invariant planes takes each vertex to a vertex two vertices away (120° {{=}} {{radic|3}} away), without passing through any intervening vertices. Each left hexagon rotates 60° (like a wheel) at the same time that it tilts sideways by 60° (in an orthogonal central plane) into its corresponding right hexagon plane. Repeated 6 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,q8}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]{{Efn|name=four hexagonal fibrations}}&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;{{Efn|name=north pole relative coordinate}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/8}=4{6/2}]]{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/4}=4{3} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|3}} chords. The 4 triangles can be seen as 8 disjoint triangles: 4 pairs of Clifford parallel [[#Great triangles|great triangles]], where two opposing great triangles lie in the same [[#Great hexagons|great hexagon central plane]], so a fibration of 4 Clifford parallel great hexagon planes is represented, as in the 4 left planes of this rotation class (table row).{{Efn|name=four hexagonal fibrations}}|name=great triangles}}&lt;br&gt;[[File:Regular_star_figure_4(3,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q8}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|{{sfrac|2𝝅|3}}
|120°
|{{radic|3}}
|1.732~
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|2𝝅|3}}
|120°
|{{radic|3}}
|1.732~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/2}=2{12}]]{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/2}=2{6} dodecagram]], each point represents two vertices, and each line represents multiple 24-cell edges. Each disjoint hexagon can be seen as a skew {12} [[W:Dodecagon|dodecagon]], a Petrie polygon of the 24-cell, by viewing it as two open skew hexagons with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅. The dodecagon projects to a single hexagon in two dimensions because it skews through all four dimensions. Those 2 disjoint skew dodecagons are the Clifford parallel circular vertex paths of the fibration's characteristic left (and right) [[#Isoclinic rotations|isoclinic rotation]].{{Efn|name=isoclinic geodesic}} The 4 Clifford parallel great hexagons of the fibration are invariant planes of this rotation. The great hexagons rotate in incremental displacements of 30° like wheels ''and'' 30° orthogonally like coins flipping, displacing each vertex by 60°, as their vertices move along parallel helical isocline paths through successive Clifford parallel hexagon planes.{{Efn|Each hexagon rides on only two parallel dodecagon isoclines, not six, because only alternate vertices of each hexagon ride on different dodecagon rails; the three vertices of each great triangle inscribed in the great hexagon occupy the same dodecagon Petrie polygon, four vertices apart, and they circulate on that isocline.{{Efn|name=Clifford polygon}}}} Alternatively, the 2 hexagons can be seen as 4 disjoint hexagons: 2 pairs of Clifford parallel great hexagons, so a fibration of 4 Clifford parallel great hexagon planes is represented.{{Efn|name=four hexagonal fibrations}} This illustrates that the 2 dodecagon isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 4 great hexagons.|name=dodecagon}}&lt;br&gt;[[File:Regular_star_figure_2(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,-q8}&lt;/math&gt;&lt;br&gt;[16] 4𝝅 {12}
|colspan=4|&lt;math&gt;[32]R_{q7,-q8}&lt;/math&gt;{{Efn|The &lt;math&gt;[32]R_{q7,-q8}&lt;/math&gt; isoclinic rotation in great hexagon invariant planes takes each vertex to a vertex one vertex away (60° {{=}} {{radic|1}} away), without passing through any intervening vertices.{{Efn|At the mid-point of the isocline arc (30° away) it passes directly over the mid-point of a 24-cell edge.}} Each left hexagon rotates 30° (like a wheel) at the same time that it tilts sideways by 30° (in an orthogonal central plane) into its corresponding right hexagon plane. Repeated 12 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,-q8}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q8}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(-\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/1}={24}]]&lt;br&gt;[[File:Regular_polygon_24.svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,q7}&lt;/math&gt;&lt;br&gt;[16] 4𝝅 {1}
|colspan=4|&lt;math&gt;[32]R_{q7,q7}&lt;/math&gt;{{Efn|The &lt;math&gt;[32]R_{q7,q7}&lt;/math&gt; isoclinic rotation in great hexagon invariant planes takes each vertex through a 360° rotation and back to itself (360° {{=}} {{radic|0}} away), without passing through any intervening vertices. Each left hexagon rotates 180° (like a wheel) at the same time that it tilts sideways by 180° (in an orthogonal central plane) into its corresponding right hexagon plane. Repeated 2 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,q7}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|2𝝅
|360°
|{{radic|0}}
|0
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,-q7}&lt;/math&gt;&lt;br&gt;[16] 4𝝅 {2}
|colspan=4|&lt;math&gt;[32]R_{q7,-q7}&lt;/math&gt;{{Efn|The &lt;math&gt;[32]R_{q7,-q7}&lt;/math&gt; isoclinic rotation in hexagon invariant planes takes each vertex to a vertex three vertices away (180° {{=}} {{radic|4}} away),{{Efn|name=quaternion group}} without passing through any intervening vertices. Each left hexagon rotates 90° (like a wheel) at the same time that it tilts sideways by 90° (in an orthogonal central plane) into its corresponding right hexagon plane. Repeated 4 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,-q7}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/8}=4{6/2}]]{{Efn|name=great triangles}}&lt;br&gt;[[File:Regular_star_figure_4(3,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q7}&lt;/math&gt;&lt;br&gt;[16] 2𝝅 {6}
|colspan=4|&lt;math&gt;(-\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|𝝅
|180°
|{{radic|4}}
|2
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|2𝝅|3}}
|120°
|{{radic|3}}
|1.732~
|- style=&quot;background: #E6FFEE;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/2}=2{12}]]{{Efn|name=dodecagon}}&lt;br&gt;[[File:Regular_star_figure_2(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,q1}&lt;/math&gt;&lt;br&gt;[8] 4𝝅 {12}
|colspan=4|&lt;math&gt;[16]R_{q7,q1}&lt;/math&gt;{{Efn|The &lt;math&gt;[16]R_{q7,q1}&lt;/math&gt; isoclinic rotation in great hexagon invariant planes takes each vertex to a vertex one vertex away (60° {{=}} {{radic|1}} away), without passing through any intervening vertices. Each left hexagon rotates 30° (like a wheel) at the same time that it tilts sideways by 30° (in an orthogonal central plane) into its corresponding right square plane.{{Efn|This ''hybrid isoclinic rotation'' carries the two kinds of [[#Geodesics|central planes]] to each other: great square planes [[16-cell#Coordinates|characteristic of the 16-cell]] and great hexagon (great triangle) planes [[#Great hexagons|characteristic of the 24-cell]].{{Efn|The edges and 4𝝅 characteristic [[16-cell#Rotations|rotations of the 16-cell]] lie in the great square central planes. Rotations of this type are an expression of the [[W:Hyperoctahedral group|&lt;math&gt;B_4&lt;/math&gt; symmetry group]]. The edges and 4𝝅 characteristic [[#Rotations|rotations of the 24-cell]] lie in the great hexagon (great triangle) central planes. Rotations of this type are an expression of the [[W:F4 (mathematics)|&lt;math&gt;F_4&lt;/math&gt; symmetry group]].|name=edge rotation planes}} This is possible because some great hexagon planes lie Clifford parallel to some great square planes.{{Efn|Two great circle polygons either intersect in a common axis, or they are Clifford parallel (isoclinic) and share no vertices.{{Efn||name=two angles between central planes}} Three great squares and four great hexagons intersect at each 24-cell vertex. Each great hexagon intersects 9 distinct great squares, 3 in each of its 3 axes, and lies Clifford parallel to the other 9 great squares. Each great square intersects 8 distinct great hexagons, 4 in each of its 2 axes, and lies Clifford parallel to the other 8 great hexagons.|name=hybrid isoclinic planes}}|name=hybrid isoclinic rotation}} Repeated 12 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,q1}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[8] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]{{Efn|[[File:Regular_star_figure_6(4,1).svg|thumb|200px|The 24-cell as a compound of six non-intersecting great squares {24/6}=6{4}.]]There are 3 sets of 6 disjoint great squares in the 24-cell (of a total of [18] distinct great squares),{{Efn|The 24-cell has 18 great squares, in 3 disjoint sets of 6 mutually orthogonal great squares comprising a 16-cell.{{Efn|name=Six orthogonal planes of the Cartesian basis}} Within each 16-cell are 3 sets of 2 completely orthogonal great squares, so each great square is disjoint not only from all the great squares in the other two 16-cells, but also from one other great square in the same 16-cell. Each great square is disjoint from 13 others, and shares two vertices (an axis) with 4 others (in the same 16-cell).|name=unions of q1 q2 q3}} designated &lt;math&gt;\pm q1&lt;/math&gt;, &lt;math&gt;\pm q2&lt;/math&gt;, and &lt;math&gt;\pm q3&lt;/math&gt;. Each named set{{Efn|Because in the 24-cell each great square is completely orthogonal to another great square, the quaternion groups &lt;math&gt;q1&lt;/math&gt; and &lt;math&gt;-{q1}&lt;/math&gt; (for example) correspond to the same set of great square planes. That distinct set of 6 disjoint great squares &lt;math&gt;\pm q1&lt;/math&gt; has two names, used in the left (or right) rotational context, because it constitutes both a left and a right fibration of great squares.|name=two quaternion group names for square fibrations}} of 6 Clifford parallel{{Efn|name=Clifford parallels}} squares comprises a [[#Chiral symmetry operations|discrete fibration]] covering all 24 vertices.|name=three square fibrations}}&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1}&lt;/math&gt;&lt;br&gt;[8] 2𝝅 {4}
|colspan=4|&lt;math&gt;(1,0,0,0)&lt;/math&gt;
|- style=&quot;background: #E6FFEE;&quot;|
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: #E6FFEE;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/8}=4{6/2}]]{{Efn|name=hexagram}}&lt;br&gt;[[File:Regular_star_figure_4(3,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7,-q1}&lt;/math&gt;&lt;br&gt;[8] 4𝝅 {6/2}
|colspan=4|&lt;math&gt;[16]R_{q7,-q1}&lt;/math&gt;{{Efn|The &lt;math&gt;[16]R_{q7,-q1}&lt;/math&gt; isoclinic rotation in hexagon invariant planes takes each vertex to a vertex two vertices away (120° {{=}} {{radic|3}} away), without passing through any intervening vertices. Each left hexagon rotates 60° (like a wheel) at the same time that it tilts sideways by 60° (in an orthogonal central plane) into its corresponding right square plane.{{Efn|name=hybrid isoclinic rotation}} Repeated 6 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq7,-q1}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[8] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q1}&lt;/math&gt;&lt;br&gt;[8] 2𝝅 {4}
|colspan=4|&lt;math&gt;(-1,0,0,0)&lt;/math&gt;
|- style=&quot;background: #E6FFEE;&quot;|
|{{sfrac|2𝝅|3}}
|120°
|{{radic|3}}
|1.732~
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/1}={24}]]&lt;br&gt;[[File:Regular_polygon_24.svg|100px]]&lt;br&gt;&lt;math&gt;^{q6,q6}&lt;/math&gt;&lt;br&gt;[18] 4𝝅 {1}
|colspan=4|&lt;math&gt;[36]R_{q6,q6}&lt;/math&gt;{{Efn|The &lt;math&gt;[36]R_{q6,q6}&lt;/math&gt; isoclinic rotation in great square invariant planes takes each vertex through a 360° rotation and back to itself (360° {{=}} {{radic|0}} away), without passing through any intervening vertices. Each left square rotates 180° (like a wheel) at the same time that it tilts sideways by 180° (in an orthogonal central plane) into its corresponding right square plane. Repeated 2 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq6,q6}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6}&lt;/math&gt;&lt;br&gt;[18] 2𝝅 {4}
|colspan=4|&lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt;{{Efn|The representative coordinate &lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt; is not a vertex of the unit-radius 24-cell in standard (vertex-up) orientation, it is the center of an octahedral cell. Some of the 24-cell's lines of symmetry (Coxeter's &quot;reflecting circles&quot;) run through cell centers rather than through vertices, and quaternion group &lt;math&gt;q6&lt;/math&gt; corresponds to a set of those. However, &lt;math&gt;q6&lt;/math&gt; also corresponds to the set of great squares pictured, which lie orthogonal to those cells (completely disjoint from the cell).{{Efn|A quaternion Cartesian coordinate designates a vertex joined to a ''top vertex'' by one instance of a [[#Hypercubic chords|distinct chord]]. The conventional top vertex of a [[#Great hexagons|unit radius 4-polytope]] in ''cell-first'' orientation is &lt;math&gt;(0,0,\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2})&lt;/math&gt;. Thus e.g. &lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt; designates a {{radic|2}} chord of 90° arc-length. Each such distinct chord is an edge of a distinct [[#Geodesics|great circle polygon]], in this example a [[#Great squares|great square]], intersecting the top vertex. Great circle polygons occur in sets of Clifford parallel central planes, each set of disjoint great circles comprising a discrete [[W:Hopf fibration|Hopf fibration]] that intersects every vertex just once. One great circle polygon in each set intersects the top vertex. This quaternion coordinate &lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt; is thus representative of the 6 disjoint great squares pictured, a quaternion group{{Efn|name=quaternion group}} which comprise one distinct fibration of the [18] great squares (three fibrations of great squares) that occur in the 24-cell.{{Efn|name=three square fibrations}}|name=north cell relative coordinate}}|name=lines of symmetry}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6}&lt;/math&gt;&lt;br&gt;[18] 2𝝅 {4}
|colspan=4|&lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|2𝝅
|360°
|{{radic|0}}
|0
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6,-q6}&lt;/math&gt;&lt;br&gt;[18] 4𝝅 {2}
|colspan=4|&lt;math&gt;[36]R_{q6,-q6}&lt;/math&gt;{{Efn|The &lt;math&gt;[36]R_{q6,-q6}&lt;/math&gt; isoclinic rotation in great square invariant planes takes each vertex to a vertex 180° {{=}} {{radic|4}} away,{{Efn|name=quaternion group}} without passing through any intervening vertices. Each left square rotates 90° (like a wheel) at the same time that it tilts sideways by 90° (in an orthogonal central plane) into its corresponding right square, ''which in this rotation is the completely orthogonal plane''. Repeated 4 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq6,-q6}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6}&lt;/math&gt;&lt;br&gt;[18] 2𝝅 {4}
|colspan=4|&lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q6}&lt;/math&gt;&lt;br&gt;[18] 2𝝅 {4}
|colspan=4|&lt;math&gt;(-\tfrac{\sqrt{2}}{2},-\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|𝝅
|180°
|{{radic|4}}
|2
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/9}=3{8/3}]]{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/3}{{=}}3{4} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|2}} chords. Each disjoint square can be seen as a skew {8/3} [[W:Octagram|octagram]] with {{radic|2}} edges: two open skew squares with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅, visible in the {24/9}{{=}}3{8/3} orthogonal projection.{{Efn|[[File:Regular_star_figure_3(8,3).svg|thumb|200px|Icositetragon {24/9}{{=}}3{8/3} is a compound of three octagrams {8/3}, as the 24-cell is a compound of three 16-cells.]]This orthogonal projection of a 24-cell to a 24-gram {24/9}{{=}}3{8/3} exhibits 3 disjoint [[16-cell#Helical construction|octagram {8/3} isoclines of a 16-cell]], each of which is a circular isocline path through the 8 vertices of one of the 3 disjoint 16-cells inscribed in the 24-cell.}} The octagram projects to a single square in two dimensions because it skews through all four dimensions. Those 3 disjoint [[16-cell#Helical construction|skew octagram isoclines]] are the circular vertex paths characteristic of an [[#Helical octagrams and their isoclines|isoclinic rotation in great square planes]], in which the 6 Clifford parallel great squares are invariant rotation planes. The great squares rotate 90° like wheels ''and'' 90° orthogonally like coins flipping, displacing each vertex by 180°, so each vertex exchanges places with its antipodal vertex. Each octagram isocline circles through the 8 vertices of a disjoint 16-cell. Alternatively, the 3 squares can be seen as a fibration of 6 Clifford parallel squares.{{Efn|name=three square fibrations}} This illustrates that the 3 octagram isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 6 squares.|name=octagram}}&lt;br&gt;[[File:Regular_star_figure_3(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6,-q4}&lt;/math&gt;&lt;br&gt;[72] 4𝝅 {8/3}
|colspan=4|&lt;math&gt;[144]R_{q6,-q4}&lt;/math&gt;{{Efn|The &lt;math&gt;[144]R_{q6,-q4}&lt;/math&gt; isoclinic rotation in great square invariant planes takes each vertex to a vertex 90° {{=}} {{radic|2}} away, without passing through any intervening vertices.{{Efn|At the mid-point of the isocline arc (45° away) it passes directly over the mid-point of a 24-cell edge.}} Each left square rotates 45° (like a wheel) at the same time that it tilts sideways by 45° (in an orthogonal central plane) into its corresponding right square plane. Repeated 8 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq6,-q4}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q6}&lt;/math&gt;&lt;br&gt;[72] 2𝝅 {4}
|colspan=4|&lt;math&gt;(\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2},0,0)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q4}&lt;/math&gt;&lt;br&gt;[72] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,-\tfrac{\sqrt{2}}{2},-\tfrac{\sqrt{2}}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|𝝅
|180°
|{{radic|4}}
|2
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/1}={24}]]&lt;br&gt;[[File:Regular_polygon_24.svg|100px]]&lt;br&gt;&lt;math&gt;^{q4,q4}&lt;/math&gt;&lt;br&gt;[36] 4𝝅 {1}
|colspan=4|&lt;math&gt;[72]R_{q4,q4}&lt;/math&gt;{{Efn|The &lt;math&gt;[72]R_{q4,q4}&lt;/math&gt; isoclinic rotation in great square invariant planes takes each vertex through a 360° rotation and back to itself (360° {{=}} {{radic|0}} away), without passing through any intervening vertices. Each left square rotates 180° (like a wheel) at the same time that it tilts sideways by 180° (in an orthogonal central plane) into its corresponding right square plane. Repeated 2 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq4,q4}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q4}&lt;/math&gt;&lt;br&gt;[36] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2})&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q4}&lt;/math&gt;&lt;br&gt;[36] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,\tfrac{\sqrt{2}}{2},\tfrac{\sqrt{2}}{2})&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|2𝝅
|360°
|{{radic|0}}
|0
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: #E6FFEE;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/2}=2{12}]]{{Efn|name=dodecagon}}&lt;br&gt;[[File:Regular_star_figure_2(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2,q7}&lt;/math&gt;&lt;br&gt;[48] 4𝝅 {12}
|colspan=4|&lt;math&gt;[96]R_{q2,q7}&lt;/math&gt;{{Efn|The &lt;math&gt;[96]R_{q2,q7}&lt;/math&gt; isoclinic rotation in great hexagon invariant planes takes each vertex to a vertex one vertex away (60° {{=}} {{radic|1}} away), without passing through any intervening vertices. Each left square rotates 30° (like a wheel) at the same time that it tilts sideways by 30° (in an orthogonal central plane) into its corresponding right hexagon plane.{{Efn|name=hybrid isoclinic rotation}} Repeated 12 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq2,q7}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2}&lt;/math&gt;&lt;br&gt;[48] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,0,1)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/4}=4{6}]]&lt;br&gt;[[File:Regular_star_figure_4(6,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q7}&lt;/math&gt;&lt;br&gt;[48] 2𝝅 {6}
|colspan=4|&lt;math&gt;(\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})&lt;/math&gt;
|- style=&quot;background: #E6FFEE;&quot;|
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|3}}
|60°
|{{radic|1}}
|1
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2,-q2}&lt;/math&gt;&lt;br&gt;[9] 4𝝅 {2}
|colspan=4|&lt;math&gt;[18]R_{q2,-q2}&lt;/math&gt;{{Efn|The &lt;math&gt;[18]R_{q2,-q2}&lt;/math&gt; isoclinic rotation in great square invariant planes takes each vertex to a vertex 180° {{=}} {{radic|4}} away,{{Efn|name=quaternion group}} without passing through any intervening vertices. Each left square rotates 90° (like a wheel) at the same time that it tilts sideways by 90° (in an orthogonal central plane) into its corresponding right square plane, ''which in this rotation is the completely orthogonal plane''. Repeated 4 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq2,-q2}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2}&lt;/math&gt;&lt;br&gt;[9] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,0,1)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/6}=6{4}]]&lt;br&gt;[[File:Regular_star_figure_6(4,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q2}&lt;/math&gt;&lt;br&gt;[9] 2𝝅 {4}
|colspan=4|&lt;math&gt;(0,0,0,-1)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|𝝅
|180°
|{{radic|4}}
|2
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2,q1}&lt;/math&gt;&lt;br&gt;[12] 4𝝅 {2}
|colspan=4|&lt;math&gt;[12]R_{q2,q1}&lt;/math&gt;{{Efn|The &lt;math&gt;[12]R_{q2,q1}&lt;/math&gt; isoclinic rotation in great digon invariant planes takes each vertex to a vertex 90° {{=}} {{radic|2}} away, without passing through any intervening vertices.{{Efn|At the mid-point of the isocline arc (45° away) it passes directly over the mid-point of a 24-cell edge.}} Each left digon rotates 45° (like a wheel) at the same time that it tilts sideways by 45° (in an orthogonal central plane) into its corresponding right digon plane. Repeated 8 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq2,q1}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q2}&lt;/math&gt;&lt;br&gt;[12] 2𝝅 {2}
|colspan=4|&lt;math&gt;(0,0,0,1)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1}&lt;/math&gt;&lt;br&gt;[12] 2𝝅 {2}
|colspan=4|&lt;math&gt;(1,0,0,0)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/1}={24}]]&lt;br&gt;[[File:Regular_polygon_24.svg|100px]]&lt;br&gt;&lt;math&gt;^{q1,q1}&lt;/math&gt;&lt;br&gt;[0] 0𝝅 {1}
|colspan=4|&lt;math&gt;[1]R_{q1,q1}&lt;/math&gt;{{Efn|The &lt;math&gt;[1]R_{q1,q1}&lt;/math&gt; rotation is the ''identity operation'' of the 24-cell, in which no points move.|name=Rq1,q1}}
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1}&lt;/math&gt;&lt;br&gt;[0] 2𝝅 {2}
|colspan=4|&lt;math&gt;(1,0,0,0)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1}&lt;/math&gt;&lt;br&gt;[0] 2𝝅 {2}
|colspan=4|&lt;math&gt;(1,0,0,0)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|0
|0°
|{{radic|0}}
|0
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|- style=&quot;background: white;&quot;|
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1,-q1}&lt;/math&gt;&lt;br&gt;[12] 2𝝅 {2}
|colspan=4|&lt;math&gt;[1]R_{q1,-q1}&lt;/math&gt;{{Efn|The &lt;math&gt;[1]R_{q1,-q1}&lt;/math&gt; rotation is the ''central inversion'' of the 24-cell. This isoclinic rotation in great digon invariant planes takes each vertex to a vertex 180° {{=}} {{radic|4}} away,{{Efn|name=quaternion group}} without passing through any intervening vertices. Each left digon rotates 90° (like a wheel) at the same time that it tilts sideways by 90° (in an orthogonal central plane) into its corresponding right digon plane, ''which in this rotation is the completely orthogonal plane''. Repeated 4 times, this rotational displacement turns the 24-cell through 720° and returns it to its original orientation.|name=Rq1,-q1}} 
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{q1}&lt;/math&gt;&lt;br&gt;[12] 2𝝅 {2}
|colspan=4|&lt;math&gt;(1,0,0,0)&lt;/math&gt;
|rowspan=2|[[W:Icositetragon#Related polygons|{24/12}=12{2}]]&lt;br&gt;[[File:Regular_star_figure_12(2,1).svg|100px]]&lt;br&gt;&lt;math&gt;^{-q1}&lt;/math&gt;&lt;br&gt;[12] 2𝝅 {2}
|colspan=4|&lt;math&gt;(-1,0,0,0)&lt;/math&gt;
|- style=&quot;background: white;&quot;|
|𝝅
|180°
|{{radic|4}}
|2
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|{{sfrac|𝝅|2}}
|90°
|{{radic|2}}
|1.414~
|}

In a rotation class &lt;math&gt;[d]{R_{ql,qr}}&lt;/math&gt; each quaternion group &lt;math&gt;\pm{q_n}&lt;/math&gt; may be representative not only of its own fibration of Clifford parallel planes{{Efn|name=quaternion group}} but also of the other congruent fibrations.{{Efn|name=four hexagonal fibrations}} For example, rotation class &lt;math&gt;[4]R_{q7,q8}&lt;/math&gt; takes the 4 hexagon planes of &lt;math&gt;q7&lt;/math&gt; to the 4 hexagon planes of &lt;math&gt;q8&lt;/math&gt; which are 120° away, in an isoclinic rotation. But in a rigid rotation of this kind,{{Efn|name=invariant planes of an isoclinic rotation}} all [16] hexagon planes move in congruent rotational displacements, so this rotation class also includes &lt;math&gt;[4]R_{-q7,-q8}&lt;/math&gt;, &lt;math&gt;[4]R_{q8,q7}&lt;/math&gt; and &lt;math&gt;[4]R_{-q8,-q7}&lt;/math&gt;. The name &lt;math&gt;[16]R_{q7,q8}&lt;/math&gt; is the conventional representation for all [16] congruent plane displacements.

These rotation classes are all subclasses of &lt;math&gt;[32]R_{q7,q8}&lt;/math&gt; which has [32] distinct rotational displacements rather than [16] because there are two [[W:Chiral|chiral]] ways to perform any class of rotations, designated its ''left rotations'' and its ''right rotations''. The [16] left displacements of this class are not congruent with the [16] right displacements, but enantiomorphous like a pair of shoes.{{Efn|A ''right rotation'' is performed by rotating the left and right planes in the &quot;same&quot; direction, and a ''left rotation'' is performed by rotating left and right planes in &quot;opposite&quot; directions, according to the [[W:Right hand rule|right hand rule]] by which we conventionally say which way is &quot;up&quot; on each of the 4 coordinate axes. Left and right rotations are [[chiral]] enantiomorphous ''shapes'' (like a pair of shoes), not opposite rotational ''directions''. Both left and right rotations can be performed in either the positive or negative rotational direction (from left planes to right planes, or right planes to left planes), but that is an additional distinction.{{Efn|name=clasped hands}}|name=chirality versus direction}} Each left (or right) isoclinic rotation takes [16] left planes to [16] right planes, but the left and right planes correspond differently in the left and right rotations. The left and right rotational displacements of the same left plane take it to different right planes.

Each rotation class (table row) describes a distinct left (and right) [[#Isoclinic rotations|isoclinic rotation]]. The left (or right) rotations carry the left planes to the right planes simultaneously,{{Efn|name=plane movement in rotations}} through a characteristic rotation angle.{{Efn|name=two angles between central planes}} For example, the &lt;math&gt;[32]R_{q7,q8}&lt;/math&gt; rotation moves all [16] hexagonal planes at once by {{sfrac|2𝝅|3}} = 120° each. Repeated 6 times, this left (or right) isoclinic rotation moves each plane 720° and back to itself in the same [[W:Orientation entanglement|orientation]], passing through all 4 planes of the &lt;math&gt;q7&lt;/math&gt; left set and all 4 planes of the &lt;math&gt;q8&lt;/math&gt; right set once each.{{Efn|The &lt;math&gt;\pm q7&lt;/math&gt; and &lt;math&gt;\pm q8&lt;/math&gt; sets of planes are not disjoint; the union of any two of these four sets is a set of 6 planes. The left (versus right) isoclinic rotation of each of these rotation classes (table rows) visits a distinct left (versus right) circular sequence of the same set of 6 Clifford parallel planes.|name=union of q7 and q8}} The picture in the isocline column represents this union of the left and right plane sets. In the &lt;math&gt;[32]R_{q7,q8}&lt;/math&gt; example it can be seen as a set of 4 Clifford parallel skew [[W:Hexagram|hexagram]]s, each having one edge in each great hexagon plane, and skewing to the left (or right) at each vertex throughout the left (or right) isoclinic rotation.{{Efn|name=clasped hands}}

== Conclusions ==
Very few if any of the observations made in this paper are original, as I hope the citations demonstrate, but some new terminology has been introduced in making them. The term '''radially equilateral''' describes a uniform polytope with its edge length equal to its long radius, because such polytopes can be constructed, with their long radii, from equilateral triangles which meet at the center, each contributing two radii and an edge. The use of the noun '''isocline''', for the circular geodesic path traced by a vertex of a 4-polytope undergoing [[#Isoclinic rotations|isoclinic rotation]], may also be new in this context. The chord-path of an isocline may be called the 4-polytope's '''Clifford polygon''', as it is the skew polygonal shape of the rotational circles traversed by the 4-polytope's vertices in its characteristic [[W:Clifford displacement|Clifford displacement]].{{Sfn|Tyrrell|Semple|1971|loc=Linear Systems of Clifford Parallels|pp=34-57}}

== Acknowledgements ==
This paper is an extract of a [[24-cell|24-cell article]] collaboratively developed by Wikipedia editors. This version contains only those sections of the Wikipedia article which I authored, or which I completely rewrote. I have removed those sections principally authored by other Wikipedia editors, and illustrations and tables which I did not create myself, except for two essential rotating animations created by Wikipedia illustrator [[Wikipedia:User:JasonHise|JasonHise]] and one by Greg Egan which I have retained with attribution.{{Efn|I am the author of the footnotes to this article, except for quotations they contain. Images in tables and footnotes are from Wikimedia Commons, with attributions.}} Consequently, this version is not a complete treatment of the subject; it is missing some essential topics, and it is inadequately illustrated. As a subset of the collaboratively developed [[24-cell|24-cell article]] from which it was extracted, it is intended to gather in one place just what I have personally authored. Even so, it contains small fragments of which I am not the original author, and many editorial improvements by other Wikipedia editors. The original provenance of any sentence in this document may be ascertained precisely by consulting the complete revision history of the [[Wikipedia:24-cell]] article, in which I am identified as Wikipedia editor [[Wikipedia:User:Dc.samizdat|Dc.samizdat]].

Since I came to my own understanding of the 24-cell slowly, in the course of making additions to the [[Wikipedia:24-cell]] article, I am greatly indebted to the Wikipedia editors whose work on it preceded mine. Chief among these is Wikipedia editor [[W:User:Tomruen|Tomruen (Tom Ruen)]], the original author and principal illustrator of a great many of the Wikipedia articles on polytopes. The 24-cell article that I began with was already more accessible, to me, than even Coxeter's ''[[W:Regular Polytopes|Regular Polytopes]]'', or any other book treating the subject. I was inspired by the existence of Wikipedia articles on the 4-polytopes to study them more closely, and then became convinced by my own experience exploring this hypertext that the 4-polytopes could be understood much more readily, and could be documented most engagingly and comprehensively, if everything that researchers have discovered about them were incorporated into this single encyclopedic hypertext. Well-illustrated hypertext is naturally the most appropriate medium in which to describe a hyperspace, such as Euclidean 4-space. Another essential contributor to my dawning comprehension of 4-dimensional geometry was Wikipedia editor [[W:User:Cloudswrest|Cloudswrest (A.P. Goucher)]], who authored the section of the [[Wikipedia:24-cell]] article entitled ''[[24-cell#Cell rings|Cell rings]]'' describing the torus decomposition of the 24-cell into cell rings forming discrete Hopf fibrations, also studied by Banchoff.{{Sfn|Banchoff|2013|ps=, studied the decomposition of regular 4-polytopes into honeycombs of tori tiling the [[W:Clifford torus|Clifford torus]], showed how the honeycombs correspond to [[W:Hopf fibration|Hopf fibration]]s, and made a particular study of the [[#6-cell rings|24-cell's 4 rings of 6 octahedral cells]] with illustrations.}} Finally, J.E. Mebius's definitive Wikipedia article on ''[[W:SO(4)|SO(4)]]'', the group of ''[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]]'', informs this entire paper, which is essentially an explanation of the 24-cell's geometry as a function of its isoclinic rotations.

== Future work ==
The encyclopedia [[Wikipedia:Main_page|Wikipedia]] is not the only appropriate hypertext medium in which to explore and document the fourth dimension. Wikipedia rightly publishes only knowledge that can be sourced to previously published authorities. An encyclopedia cannot function as a research journal, in which is documented the broad, evolving edge of a field of knowledge, well before the observations made there have settled into a consensus of accepted facts. Moreover, an encyclopedia article must not become a textbook, or attempt to be the definitive whole story on a topic, or have too many footnotes! At some point in my enlargement of the [[Wikipedia:24-cell]] article, it began to transgress upon these limits, and other Wikipedia editors began to prune it back, appropriately for an encyclopedia article. I therefore sought out a home for expanded, more-than-encyclopedic versions of it and the other 4-polytope articles, where they could be enlarged by active researchers, beyond the scope of the Wikipedia encyclopedia articles.

Fortunately [[Main_page|Wikiversity]] provides just such a medium: an alternate hypertext web compatible with Wikipedia, but without the constraint of consisting of encyclopedia articles alone. A non-profit collaborative space for students and researchers, Wikiversity hosts all kinds of hypertext learning resources, such as hypertext textbooks which enlarge upon topics covered by Wikipedia, and research journals covering various fields of study which accept papers for peer review and publication. A hypertext article hosted at Wikiversity may contain links to any Wikipedia or Wikiversity article. This paper, for example, is hosted at Wikiversity, but most of its links are to Wikipedia encyclopedia articles.

Three consistent versions of the 24-cell article now exist, including this paper. The most complete version is the expanded [[24-cell]] article hosted at Wikiversity, which includes everything in the other two versions except these acknowledgments, plus additional learning resources. The original encyclopedia version, the [[Wikipedia:24-cell]] article, should rightly be an abridged version of the expanded Wikiversity [[24-cell]] article, from which extra content inappropriate for an encyclopedia article has been excluded.

== Notes ==
{{Regular convex 4-polytopes Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite book | last=Kepler | first=Johannes | author-link=W:Johannes Kepler | title=Harmonices Mundi (The Harmony of the World) | title-link=W:Harmonices Mundi | publisher=Johann Planck | year=1619}}
* {{Cite book | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1973 | orig-year=1948 | title=Regular Polytopes | publisher=Dover | place=New York | edition=3rd | title-link=W:Regular Polytopes (book) }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1991 | title=Regular Complex Polytopes | place=Cambridge | publisher=Cambridge University Press | edition=2nd }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1995 | title=Kaleidoscopes: Selected Writings of H.S.M. Coxeter | publisher=Wiley-Interscience Publication | edition=2nd | isbn=978-0-471-01003-6 | url=https://archive.org/details/kaleidoscopessel0000coxe | editor1-last=Sherk | editor1-first=F. Arthur | editor2-last=McMullen | editor2-first=Peter | editor3-last=Thompson | editor3-first=Anthony C. | editor4-last=Weiss | editor4-first=Asia Ivic | url-access=registration }}
** (Paper 3) H.S.M. Coxeter, ''Two aspects of the regular 24-cell in four dimensions''
** (Paper 22) H.S.M. Coxeter, ''Regular and Semi Regular Polytopes I'', [Math. Zeit. 46 (1940) 380–407, MR 2,10]
** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', [Math. Zeit. 188 (1985) 559-591]
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
* {{Cite book | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1968 | title=The Beauty of Geometry: Twelve Essays | publisher=Dover | place=New York | edition=2nd }}
* {{Cite journal | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1989 | title=Trisecting an Orthoscheme | journal=Computers Math. Applic. | volume=17 | issue=1–3 | pages=59–71 | doi=10.1016/0898-1221(89)90148-X | doi-access=free }}
* {{Citation | last=Coxeter | first=H.S.M. | author-link=W:Harold Scott MacDonald Coxeter | year=1970 | title=Twisted Honeycombs | place=Providence, Rhode Island | journal=Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics | publisher=American Mathematical Society | volume=4 }} 
* {{Cite journal|last=Stillwell|first=John|date=January 2001|title=The Story of the 120-Cell|url=https://www.ams.org/notices/200101/fea-stillwell.pdf|journal=Notices of the AMS|volume=48|issue=1|pages=17–25}}
* {{cite book|last=Banchoff|first=Thomas F.|chapter=Torus Decompostions of Regular Polytopes in 4-space|date=2013|title=Shaping Space|url=https://archive.org/details/shapingspaceexpl00sene|url-access=limited|pages=[https://archive.org/details/shapingspaceexpl00sene/page/n249 257]–266|editor-last=Senechal|editor-first=Marjorie|publisher=Springer New York|doi=10.1007/978-0-387-92714-5_20|isbn=978-0-387-92713-8}}
* {{Cite arXiv | eprint=1903.06971 | last=Copher | first=Jessica | year=2019 | title=Sums and Products of Regular Polytopes' Squared Chord Lengths | class=math.MG }}
*{{Citation | last=Goucher | first=A.P. | title=Spin groups | date=19 November 2019 | journal=Complex Projective 4-Space | url=https://cp4space.hatsya.com/2012/11/19/spin-groups/ }}
*{{Citation | last=Goucher | first=A.P. | title=Subsumptions of regular polytopes | date=1 October 2020 | journal=Complex Projective 4-Space | url=https://cp4space.hatsya.com/2020/10/01/subsumptions-of-regular-polytopes }}
* {{Cite thesis|url= http://resolver.tudelft.nl/uuid:dcffce5a-0b47-404e-8a67-9a3845774d89 |title=Symmetry groups of regular polytopes in three and four dimensions|last=van Ittersum |first=Clara|year=2020|publisher=[[W:Delft University of Technology|Delft University of Technology]]}}
* {{cite arXiv|last1=Kim|first1=Heuna|last2=Rote|first2=G.|date=2016|title=Congruence Testing of Point Sets in 4 Dimensions|class=cs.CG|eprint=1603.07269}}
* {{Cite journal|last1=Perez-Gracia|first1=Alba|last2=Thomas|first2=Federico|date=2017|title=On Cayley's Factorization of 4D Rotations and Applications|url=https://upcommons.upc.edu/bitstream/handle/2117/113067/1749-ON-CAYLEYS-FACTORIZATION-OF-4D-ROTATIONS-AND-APPLICATIONS.pdf|journal=Adv. Appl. Clifford Algebras|volume=27|pages=523–538|doi=10.1007/s00006-016-0683-9|hdl=2117/113067|s2cid=12350382|hdl-access=free}}
* {{Cite journal|last1=Waegell|first1=Mordecai|last2=Aravind|first2=P. K.|date=2009-11-12|title=Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem|journal=Journal of Physics A: Mathematical and Theoretical|volume=43|issue=10|page=105304|language=en|doi=10.1088/1751-8113/43/10/105304|arxiv=0911.2289|s2cid=118501180}}
* {{Cite book|title=Generalized Clifford parallelism|last1=Tyrrell|first1=J. A.|last2=Semple|first2=J.G.|year=1971|publisher=[[W:Cambridge University Press|Cambridge University Press]]|url=https://archive.org/details/generalizedcliff0000tyrr|isbn=0-521-08042-8}}
* {{Cite journal | last1=Mamone|first1=Salvatore | last2=Pileio|first2=Giuseppe | last3=Levitt|first3=Malcolm H. | year=2010 | title=Orientational Sampling Schemes Based on Four Dimensional Polytopes | journal=Symmetry | volume=2 |issue=3 | pages=1423–1449 | doi=10.3390/sym2031423 |bibcode=2010Symm....2.1423M |doi-access=free }}
* {{Cite thesis|title=Applications of Quaternions to Dynamical Simulation, Computer Graphics and Biomechanics|last=Mebius|first=Johan|date=July 2015|publisher=[[W:Delft University of Technology|Delft University of Technology]]|orig-date=11 Jan 1994|doi=10.13140/RG.2.1.3310.3205}}
* {{Cite book|title=Elementary particles and the laws of physics|last1=Feynman|first1=Richard|last2=Weinberg|first2=Steven|publisher=Cambridge University Press|year=1987}}
* {{Cite journal|last=Dorst|first=Leo|title=Conformal Villarceau Rotors|year=2019|journal=Advances in Applied Clifford Algebras|volume=29|issue=44|doi=10.1007/s00006-019-0960-5 |s2cid=253592159 |doi-access=free}}
* {{Cite journal|last1=Koca|first1=Mehmet|last2=Al-Ajmi|first2=Mudhahir|last3=Koc|first3=Ramazan|date=November 2007|title=Polyhedra obtained from Coxeter groups and quaternions|journal=Journal of Mathematical Physics|volume=48|issue=11|pages=113514|doi=10.1063/1.2809467|bibcode=2007JMP....48k3514K |url=https://www.researchgate.net/publication/234907424}}
* {{Citation|author-last=Hise|author-first=Jason|date=2011|author-link=W:User:JasonHise|title=A 3D projection of a 24-cell performing a simple rotation|title-link=Wikimedia:File:24-cell.gif|journal=Wikimedia Commons}}
* {{Citation|author-last=Hise|author-first=Jason|date=2007|author-link=W:User:JasonHise|title=A 3D projection of a 24-cell performing a double rotation|title-link=Wikimedia:File:24-cell-orig.gif|journal=Wikimedia Commons}}
* {{Citation|author-last=Egan|author-first=Greg|date=2019|title=A 24-cell containing red, green, and blue 16-cells performing a double rotation|title-link=Wikimedia:File:24-cell-3CP.gif|journal=Wikimedia Commons}}
* {{Cite web|last=Egan|first=Greg|date=23 December 2021|title=Symmetries and the 24-cell|url=https://www.gregegan.net/SCIENCE/24-cell/24-cell.html|author-link=W:Greg Egan|website=gregegan.net|access-date=10 October 2022}}
{{Refend}}</text>
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Analogous to hard and soft [[properties of Boolean functions]], there are also hard and soft permutations.

A permutation is '''hard''', when the domain is the infinite set of all Boolean functions. &amp;nbsp; &lt;small&gt;E.g. from BF to its complement.&lt;/small&gt;&lt;br&gt;
A permutation is '''soft''', when the domain is the finite set of BF with a given arity. &amp;nbsp; &lt;small&gt;E.g. from BF to its [[Zhegalkin twins|twin]]&lt;/small&gt;.

Interesting permutations of BF are often [[Walsh permutation]]s. Each corresponds to a compression matrix &lt;math&gt;2^{arity}&lt;/math&gt;.&lt;br&gt;
&lt;small&gt;The complement is a notable permutation that is not. &amp;nbsp; &lt;span style=&quot;opacity: .5;&quot;&gt;(Neither is the {{boolf-prop|dual}}, because it involves the complement.)&lt;/span&gt;&lt;/small&gt;

Each BF can be represented by its truth table or its Zhegalkin index.&lt;br&gt;
Therefore, each permutation of BF can be represented by four permutations of integers.&lt;br&gt;
If the permutation is hard, the corresponding permutation of Zhegalkin indices is infinite.

==[[Zhegalkin matrix|Zhegalkin permutation]]==

This is the soft permutation between [[Zhegalkin twins|twins]], linking truth tables and Zhegalkin indices.
Its compression matrix is the lower Sierpinski triangle.

{{Collapsible START|{{House number arity|3}}|collapsed wide}}
[[File:Zhegalkin 256.svg|1200px]]
{{Collapsible END}}

==Sierpinski permutation==

The {{boolf-prop|reverse}} is a hard permutation between BF.&lt;br&gt;
The permutation between their Zhegalkin indices is the Sierpinski permutation.&lt;br&gt;
Its compression matrix is the upper Sierpinski triangle.

[[c:Category:8-ary Walsh functions in octeract matrix]], [[Boolf prop/3-ary/reverse splice]]

{{Collapsible START|{{House number arity|3}}|collapsed wide}}
[[File:Reverse 3; Z to Z; long.svg|1200px]]
{{Collapsible END}}


==[[Lector and mentor of Boolean functions]]==

The mentor permutation might be called '''semi-hard''', because it is an infinite permutation between pairs of complements.

==[[Serration of Boolean functions]]==

The serrator permutation is hard.


[[Category:Studies of Boolean functions]]</text>
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==Introduction==
The theorem of continuity for linear mappings provides equivalent conditions for stiffness, with topology-producing functionals [[norms, metrics, topology|norms]], [[seminorm|seminorms]], [[gauge functional|gauge functionals]].
* '''[[/Normed spaces/|Normed spaces]] - TCN''' The theorem of continuity for normed spaces is a special case of the more general case for [[Topological vector space|topological vector spaces]] equivalent conditions are formulated for the stiffness of linear mappings over [[norms, metric, topology|norms]].
* '''[[/topological vector spaces/|Topological vector spaces]] - TCT''' This theorem generalizes the continuity of linear mapping for [[Topological vector space|topological vector spaces]] and [[gauge functionals]].

===Linear mappings - finite dimensional vector spaces===
A linear mapping &lt;math display=&quot;inline&quot;&gt;
  T: V\to W
&lt;/math&gt; of a finite dimensional vector space &lt;math display=&quot;inline&quot;&gt;
  V
&lt;/math&gt; over the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; into a vector space &lt;math display=&quot;inline&quot;&gt;
  W
&lt;/math&gt; over the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; is ''always continuous''.

===Linear mappings - not continuous===
Linear mapping &lt;math display=&quot;inline&quot;&gt;
  T: V\to W
&lt;/math&gt; of an infinite-dimensional &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt;-vector space &lt;math display=&quot;inline&quot;&gt;
  V
&lt;/math&gt; into a &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; vector space &lt;math display=&quot;inline&quot;&gt;
  W
&lt;/math&gt; are also not continuous (see Examples).

==Continuity for linear mapping - normed spaces==
Let &lt;math display=&quot;inline&quot;&gt;
  (X,\|\cdot\|_{X})
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (Y,\|\cdot\|_{Y})
&lt;/math&gt; normed spaces above the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; and

:&lt;math display=&quot;block&quot;&gt;
  T : X \rightarrow Y 
&lt;/math&gt; a linear mapping, the following statements are equivalent:
* (1) ''T'' is steady at every point &lt;math display=&quot;inline&quot;&gt;
  x \in X
&lt;/math&gt;
* (2) ''T'' is steady in the zero vector &lt;math display=&quot;inline&quot;&gt;
  0_{X} \in X
&lt;/math&gt;
* (3) There is a &lt;math display=&quot;inline&quot;&gt;
  M &gt; 0 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
   \| T(x) \|_{Y} \leq M 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  x \in X
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
  \| x \|_{X} \leq 1 
&lt;/math&gt;
* (4) There is a &lt;math display=&quot;inline&quot;&gt;
  M &gt; 0 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
   \| T(x) \|_{Y} \leq M \cdot \| x \|_{X} 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  x \in X
&lt;/math&gt;,

==Proof==
The [[/Normed Space/|proof of equivalence]] is performed by a [[w:en:Ringschluss|cycle of implications]] in the following way (1) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (2) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (3) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (4) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (1)

==Corrollary of TCN for bilinear mappings==
The theorem of continuity can be transfered to [[w:en:bilinear map|bilinear mappings]] and normed spaces:
Let &lt;math display=&quot;inline&quot;&gt;
  (X_1,\|\cdot\|_{X_1})
&lt;/math&gt;, &lt;math display=&quot;inline&quot;&gt;
  (X_2,\|\cdot\|_{X_2})
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (Y,\|\cdot\|_{Y})
&lt;/math&gt; normed spaces above the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; and

:&lt;math display=&quot;block&quot;&gt;
  T : X_1 \times X_2 \rightarrow Y 
&lt;/math&gt; a bilinear mapping, the following statements are equivalent:
* (1) ''T'' is steady at every point &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X_1 \times X_2 
&lt;/math&gt;
* (2) ''T'' is constantly in the zero vector &lt;math display=&quot;inline&quot;&gt;
  (0_{X_1}, 0_{X_2})\in X_1 \times X_2 
&lt;/math&gt;
* (3) There is a &lt;math display=&quot;inline&quot;&gt;
  M &gt; 0 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
   \| T(x_1,x_2) \|_{Y} \leq M 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
  \| (x_1,x_2) \| := \max \{ \|x_1\|_{X_1}, \|x_2\|_{X_2} \}\leq 1 
&lt;/math&gt;
* (4) There is a &lt;math display=&quot;inline&quot;&gt;
  M &gt; 0 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
   \| T(x_1,x_2) \|_{Y} \leq M \cdot \| x_1 \|_{X_1} \cdot \|x_2 \|_{X_2} 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X_1 \times X_2 
&lt;/math&gt;,

===Remark - Product space as vector space===
The product space &lt;math display=&quot;inline&quot;&gt;
  X_1 \times X_2 
&lt;/math&gt; is naturally converted into a &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt;-vector space through the following operations &lt;math display=&quot;inline&quot;&gt;
  \oplus , \ \odot 
&lt;/math&gt;:

:&lt;math display=&quot;block&quot;&gt;
   
  \begin{array}{rcl}
  (x_1,x_2) \oplus (y_1,y_2)
            &amp; := &amp;  
   (x_1+y_1,x_2+y_2) 
            \\
   \lambda \odot (x_1,x_2)
            &amp; := &amp; 
 (\lambda \cdot x_1, \lambda \cdot  x_2)
            \\
          \end{array}

&lt;/math&gt;
With &lt;math display=&quot;inline&quot;&gt;
  \| (x_1,x_2) \| := \max \{ \|x_1\|_{X_1}, \|x_2\|_{X_2} \} 
&lt;/math&gt; the product space &lt;math display=&quot;inline&quot;&gt;
  X_1 \times X_2 
&lt;/math&gt; also becomes a [[norms, metrics, topology|normed space]].

===Application of Corrolary===
It is helpful for the [[Topologization lemma for algebras|Topologization lemma for algebras]] to prove the stiffness to a point. scalar multiplication and the multiplication on the algebra are in this context [[w:en:bilineare mapping|bilineare mappings]]. For example, &lt;math display=&quot;inline&quot;&gt;
   ( X_1,\|\cdot \|_{_{X_1}} ) := (\mathbb{K}, |\cdot |)
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (X_2,\|\cdot \|_{_{X_2}} )  := (A, \|\cdot \|)
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
  \|\cdot \|:A\to \mathbb{R}_o^{+} 
&lt;/math&gt; are the [[w:en:Submultiplicativity|submultiplicative]] standard on the algebra &lt;math display=&quot;inline&quot;&gt;
  A
&lt;/math&gt;.

===Task - Proof Corollary===
Prove the above corollary using the ideas from the theorem of continuity for linear mappings on normed spaces. Notes:
* Use the equivalence of
&lt;math display=&quot;inline&quot;&gt;
  
  \begin{array}{rcl}
         \| (x_1,x_2) \|  &amp; := &amp; \max \{ \|x_1\|_{X_1}, \|x_2\|_{X_2} \}\leq 1 \\
         &amp;   \Longleftrightarrow  &amp;  \|x_1\|_{X_1} \leq 1 \wedge \|x_2\|_{X_2} \leq 1 \\         
          \end{array}
 
&lt;/math&gt;.
* Use the linearity in each component to estimate &lt;math display=&quot;inline&quot;&gt;
  (3) \to (4)
&lt;/math&gt;.

===Task - equivalence of norms - product space===
In the above corollar, a standard &lt;math display=&quot;inline&quot;&gt;
  \| (x_1,x_2) \| := \max \{ \|x_1\|_{X_1}, \|x_2\|_{X_2} \} 
&lt;/math&gt; is defined on &lt;math display=&quot;inline&quot;&gt;
  X_1 \times X_2 
&lt;/math&gt;. Show that &lt;math display=&quot;inline&quot;&gt;
  \| (x_1,x_2) \|_\ast :=  \|x_1\|_{X_1} + \|x_2\|_{X_2} 
&lt;/math&gt; is a [[Äquivalenz von norms|äquivalente Norm]] on &lt;math display=&quot;inline&quot;&gt;
  X_1 \times X_2 
&lt;/math&gt;.

==Operator standard==
The condition (4) from the stiffness set for linear mappings leads to the introduction of the operator space. This makes the vector space of the steady linear functions &lt;math display=&quot;inline&quot;&gt;
  \mathcal{L}_C(V,W)
&lt;/math&gt; a subset of all linear mappings &lt;math display=&quot;inline&quot;&gt;
  \mathcal{L}(V,W)
&lt;/math&gt; itself a normedn space. (the index &lt;math display=&quot;inline&quot;&gt;
  C
&lt;/math&gt; in &lt;math display=&quot;inline&quot;&gt;
  \mathcal{L}_C(V,W)
&lt;/math&gt; stands for &quot;continuous&quot;.

===Alternative statement===
Alternatively to (3), the statement can also be formulated as follows:
: There is a &lt;math display=&quot;inline&quot;&gt;
  M &gt; 0 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
   \| T \|_{\mathcal{L}} :=  \sup \{ \| T(x) \|_{Y} \, : \, \| x \|_{X} = 1 \} \leq M
&lt;/math&gt;
This is equivalent to
: 698-1047-1747202468649-341-68

===Definition: Operatornorm===
Be &lt;math display=&quot;inline&quot;&gt;
  (V,\|\cdot\|_V)
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (W,\|\cdot\|_W)
&lt;/math&gt; [[w:en:Normierter space|normed vector spaces]] above the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  \mathcal{L}(V,W):= \{T\colon V \to W \mid T\ \text{linear} \}
&lt;/math&gt; the set of linear mapping of (698-1047-174720246 is &lt;math display=&quot;inline&quot;&gt;
  T\colon V \rightarrow W
&lt;/math&gt; [[w:en:linearer Operator|linearer Operator]]. Then the operator standard

:&lt;math display=&quot;block&quot;&gt;
   \| {\cdot} \|_{\mathcal{L}} \;  \colon \; \mathcal{L}(V,W)  \to \mathbb{R}^+_0 \cup \{\infty\}
&lt;/math&gt;
concerning [[w:en:Norm (Mathematics)|Vektornormen]] &lt;math display=&quot;inline&quot;&gt;
  \| \cdot \|_V
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  \| \cdot \|_W
&lt;/math&gt; by

:&lt;math display=&quot;block&quot;&gt;
   \|T\|_{\mathcal{L}} := \inf \left\{ M\ge 0 \mid \forall v\in V\colon \|T(v)\|_W \le M \,\|v\|_V\right\}
&lt;/math&gt;
defined.

===Comments - Operatornorm===
The operator standard &lt;math display=&quot;inline&quot;&gt;
   \|T\|_{\mathcal{L}}
&lt;/math&gt; provides a smallest upper barrier for the stretching of vectors from the one-piece ball in &lt;math display=&quot;inline&quot;&gt;
  (X,\|\cdot \|_X)
&lt;/math&gt;.

===Linear mappings with finite definition range===
For finite-dimensional vector spaces, this distinction is not necessary because each finite-dimensional linear mapping is continuous.

====Task 1====
Prove the set that linear mappings with a finite definition range &lt;math display=&quot;inline&quot;&gt;
  V
&lt;/math&gt; are steady.

====Evidence====
Let&lt;math display=&quot;inline&quot;&gt;
  dim(V)=n
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  B=(b_1,\ldots , b_n)
&lt;/math&gt; have a base of nominated vectors for &lt;math display=&quot;inline&quot;&gt;
  V
&lt;/math&gt; (i.e. &lt;math display=&quot;inline&quot;&gt;
  \|b_k\|_V = 1
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
   k \in \{1,\ldots , n\}
&lt;/math&gt;.
* Use the statement (3) from the grade for linear mappings.
* Select &lt;math display=&quot;inline&quot;&gt;
  v
&lt;/math&gt; from the completed single ball &lt;math display=&quot;inline&quot;&gt;
   \overline{ B_1^{\|\cdot\|_V}(0_V) }
&lt;/math&gt;.
* Set &lt;math display=&quot;inline&quot;&gt;
  v
&lt;/math&gt; as [[w:en:Linearkombination|Linearkombination]] of the base vectors.
* Estimate the standard &lt;math display=&quot;inline&quot;&gt;
  \left\| T(v) \right\|_W
&lt;/math&gt;.

===Note: Stability and Standard Limitation===
For continuous linear mapping of a normaledn space &lt;math display=&quot;inline&quot;&gt;
  (V,\|\cdot\|_{V})
&lt;/math&gt; according to &lt;math display=&quot;inline&quot;&gt;
  (W,\|\cdot\|_{W})
&lt;/math&gt;, the image &lt;math display=&quot;inline&quot;&gt;
  T\left( \overline{B_1^{\|\cdot\|_{V}} (0_V) } \right)
&lt;/math&gt; of the completed single ball &lt;math display=&quot;inline&quot;&gt;
  \overline{B_1^{\|\cdot\|_{V}} (0_V) }
&lt;/math&gt; is limited to the standard (698-1047-174720246.

==Stability set for linear mapping on topological vector spaces==
Bee &lt;math display=&quot;inline&quot;&gt;
  (X,\|\cdot\|_{\mathcal{A}})
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (Y,\|\cdot\|_{\widetilde{\mathcal{A}}})
&lt;/math&gt; [[Topologischer vector space|topological vector spaces]] with the systems of [[gauge functional|topologieerzeugenden gauge functionals]] above the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; and

:&lt;math display=&quot;block&quot;&gt;
  T : X \rightarrow Y 
&lt;/math&gt; a linear mapping, the following statements are equivalent:
* (1) ''T'' is steady at every point &lt;math display=&quot;inline&quot;&gt;
  x \in X
&lt;/math&gt;
* (2) ''T'' is steady in the zero vector &lt;math display=&quot;inline&quot;&gt;
  0_{X} \in X
&lt;/math&gt;
* (3) &lt;math display=&quot;inline&quot;&gt;
  \forall_{ \widetilde{\alpha} \in \widetilde{\mathcal{A}} } \exists_{\alpha \in \mathcal{A}, \, M_{\alpha} &gt; 0 } \forall_{x\in X} \, : \, \| x \|_{\alpha} \leq 1 \Longrightarrow  \| T(x) \|_{\widetilde{\alpha}} \leq M_{\alpha} 
&lt;/math&gt;
* (4) &lt;math display=&quot;inline&quot;&gt;
  \forall_{ \widetilde{\alpha} \in \widetilde{\mathcal{A}} } \exists_{\alpha \in \mathcal{A}, \, M_{\alpha} &gt; 0 } \forall_{x\in X} \, : \,\| T(x) \|_{\widetilde{\alpha}} \leq M_{\alpha} \cdot \| x \|_{\alpha} 
&lt;/math&gt;,

==Proof SLAT==
Also the [[/topological vector spaces/|Stetigkeitssatz für Lineare mapping auf topologischen vector spaces (SLAT)]] becomes as
[[/topological vector spaces/|Ringschluss]] of (1) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (2) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (3) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (4) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (1).

==Korrollar SLAT for bilinear mappings==
The assessment of the stiffness rate applies analogously to [[w:en:bilineare mapping|bilineare mappings]] and normed spaces:
Bee &lt;math display=&quot;inline&quot;&gt;
  (X_1,\|\cdot\|_{\mathcal{A}_1})
&lt;/math&gt;, &lt;math display=&quot;inline&quot;&gt;
  (X_2,\|\cdot\|_{ \mathcal{A}_2} ) 
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (Y,\|\cdot\|_{\widetilde{\mathcal{A}}})
&lt;/math&gt; normed spaces above the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; and

:&lt;math display=&quot;block&quot;&gt;
  T : X_1 \times X_2 \rightarrow Y 
&lt;/math&gt; a bilinear mapping, the following statements are equivalent:
* (1) ''T'' is steady at every point &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X_1 \times X_2 
&lt;/math&gt;
* (2) 'T'' is steady in the zero vector &lt;math display=&quot;inline&quot;&gt;
  (0_{X_1}, 0_{X_2})\in X_1 \times X_2 
&lt;/math&gt;
(3) &lt;math display=&quot;inline&quot;&gt;
  \forall_{ \widetilde{\alpha} \in \widetilde{\mathcal{A}} } \exists_{\alpha_1 \in \mathcal{A}_1, \alpha_2 \in \mathcal{A}_2,\, M &gt; 0 } \forall_{(x_1,x_2) \in X_1\times X_2} \, :  \| T(x_1,x_2) \|_{\widetilde{\alpha}} \leq M 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X_1 \times X_2 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
  \| (x_1,x_2) \|_{(\alpha_1,\alpha_1)} := \max \{ \|x_1\|_{\alpha_1}, \|x_2\|_{\alpha_2} \}\leq 1 
&lt;/math&gt;
* (4) &lt;math display=&quot;inline&quot;&gt;
  \forall_{ \widetilde{\alpha} \in \widetilde{\mathcal{A}} } \exists_{\alpha_1 \in \mathcal{A}_1, \alpha_2 \in \mathcal{A}_2,\, M &gt; 0 } \forall_{(x_1,x_2) \in X_1\times X_2} \, : \,  \| T(x_1,x_2) \|_{\widetilde{\alpha}} \leq M \cdot \| x_1 \|_{\alpha_1} \cdot \|x_2 \|_{\alpha_2} 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X_1 \times X_2 
&lt;/math&gt;,

==measure functional and partial order==
The index quantities &lt;math display=&quot;inline&quot;&gt;
  I
&lt;/math&gt; of the nets are selected as a function of the index quantity of the measured functionals. &lt;math display=&quot;inline&quot;&gt;
   I:= \mathcal{A} \times \mathbb{R}^+ 
&lt;/math&gt; is a suitable choice (see [[gauge functionale und partielle Ordnung|gauge functionale und partielle Ordnung]].

==See also==
* [[/Normierte Räume/|Stetigkeitssatz für normed Räume]]
* [[/topological vector spaces/|Stetigkeitssatz für topological vector spaces]]
* [[w:en:bilineare mapping|bilineare mappings]]
* [[nets (Mathematics)|nets]]
* [[Functional Analysis/Hahn-Banach - normed Räume|Hahn-Banach - normed Räume]]
* [[Functional Analysis|Functional Analysis]]
* [[w:en:Kontraposition|Kontraposition]]
* [[norms,_Metriken,_topology#Def%3A_Konvergenz_im_normedn_space|Konvergenz in normedn Räumen]]
* [[normsäquivalenzsatz|normsäquivalenzsatz]]
* [[Measure Theory on topological spaces/Stetigkeit von mappings in topologischen Räumen|Stetigkeit in topologischen Räumen]]
* [[w:en:Submultiplikativität|Submultiplikativität]]
* [[Measure Theory on topological spaces|Measure Theory on topological spaces]]


== Page Information ==
=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Stetigkeitssatz%20f%C3%BCr%20lineare%20Abbildungen Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Stetigkeitssatz für lineare Abbildungen|Stetigkeitssatz für lineare Abbildungen]] 
* URL: https://de.wikiversity.org/wiki/Stetigkeitssatz%20f%C3%BCr%20lineare%20Abbildungen
* Date: 5/14/2025 8:05

&lt;span type=&quot;translate&quot; src=&quot;Stetigkeitssatz für lineare Abbildungen&quot; srclang=&quot;de&quot; date=&quot;5/14/2025&quot; time=&quot;8:05&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Stetigkeitssatz für lineare Abbildungen]]
&lt;/noinclude&gt;

[[Category:Theorems]]</text>
      <sha1>9uruyu2bgrcj3w01lx510mal8c2fxe6</sha1>
    </revision>
    <revision>
      <id>2720844</id>
      <parentid>2720843</parentid>
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        <id>6645</id>
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==Introduction==
The theorem of continuity for linear mappings provides equivalent conditions for stiffness, with topology-producing functionals [[norms, metrics, topology|norms]], [[seminorm|seminorms]], [[gauge functional|gauge functionals]].
* '''[[/Normed spaces/|Normed spaces]] - TCN''' The theorem of continuity for normed spaces is a special case of the more general case for [[Topological vector space|topological vector spaces]] equivalent conditions are formulated for the stiffness of linear mappings over [[norms, metric, topology|norms]].
* '''[[/topological vector spaces/|Topological vector spaces]] - TCT''' This theorem generalizes the continuity of linear mapping for [[Topological vector space|topological vector spaces]] and [[gauge functionals]].

===Linear mappings - finite dimensional vector spaces===
A linear mapping &lt;math display=&quot;inline&quot;&gt;
  T: V\to W
&lt;/math&gt; of a finite dimensional vector space &lt;math display=&quot;inline&quot;&gt;
  V
&lt;/math&gt; over the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; into a vector space &lt;math display=&quot;inline&quot;&gt;
  W
&lt;/math&gt; over the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; is ''always continuous''.

===Linear mappings - not continuous===
Linear mapping &lt;math display=&quot;inline&quot;&gt;
  T: V\to W
&lt;/math&gt; of an infinite-dimensional &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt;-vector space &lt;math display=&quot;inline&quot;&gt;
  V
&lt;/math&gt; into a &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; vector space &lt;math display=&quot;inline&quot;&gt;
  W
&lt;/math&gt; are also not continuous (see Examples).

==Continuity for linear mapping - normed spaces==
Let &lt;math display=&quot;inline&quot;&gt;
  (X,\|\cdot\|_{X})
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (Y,\|\cdot\|_{Y})
&lt;/math&gt; normed spaces above the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; and

:&lt;math display=&quot;block&quot;&gt;
  T : X \rightarrow Y 
&lt;/math&gt; a linear mapping, the following statements are equivalent:
* (1) ''T'' is steady at every point &lt;math display=&quot;inline&quot;&gt;
  x \in X
&lt;/math&gt;
* (2) ''T'' is steady in the zero vector &lt;math display=&quot;inline&quot;&gt;
  0_{X} \in X
&lt;/math&gt;
* (3) There is a &lt;math display=&quot;inline&quot;&gt;
  M &gt; 0 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
   \| T(x) \|_{Y} \leq M 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  x \in X
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
  \| x \|_{X} \leq 1 
&lt;/math&gt;
* (4) There is a &lt;math display=&quot;inline&quot;&gt;
  M &gt; 0 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
   \| T(x) \|_{Y} \leq M \cdot \| x \|_{X} 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  x \in X
&lt;/math&gt;,

==Proof==
The [[/Normed Space/|proof of equivalence]] is performed by a [[w:en:Ringschluss|cycle of implications]] in the following way (1) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (2) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (3) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (4) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (1)

==Corrollary of TCN for bilinear mappings==
The theorem of continuity can be transfered to [[w:en:bilinear map|bilinear mappings]] and normed spaces:
Let &lt;math display=&quot;inline&quot;&gt;
  (X_1,\|\cdot\|_{X_1})
&lt;/math&gt;, &lt;math display=&quot;inline&quot;&gt;
  (X_2,\|\cdot\|_{X_2})
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (Y,\|\cdot\|_{Y})
&lt;/math&gt; normed spaces above the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; and

:&lt;math display=&quot;block&quot;&gt;
  T : X_1 \times X_2 \rightarrow Y 
&lt;/math&gt; a bilinear mapping, the following statements are equivalent:
* (1) ''T'' is steady at every point &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X_1 \times X_2 
&lt;/math&gt;
* (2) ''T'' is constantly in the zero vector &lt;math display=&quot;inline&quot;&gt;
  (0_{X_1}, 0_{X_2})\in X_1 \times X_2 
&lt;/math&gt;
* (3) There is a &lt;math display=&quot;inline&quot;&gt;
  M &gt; 0 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
   \| T(x_1,x_2) \|_{Y} \leq M 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
  \| (x_1,x_2) \| := \max \{ \|x_1\|_{X_1}, \|x_2\|_{X_2} \}\leq 1 
&lt;/math&gt;
* (4) There is a &lt;math display=&quot;inline&quot;&gt;
  M &gt; 0 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
   \| T(x_1,x_2) \|_{Y} \leq M \cdot \| x_1 \|_{X_1} \cdot \|x_2 \|_{X_2} 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X_1 \times X_2 
&lt;/math&gt;,

===Remark - Product space as vector space===
The product space &lt;math display=&quot;inline&quot;&gt;
  X_1 \times X_2 
&lt;/math&gt; is naturally converted into a &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt;-vector space through the following operations &lt;math display=&quot;inline&quot;&gt;
  \oplus , \ \odot 
&lt;/math&gt;:

:&lt;math display=&quot;block&quot;&gt;
   
  \begin{array}{rcl}
  (x_1,x_2) \oplus (y_1,y_2)
            &amp; := &amp;  
   (x_1+y_1,x_2+y_2) 
            \\
   \lambda \odot (x_1,x_2)
            &amp; := &amp; 
 (\lambda \cdot x_1, \lambda \cdot  x_2)
            \\
          \end{array}

&lt;/math&gt;
With &lt;math display=&quot;inline&quot;&gt;
  \| (x_1,x_2) \| := \max \{ \|x_1\|_{X_1}, \|x_2\|_{X_2} \} 
&lt;/math&gt; the product space &lt;math display=&quot;inline&quot;&gt;
  X_1 \times X_2 
&lt;/math&gt; also becomes a [[norms, metrics, topology|normed space]].

===Application of Corrolary===
It is helpful for the [[Topologization lemma for algebras|Topologization lemma for algebras]] to prove the stiffness to a point. scalar multiplication and the multiplication on the algebra are in this context [[w:en:bilineare mapping|bilineare mappings]]. For example, &lt;math display=&quot;inline&quot;&gt;
   ( X_1,\|\cdot \|_{_{X_1}} ) := (\mathbb{K}, |\cdot |)
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (X_2,\|\cdot \|_{_{X_2}} )  := (A, \|\cdot \|)
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
  \|\cdot \|:A\to \mathbb{R}_o^{+} 
&lt;/math&gt; are the [[w:en:Submultiplicativity|submultiplicative]] standard on the algebra &lt;math display=&quot;inline&quot;&gt;
  A
&lt;/math&gt;.

===Task - Proof Corollary===
Prove the above corollary using the ideas from the theorem of continuity for linear mappings on normed spaces. Notes:
* Use the equivalence of
&lt;math display=&quot;inline&quot;&gt;
  
  \begin{array}{rcl}
         \| (x_1,x_2) \|  &amp; := &amp; \max \{ \|x_1\|_{X_1}, \|x_2\|_{X_2} \}\leq 1 \\
         &amp;   \Longleftrightarrow  &amp;  \|x_1\|_{X_1} \leq 1 \wedge \|x_2\|_{X_2} \leq 1 \\         
          \end{array}
 
&lt;/math&gt;.
* Use the linearity in each component to estimate &lt;math display=&quot;inline&quot;&gt;
  (3) \to (4)
&lt;/math&gt;.

===Task - equivalence of norms - product space===
In the above corollar, a standard &lt;math display=&quot;inline&quot;&gt;
  \| (x_1,x_2) \| := \max \{ \|x_1\|_{X_1}, \|x_2\|_{X_2} \} 
&lt;/math&gt; is defined on &lt;math display=&quot;inline&quot;&gt;
  X_1 \times X_2 
&lt;/math&gt;. Show that &lt;math display=&quot;inline&quot;&gt;
  \| (x_1,x_2) \|_\ast :=  \|x_1\|_{X_1} + \|x_2\|_{X_2} 
&lt;/math&gt; is a [[Äquivalenz von norms|äquivalente Norm]] on &lt;math display=&quot;inline&quot;&gt;
  X_1 \times X_2 
&lt;/math&gt;.

==Operator standard==
The condition (4) from the stiffness set for linear mappings leads to the introduction of the operator space. This makes the vector space of the steady linear functions &lt;math display=&quot;inline&quot;&gt;
  \mathcal{L}_C(V,W)
&lt;/math&gt; a subset of all linear mappings &lt;math display=&quot;inline&quot;&gt;
  \mathcal{L}(V,W)
&lt;/math&gt; itself a normedn space. (the index &lt;math display=&quot;inline&quot;&gt;
  C
&lt;/math&gt; in &lt;math display=&quot;inline&quot;&gt;
  \mathcal{L}_C(V,W)
&lt;/math&gt; stands for &quot;continuous&quot;.

===Alternative statement===
Alternatively to (3), the statement can also be formulated as follows:
: There is a &lt;math display=&quot;inline&quot;&gt;
  M &gt; 0 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
   \| T \|_{\mathcal{L}} :=  \sup \{ \| T(x) \|_{Y} \, : \, \| x \|_{X} = 1 \} \leq M
&lt;/math&gt;
This is equivalent to
: 698-1047-1747202468649-341-68

===Definition: Operatornorm===
Be &lt;math display=&quot;inline&quot;&gt;
  (V,\|\cdot\|_V)
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (W,\|\cdot\|_W)
&lt;/math&gt; [[w:en:Normierter space|normed vector spaces]] above the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  \mathcal{L}(V,W):= \{T\colon V \to W \mid T\ \text{linear} \}
&lt;/math&gt; the set of linear mapping of (698-1047-174720246 is &lt;math display=&quot;inline&quot;&gt;
  T\colon V \rightarrow W
&lt;/math&gt; [[w:en:linearer Operator|linearer Operator]]. Then the operator standard

:&lt;math display=&quot;block&quot;&gt;
   \| {\cdot} \|_{\mathcal{L}} \;  \colon \; \mathcal{L}(V,W)  \to \mathbb{R}^+_0 \cup \{\infty\}
&lt;/math&gt;
concerning [[w:en:Norm (Mathematics)|Vektornormen]] &lt;math display=&quot;inline&quot;&gt;
  \| \cdot \|_V
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  \| \cdot \|_W
&lt;/math&gt; by

:&lt;math display=&quot;block&quot;&gt;
   \|T\|_{\mathcal{L}} := \inf \left\{ M\ge 0 \mid \forall v\in V\colon \|T(v)\|_W \le M \,\|v\|_V\right\}
&lt;/math&gt;
defined.

===Comments - Operatornorm===
The operator standard &lt;math display=&quot;inline&quot;&gt;
   \|T\|_{\mathcal{L}}
&lt;/math&gt; provides a smallest upper barrier for the stretching of vectors from the one-piece ball in &lt;math display=&quot;inline&quot;&gt;
  (X,\|\cdot \|_X)
&lt;/math&gt;.

===Linear mappings with finite definition range===
For finite-dimensional vector spaces, this distinction is not necessary because each finite-dimensional linear mapping is continuous.

====Task 1====
Prove the set that linear mappings with a finite definition range &lt;math display=&quot;inline&quot;&gt;
  V
&lt;/math&gt; are steady.

====Evidence====
Let&lt;math display=&quot;inline&quot;&gt;
  dim(V)=n
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  B=(b_1,\ldots , b_n)
&lt;/math&gt; have a base of nominated vectors for &lt;math display=&quot;inline&quot;&gt;
  V
&lt;/math&gt; (i.e. &lt;math display=&quot;inline&quot;&gt;
  \|b_k\|_V = 1
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
   k \in \{1,\ldots , n\}
&lt;/math&gt;.
* Use the statement (3) from the grade for linear mappings.
* Select &lt;math display=&quot;inline&quot;&gt;
  v
&lt;/math&gt; from the completed single ball &lt;math display=&quot;inline&quot;&gt;
   \overline{ B_1^{\|\cdot\|_V}(0_V) }
&lt;/math&gt;.
* Set &lt;math display=&quot;inline&quot;&gt;
  v
&lt;/math&gt; as [[w:en:Linearkombination|Linearkombination]] of the base vectors.
* Estimate the standard &lt;math display=&quot;inline&quot;&gt;
  \left\| T(v) \right\|_W
&lt;/math&gt;.

===Note: Stability and Standard Limitation===
For continuous linear mapping of a normaledn space &lt;math display=&quot;inline&quot;&gt;
  (V,\|\cdot\|_{V})
&lt;/math&gt; according to &lt;math display=&quot;inline&quot;&gt;
  (W,\|\cdot\|_{W})
&lt;/math&gt;, the image &lt;math display=&quot;inline&quot;&gt;
  T\left( \overline{B_1^{\|\cdot\|_{V}} (0_V) } \right)
&lt;/math&gt; of the completed single ball &lt;math display=&quot;inline&quot;&gt;
  \overline{B_1^{\|\cdot\|_{V}} (0_V) }
&lt;/math&gt; is limited to the standard (698-1047-174720246.

==Stability set for linear mapping on topological vector spaces==
Bee &lt;math display=&quot;inline&quot;&gt;
  (X,\|\cdot\|_{\mathcal{A}})
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (Y,\|\cdot\|_{\widetilde{\mathcal{A}}})
&lt;/math&gt; [[Topologischer vector space|topological vector spaces]] with the systems of [[gauge functional|topologieerzeugenden gauge functionals]] above the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; and

:&lt;math display=&quot;block&quot;&gt;
  T : X \rightarrow Y 
&lt;/math&gt; a linear mapping, the following statements are equivalent:
* (1) ''T'' is steady at every point &lt;math display=&quot;inline&quot;&gt;
  x \in X
&lt;/math&gt;
* (2) ''T'' is steady in the zero vector &lt;math display=&quot;inline&quot;&gt;
  0_{X} \in X
&lt;/math&gt;
* (3) &lt;math display=&quot;inline&quot;&gt;
  \forall_{ \widetilde{\alpha} \in \widetilde{\mathcal{A}} } \exists_{\alpha \in \mathcal{A}, \, M_{\alpha} &gt; 0 } \forall_{x\in X} \, : \, \| x \|_{\alpha} \leq 1 \Longrightarrow  \| T(x) \|_{\widetilde{\alpha}} \leq M_{\alpha} 
&lt;/math&gt;
* (4) &lt;math display=&quot;inline&quot;&gt;
  \forall_{ \widetilde{\alpha} \in \widetilde{\mathcal{A}} } \exists_{\alpha \in \mathcal{A}, \, M_{\alpha} &gt; 0 } \forall_{x\in X} \, : \,\| T(x) \|_{\widetilde{\alpha}} \leq M_{\alpha} \cdot \| x \|_{\alpha} 
&lt;/math&gt;,

==Proof SLAT==
Also the [[/topological vector spaces/|Stetigkeitssatz für Lineare mapping auf topologischen vector spaces (SLAT)]] becomes as
[[/topological vector spaces/|Ringschluss]] of (1) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (2) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (3) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (4) &lt;math display=&quot;inline&quot;&gt;
  \Rightarrow
&lt;/math&gt; (1).

==Korrollar SLAT for bilinear mappings==
The assessment of the stiffness rate applies analogously to [[w:en:bilineare mapping|bilineare mappings]] and normed spaces:
Bee &lt;math display=&quot;inline&quot;&gt;
  (X_1,\|\cdot\|_{\mathcal{A}_1})
&lt;/math&gt;, &lt;math display=&quot;inline&quot;&gt;
  (X_2,\|\cdot\|_{ \mathcal{A}_2} ) 
&lt;/math&gt; and &lt;math display=&quot;inline&quot;&gt;
  (Y,\|\cdot\|_{\widetilde{\mathcal{A}}})
&lt;/math&gt; normed spaces above the field &lt;math display=&quot;inline&quot;&gt;
  \mathbb{K}
&lt;/math&gt; and

:&lt;math display=&quot;block&quot;&gt;
  T : X_1 \times X_2 \rightarrow Y 
&lt;/math&gt; a bilinear mapping, the following statements are equivalent:
* (1) ''T'' is steady at every point &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X_1 \times X_2 
&lt;/math&gt;
* (2) ''T'' is steady in the zero vector &lt;math display=&quot;inline&quot;&gt;
  (0_{X_1}, 0_{X_2})\in X_1 \times X_2 
&lt;/math&gt;
(3) &lt;math display=&quot;inline&quot;&gt;
  \forall_{ \widetilde{\alpha} \in \widetilde{\mathcal{A}} } \exists_{\alpha_1 \in \mathcal{A}_1, \alpha_2 \in \mathcal{A}_2,\, M &gt; 0 } \forall_{(x_1,x_2) \in X_1\times X_2} \, :  \| T(x_1,x_2) \|_{\widetilde{\alpha}} \leq M 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X_1 \times X_2 
&lt;/math&gt; with &lt;math display=&quot;inline&quot;&gt;
  \| (x_1,x_2) \|_{(\alpha_1,\alpha_1)} := \max \{ \|x_1\|_{\alpha_1}, \|x_2\|_{\alpha_2} \}\leq 1 
&lt;/math&gt;
* (4) &lt;math display=&quot;inline&quot;&gt;
  \forall_{ \widetilde{\alpha} \in \widetilde{\mathcal{A}} } \exists_{\alpha_1 \in \mathcal{A}_1, \alpha_2 \in \mathcal{A}_2,\, M &gt; 0 } \forall_{(x_1,x_2) \in X_1\times X_2} \, : \,  \| T(x_1,x_2) \|_{\widetilde{\alpha}} \leq M \cdot \| x_1 \|_{\alpha_1} \cdot \|x_2 \|_{\alpha_2} 
&lt;/math&gt; for all &lt;math display=&quot;inline&quot;&gt;
  (x_1,x_2) \in X_1 \times X_2 
&lt;/math&gt;,

==measure functional and partial order==
The index quantities &lt;math display=&quot;inline&quot;&gt;
  I
&lt;/math&gt; of the nets are selected as a function of the index quantity of the measured functionals. &lt;math display=&quot;inline&quot;&gt;
   I:= \mathcal{A} \times \mathbb{R}^+ 
&lt;/math&gt; is a suitable choice (see [[gauge functionale und partielle Ordnung|gauge functionale und partielle Ordnung]].

==See also==
* [[/Normierte Räume/|Stetigkeitssatz für normed Räume]]
* [[/topological vector spaces/|Stetigkeitssatz für topological vector spaces]]
* [[w:en:bilineare mapping|bilineare mappings]]
* [[nets (Mathematics)|nets]]
* [[Functional Analysis/Hahn-Banach - normed Räume|Hahn-Banach - normed Räume]]
* [[Functional Analysis|Functional Analysis]]
* [[w:en:Kontraposition|Kontraposition]]
* [[norms,_Metriken,_topology#Def%3A_Konvergenz_im_normedn_space|Konvergenz in normedn Räumen]]
* [[normsäquivalenzsatz|normsäquivalenzsatz]]
* [[Measure Theory on topological spaces/Stetigkeit von mappings in topologischen Räumen|Stetigkeit in topologischen Räumen]]
* [[w:en:Submultiplikativität|Submultiplikativität]]
* [[Measure Theory on topological spaces|Measure Theory on topological spaces]]


== Page Information ==
=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Stetigkeitssatz%20f%C3%BCr%20lineare%20Abbildungen Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Stetigkeitssatz für lineare Abbildungen|Stetigkeitssatz für lineare Abbildungen]] 
* URL: https://de.wikiversity.org/wiki/Stetigkeitssatz%20f%C3%BCr%20lineare%20Abbildungen
* Date: 5/14/2025 8:05

&lt;span type=&quot;translate&quot; src=&quot;Stetigkeitssatz für lineare Abbildungen&quot; srclang=&quot;de&quot; date=&quot;5/14/2025&quot; time=&quot;8:05&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Stetigkeitssatz für lineare Abbildungen]]
&lt;/noinclude&gt;

[[Category:Theorems]]</text>
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      <text bytes="114" sha1="qbybt4euvvws7nsbmbom4jj1yzlfzl5" xml:space="preserve">&lt;big&gt;&lt;big&gt;&lt;big&gt;&lt;big&gt;&lt;big&gt;&lt;big&gt;Zubaer Hossain Kaif&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;
{{#babel:plain=1|bn-N|en-2}}</text>
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      <text bytes="935" sha1="15hz3xflbtiqmdiq5qe4p8p7ght6kbt" xml:space="preserve">=== How to make a participant page ===

# go to the  [[AIXworkbench/Working-Groups/June-2025-Working-Group/Participants/Template|Participant Template]] page, click edit, select all, copy.

# Create your own page at: &lt;code&gt;AIXworkbench/Working-Groups/June-2025-Working-Group/Participants/YourName&lt;/code&gt;, press return, &quot;Create&quot; [[File:Screenshot of editing wikiversity page.png|center|100%|thumb|Screenshot showing how to nane url]]
# paste the contents of your buffer (step 1), save the page, and then re-edit it to update the contents.

''This [https://www.youtube.com/watch?v=hRyLD4nQMB8 video] provides a step-by-step walkthrough for creating a participant page for this project''

== Participants ==
&lt;div style=&quot;border: 2px solid #a3d3ff; background-color: #f0f8ff; padding: 15px; margin: 10px 0;&quot;&gt;

{{Special:PrefixIndex/AIXworkbench/Working-Groups/June-2025-Working-Group/Participants|hideroot=1|stripprefix=1|columns=1}}

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      <text bytes="30220" sha1="ebtimxhxvkuyqaysmmuumblxwymakn2" xml:space="preserve">== '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' =

== '''8.1 Purpose''' ==

This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated.

== '''8.2 Toolchain and Workflow''' ==

AI tools like ChatGPT are used to analyze, compare, and refine theories

Tables and frameworks are generated collaboratively using open formats

Contributors submit input via email or editing suggestions

Ratings and evaluations are dynamically updated based on ongoing analysis

== '''8.3 AI-Based Rating System: Motivation and Procedure''' ==

To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''.

This system is designed to be:

Transparent – Each rating is justified through AI’s large-scale reference analysis.

Dynamic – Contributors may submit additional materials to request re-evaluation.

Consistent – All evaluations are performed by the same AI logic, eliminating personal bias.

Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted.

This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate.

== '''8.4 Open Participation''' ==

This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to:

Describe their framework in terms of assumptions, predictions, and compatibility

Suggest how their model could be tested or falsified

Provide references or original materials for AI evaluation

All analysis is open, and contributors may propose improvements at any time.

== '''8.5 Understanding the Star Ratings''' ==

The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied.

'''8.5.1. Empirical Adequacy'''  
Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower.

'''8.5.2. Internal Consistency'''  
Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions.

'''8.5.3. Predictive Power'''  
Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings.

'''8.5.4. Cross-Disciplinary Compatibility'''  
Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score.

'''8.5.5. Conceptual Clarity and Simplicity'''  
Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification.

'''8.5.6. Heuristic Value'''  
Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential.

'''8.5.7. Historical and Philosophical Insight'''  
Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here.

'''8.5.8. Mathematical Rigor'''  
Does the theory provide clear mathematical formulations, derivations, and quantitative predictions? Theories are valued for their use of equations to express core principles, ensure internal consistency, and generate testable results.


Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail.


=== '''8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor)''' ===

''Note: In July 2025, an eighth evaluation criterion was added: '''Mathematical Rigor'''. The total score is now out of 40 stars instead of 35.  ''
''All ratings are expressed in whole stars (★), without fractional values, to ensure clarity in display and consistency with the visual format of this table.''  
''Theories are listed in the same order as in Section 8.8.''

{| class=&quot;wikitable&quot;
! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HP''' !! '''MR''' !! '''Total (★/40)'''
|-
| '''General Relativity''' || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || ★★★★★ || '''37'''
|-
| '''Newtonian Gravity''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''33'''
|-
| '''MOND''' || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || '''26'''
|-
| '''Emergent Gravity''' || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''24'''
|-
| '''Big Bang''' || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || '''35'''
|-
| '''Steady State Theory''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23'''
|-
| '''Big Crunch''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Big Bounce''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Cosmic Influx Theory (CIT)''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || '''33'''
|-
| '''Spiral Cosmology''' || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''21'''
|}

''Legend:''  
''EA = Empirical Adequacy IC = Internal Consistency PP = Predictive Power CC = Cross-Disciplinary Compatibility  ''
''CS = Conceptual Simplicity HV = Heuristic Value HP = Historical/Philosophical Insight MR = Mathematical Rigor''


&lt;!-- Add a blank line here --&gt;

== '''8.7 Requesting Detailed Justification''' ==

“Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by:

1. Visiting the '''discussion page''' of this Wikiversity chapter.
  
2. Mentioning the theory by name and explicitly asking for the detailed breakdown.
  
3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. 

These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented.

If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership.

'''Mainstream theories are subject to the same critical standard.'''  
If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed.

If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''.

== '''8.8 Detailed Evaluations of Theories''' ==

This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes.

=== '''8.8.1 General Relativity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Matches a wide range of observations: gravitational lensing, GPS corrections, perihelion precession, black hole dynamics, and gravitational waves. Supported by multiple experiments. || ★★★★★
|-
| '''Internal Consistency''' || Highly consistent within its differential geometric framework. Built upon Einstein's field equations with tensor calculus. Few internal contradictions, though extensions (e.g. quantum gravity) face challenges. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted gravitational redshift, time dilation, frame-dragging, and gravitational waves. Continues to guide observations in astrophysics. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with cosmology and astrophysics. Some tension with quantum theory. Less integrated with planetary geology or biology. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex mathematical structure makes it less intuitive. Conceptually abstract (spacetime curvature, geodesics). Clarity improves with education, but simplicity is low. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired vast developments in cosmology, black hole theory, and relativistic astrophysics. Foundation for modern gravitational physics. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Deep philosophical implications about space, time, and causality. Represents a major shift from Newtonian absolute space. Influenced 20th-century philosophy of science. || ★★★★★
|-
| '''Mathematical Rigor''' || Built upon advanced mathematics: Riemannian geometry, Einstein field equations, tensor calculus. Equations are precise, formal, and deeply embedded in differential geometry. || ★★★★★
|}

'''Total: 39/40'''

=== '''8.8.2 Newtonian Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Accurately describes gravitational interactions for most macroscopic systems (planets, satellites, projectiles) under low-speed, weak-field conditions. Deviates in extreme conditions (e.g. near black holes). || ★★★★☆
|-
| '''Internal Consistency''' || Mathematically self-consistent with inverse-square law and Newton's laws of motion. Assumes instantaneous action at a distance, which conflicts with relativity. || ★★★★☆
|-
| '''Predictive Power''' || Predicts planetary orbits, tides, escape velocities, and Keplerian motion. Fails for relativistic effects (e.g. Mercury’s precession, gravitational lensing). || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Well-integrated in classical mechanics, astronomy, and engineering. Less compatible with modern cosmology or relativistic frameworks. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple and intuitive: gravity as a force between masses. Easily grasped and widely taught. || ★★★★★
|-
| '''Heuristic Value''' || Inspired centuries of scientific discovery and classical mechanics. Still used in teaching and engineering. Limited in modern theoretical development. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Founded classical physics. Major leap in scientific method and mathematical modeling. Paved the way for Enlightenment-era science. || ★★★★★
|-
| '''Mathematical Rigor''' || Clear and elegant use of calculus and vector algebra (e.g. \(\displaystyle F = G \frac{m_1 m_2}{r^2}\)). Highly accessible and historically groundbreaking, but lacks deeper geometric or relativistic structures. || ★★★★☆
|}

'''Total: 33/40'''

=== '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Fits galactic rotation curves without invoking dark matter. Matches Tully-Fisher relation. Performance weakens at cluster and cosmological scales. || ★★★★☆
|-
| '''Internal Consistency''' || Original formulation is non-relativistic and phenomenological. Several relativistic extensions (e.g. TeVeS) exist but introduce complexity and fine-tuning. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts galaxy dynamics from baryonic matter alone. Less predictive at larger scales or in non-galactic contexts. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Primarily astrophysical. Some tension with cosmology, structure formation, and gravitational lensing. Not aligned with particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple at galactic scale: modifies acceleration below a threshold \(a_0\). Extensions are less intuitive. || ★★★★☆
|-
| '''Heuristic Value''' || Challenges dark matter paradigm and motivates alternate gravity models. Sparked theoretical and observational debate. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Offers a conceptual challenge to Newton/Einstein gravity. Philosophically provocative, but limited historical lineage. || ★★★☆☆
|-
| '''Mathematical Rigor''' || Employs interpolating functions and modified Poisson equations. Relativistic extensions (e.g. TeVeS) involve tensor-vector-scalar frameworks. Rigorous in parts, but lacks unified formalism. || ★★★☆☆
|}

'''Total: 28/40'''

=== '''8.8.4 Emergent Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Entropic_gravity Emergent / Entropic Gravity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Attempts to account for galactic rotation without dark matter by linking gravity to entropy and information. Some results match MOND-like behavior, but broad observational support remains limited. || ★★★☆☆
|-
| '''Internal Consistency''' || Theoretical framework draws from thermodynamics, holography, and information theory. Conceptually coherent, but not fully developed as a unified physical model. || ★★★☆☆
|-
| '''Predictive Power''' || Offers qualitative insights but lacks precise predictive capabilities in most contexts. No wide adoption for simulations or system modeling. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates ideas from black hole thermodynamics, quantum information, and spacetime geometry. Weak integration with observational astronomy or geology. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Abstract and speculative. Concepts like entropic forces and holographic screens are not intuitive for most readers. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates discussion about the nature of spacetime and gravity. Has inspired new theoretical directions in quantum gravity and information theory. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Philosophically intriguing: redefines gravity as emergent rather than fundamental. Links to ideas from Bekenstein and Hawking. || ★★★★☆
|-
| '''Mathematical Rigor''' || Relies on concepts from thermodynamics (e.g. entropy gradients), statistical mechanics, and quantum gravity. Uses integral relations and variational principles, but lacks a standardized set of equations for general use. || ★★★☆☆
|}

'''Total: 26/40'''

=== '''8.8.5 Big Bang – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strongly supported by cosmic microwave background (CMB), redshift-distance relation (Hubble law), and light element abundances (BBN). Matches large-scale structure data. || ★★★★★
|-
| '''Internal Consistency''' || Internally coherent within ΛCDM framework, but requires inflation, dark matter, and dark energy as add-ons. Ongoing tensions (e.g. Hubble constant) exist. || ★★★★☆
|-
| '''Predictive Power''' || Predicts relative abundances of H, He, and Li; CMB anisotropies; and cosmic redshift patterns. Inflationary models extend this with testable signatures. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Integrated with particle physics, astrophysics, and thermodynamics. Weak links to geology or planetary science. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Early universe models are mathematically tractable but conceptually dense (singularity, inflation, horizon problem). Requires non-observable initial conditions. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired decades of cosmological research, observations, and satellite missions. Drives development of new models (e.g. inflation, dark sector). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Marks a shift from steady-state models to dynamic cosmology. Raises deep questions about origins, causality, and the nature of time. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on solutions to Einstein’s field equations (e.g. FLRW metric), Friedmann equations, and thermodynamic models. Uses differential equations and relativistic cosmology extensively. || ★★★★★
|}

'''Total: 38/40'''

=== '''8.8.6 Steady State Theory – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Cosmology]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Early successes with radio‐source counts, but contradicted by the cosmic microwave background, evolving galaxy populations, and quasar statistics. || ★★☆☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within the “perfect cosmological principle,” requiring continuous matter creation at a fixed rate. Logical but invokes an ad-hoc creation field (C-field). || ★★★☆☆
|-
| '''Predictive Power''' || Predicted constant large-scale density and specific radio‐source number counts; few successful novel predictions beyond its initial scope. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Limited overlap with modern astrophysics and particle physics; conflicts with nucleosynthesis and CMB observations. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively simple: Universe is homogeneous in space **and** time, avoiding an initial singularity. Minimal parameter set. || ★★★★☆
|-
| '''Heuristic Value''' || Historically spurred observational tests that ultimately favored Big Bang models; now mainly of pedagogical interest. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Embodies the perfect cosmological principle and continuous-creation idea, provoking debates on temporality and cosmological assumptions. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs Friedmann-like solutions with a creation term; uses relativistic field equations but lacks the richer formal development of ΛCDM or GR extensions. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.7 Big Crunch – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Once considered viable if cosmic density exceeded the critical value. Current observations (accelerating expansion, dark energy) contradict its key assumptions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretically consistent as a time-reversed Big Bang within general relativity. Requires high matter density and no (or reversing) dark energy. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts a decelerating expansion turning to collapse. Testable in principle, but not supported by current data. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with thermodynamic and relativistic models of entropy and time symmetry, but unsupported by astronomical data. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively mirrors Big Bang, offering closure and symmetry. Simple in concept, but difficult to reconcile with observed acceleration. || ★★★☆☆
|-
| '''Heuristic Value''' || Motivated theoretical discussion on cosmological fate and cyclic models. Limited influence in current cosmology. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Explores cosmological temporality and finitude. Once a philosophically compelling counterbalance to eternal expansion. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on time-reversible solutions to Friedmann equations and relativistic cosmology. Rigorous within GR but not extended in modern frameworks. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.8 Big Bounce – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || No direct observational evidence yet. Some loop quantum cosmology models suggest signatures in the CMB, but these remain speculative. || ★★☆☆☆
|-
| '''Internal Consistency''' || Offers a logically coherent alternative to singularity-based models. Dependent on quantum gravity frameworks (e.g. loop quantum gravity) that remain under development. || ★★★☆☆
|-
| '''Predictive Power''' || Provides potential testable differences in early universe structure and CMB fluctuations. Predictions are still uncertain and model-dependent. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges general relativity with quantum mechanics. Limited overlap with geology or observational astronomy. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex and abstract. The idea of a cyclical universe is conceptually appealing, but quantum corrections are not intuitive. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates exploration of singularity resolution and quantum gravity cosmologies. Encourages investigation of pre-Big Bang conditions. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Resonates with ancient cyclical cosmologies and philosophical ideas of eternal recurrence. Reframes the question of origins. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on extensions of Friedmann equations using loop quantum corrections or other quantum gravity approaches. Some models are mathematically formal, but the field is still unsettled. || ★★★☆☆
|}

'''Total: 24/40'''

=== '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' ===

''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆
|-
| '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆
|-
| '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆
|-
| '''Mathematical Rigor''' || Provides original equations (e.g. for \(D_{\text{pref}}\), \(G = (\gamma - 1)/4\pi\), \(\kappa = v_{\text{RMS}}^2 / c^4\)) and consistent dimensional analysis. Excel-based datasets link math to observations. Lacks field-theoretic formalism. || ★★★★☆
|}

'''Total: 34/40'''

=== '''8.8.10 Spiral Cosmology – AI Rating Summary''' ===

''Related link:'' [https://www.academia.edu/103005946/Cosmology_as_Spiral_Evolution Spiral Cosmology on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers visual and structural explanations for spiral galaxy morphology and cosmic rotation patterns. Less directly tied to quantitative data or tested predictions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Conceptually consistent in proposing self-similar spiral evolution at multiple scales, but lacks a developed dynamic or energetic framework. || ★★☆☆☆
|-
| '''Predictive Power''' || Suggests qualitative evolutionary stages and possible cyclic features, but does not provide specific numerical predictions. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Makes symbolic and philosophical connections across cosmology, biology, and culture. Scientific integration with physical fields is minimal. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Emphasizes intuitive and visual structures (e.g. spirals), which are accessible but may oversimplify physical complexity. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulates reflection on cosmic structure, symmetry, and recursion. Encourages reinterpretation of known forms (e.g. galaxies, DNA, hurricanes). || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Reconnects with ancient and Renaissance cosmologies linking form and function across scales. Offers metaphysical resonance. || ★★★★☆
|-
| '''Mathematical Rigor''' || Utilizes geometric symbolism (e.g. spiral ratios, golden mean) but lacks physical equations or dynamical systems modeling. No quantitative derivations. || ★★☆☆☆
|}

'''Total: 23/40'''

==== '''8.9 – Additional Alternative Cosmological Theories (Under Evaluation)''' ====
* '''Topological Field Framework (Hall)''' – Proposes that fundamental constants such as G, c, and Λ emerge from topological constraints in higher-dimensional field configurations. The theory has high internal logic, mathematical consistency, and geometric depth. Empirical validation depends on measurable predictions, but its interdisciplinary integration (e.g., quantum geometry, general relativity) offers high conceptual promise.

* '''Conformal Gravity (Mannheim–Kazanas)''' – Eliminates the need for dark matter by applying conformal symmetry to gravitational equations. It explains galactic rotation curves and lensing without exotic particles. Predictive power is strong on galactic scales, but it faces challenges with early-universe data. Internally consistent and testable, though its cosmological compatibility is debated.

* '''Quasi-Steady State Cosmology (QSSC)''' – A cyclic, non-Big Bang model incorporating continuous matter creation via a “C-field.” It accounts for redshift and some cosmic structure without expansion from a singularity. Empirical adequacy is mixed due to tension with CMB and elemental abundance observations. Still, its falsifiability and explanatory ambition support its inclusion in theoretical discourse.

* '''Dynamic Universe (Tuomo Suntola)''' – A model based on zero-energy balance and time-evolving geometry, predicting cosmic constants from dynamic curvature. Offers conceptual simplicity and mathematical consistency. Deviates from mainstream relativity but maintains coherence. Predictions related to H₀ and time-scaling allow for observational tests and empirical challenge.


'''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]'''</text>
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      <text bytes="30216" sha1="m9hpj0kbh27br7rifaircahsjr6temq" xml:space="preserve">== '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' =

== '''8.1 Purpose''' ==

This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated.

== '''8.2 Toolchain and Workflow''' ==

AI tools like ChatGPT are used to analyze, compare, and refine theories

Tables and frameworks are generated collaboratively using open formats

Contributors submit input via email or editing suggestions

Ratings and evaluations are dynamically updated based on ongoing analysis

== '''8.3 AI-Based Rating System: Motivation and Procedure''' ==

To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''.

This system is designed to be:

Transparent – Each rating is justified through AI’s large-scale reference analysis.

Dynamic – Contributors may submit additional materials to request re-evaluation.

Consistent – All evaluations are performed by the same AI logic, eliminating personal bias.

Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted.

This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate.

== '''8.4 Open Participation''' ==

This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to:

Describe their framework in terms of assumptions, predictions, and compatibility

Suggest how their model could be tested or falsified

Provide references or original materials for AI evaluation

All analysis is open, and contributors may propose improvements at any time.

== '''8.5 Understanding the Star Ratings''' ==

The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied.

'''8.5.1. Empirical Adequacy'''  
Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower.

'''8.5.2. Internal Consistency'''  
Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions.

'''8.5.3. Predictive Power'''  
Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings.

'''8.5.4. Cross-Disciplinary Compatibility'''  
Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score.

'''8.5.5. Conceptual Clarity and Simplicity'''  
Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification.

'''8.5.6. Heuristic Value'''  
Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential.

'''8.5.7. Historical and Philosophical Insight'''  
Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here.

'''8.5.8. Mathematical Rigor'''  
Does the theory provide clear mathematical formulations, derivations, and quantitative predictions? Theories are valued for their use of equations to express core principles, ensure internal consistency, and generate testable results.


Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail.


=== '''8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor)''' ===

''Note: In July 2025, an eighth evaluation criterion was added: '''Mathematical Rigor'''. The total score is now out of 40 stars instead of 35.  ''
''All ratings are expressed in whole stars (★), without fractional values, to ensure clarity in display and consistency with the visual format of this table.''  
''Theories are listed in the same order as in Section 8.8.''

{| class=&quot;wikitable&quot;
! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HP''' !! '''MR''' !! '''Total (★/40)'''
|-
| '''General Relativity''' || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || ★★★★★ || '''37'''
|-
| '''Newtonian Gravity''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''33'''
|-
| '''MOND''' || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || '''26'''
|-
| '''Emergent Gravity''' || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''24'''
|-
| '''Big Bang''' || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || '''35'''
|-
| '''Steady State Theory''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23'''
|-
| '''Big Crunch''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Big Bounce''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Cosmic Influx Theory (CIT)''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || '''33'''
|-
| '''Spiral Cosmology''' || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''21'''
|}

''Legend:''  
''EA = Empirical Adequacy IC = Internal Consistency PP = Predictive Power CC = Cross-Disciplinary Compatibility  ''
''CS = Conceptual Simplicity HV = Heuristic Value HP = Historical/Philosophical Insight MR = Mathematical Rigor''


&lt;!-- Add a blank line here --&gt;

== '''8.7 Requesting Detailed Justification''' ==

“Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by:

1. Visiting the '''discussion page''' of this Wikiversity chapter.
  
2. Mentioning the theory by name and explicitly asking for the detailed breakdown.
  
3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. 

These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented.

If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership.

'''Mainstream theories are subject to the same critical standard.'''  
If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed.

If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''.

== '''8.8 Detailed Evaluations of Theories''' ==

This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes.

=== '''8.8.1 General Relativity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Matches a wide range of observations: gravitational lensing, GPS corrections, perihelion precession, black hole dynamics, and gravitational waves. Supported by multiple experiments. || ★★★★★
|-
| '''Internal Consistency''' || Highly consistent within its differential geometric framework. Built upon Einstein's field equations with tensor calculus. Few internal contradictions, though extensions (e.g. quantum gravity) face challenges. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted gravitational redshift, time dilation, frame-dragging, and gravitational waves. Continues to guide observations in astrophysics. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with cosmology and astrophysics. Some tension with quantum theory. Less integrated with planetary geology or biology. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex mathematical structure makes it less intuitive. Conceptually abstract (spacetime curvature, geodesics). Clarity improves with education, but simplicity is low. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired vast developments in cosmology, black hole theory, and relativistic astrophysics. Foundation for modern gravitational physics. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Deep philosophical implications about space, time, and causality. Represents a major shift from Newtonian absolute space. Influenced 20th-century philosophy of science. || ★★★★★
|-
| '''Mathematical Rigor''' || Built upon advanced mathematics: Riemannian geometry, Einstein field equations, tensor calculus. Equations are precise, formal, and deeply embedded in differential geometry. || ★★★★★
|}

'''Total: 39/40'''

=== '''8.8.2 Newtonian Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Accurately describes gravitational interactions for most macroscopic systems (planets, satellites, projectiles) under low-speed, weak-field conditions. Deviates in extreme conditions (e.g. near black holes). || ★★★★☆
|-
| '''Internal Consistency''' || Mathematically self-consistent with inverse-square law and Newton's laws of motion. Assumes instantaneous action at a distance, which conflicts with relativity. || ★★★★☆
|-
| '''Predictive Power''' || Predicts planetary orbits, tides, escape velocities, and Keplerian motion. Fails for relativistic effects (e.g. Mercury’s precession, gravitational lensing). || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Well-integrated in classical mechanics, astronomy, and engineering. Less compatible with modern cosmology or relativistic frameworks. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple and intuitive: gravity as a force between masses. Easily grasped and widely taught. || ★★★★★
|-
| '''Heuristic Value''' || Inspired centuries of scientific discovery and classical mechanics. Still used in teaching and engineering. Limited in modern theoretical development. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Founded classical physics. Major leap in scientific method and mathematical modeling. Paved the way for Enlightenment-era science. || ★★★★★
|-
| '''Mathematical Rigor''' || Clear and elegant use of calculus and vector algebra (e.g. \(\displaystyle F = G \frac{m_1 m_2}{r^2}\)). Highly accessible and historically groundbreaking, but lacks deeper geometric or relativistic structures. || ★★★★☆
|}

'''Total: 33/40'''

=== '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Fits galactic rotation curves without invoking dark matter. Matches Tully-Fisher relation. Performance weakens at cluster and cosmological scales. || ★★★★☆
|-
| '''Internal Consistency''' || Original formulation is non-relativistic and phenomenological. Several relativistic extensions (e.g. TeVeS) exist but introduce complexity and fine-tuning. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts galaxy dynamics from baryonic matter alone. Less predictive at larger scales or in non-galactic contexts. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Primarily astrophysical. Some tension with cosmology, structure formation, and gravitational lensing. Not aligned with particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple at galactic scale: modifies acceleration below a threshold \(a_0\). Extensions are less intuitive. || ★★★★☆
|-
| '''Heuristic Value''' || Challenges dark matter paradigm and motivates alternate gravity models. Sparked theoretical and observational debate. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Offers a conceptual challenge to Newton/Einstein gravity. Philosophically provocative, but limited historical lineage. || ★★★☆☆
|-
| '''Mathematical Rigor''' || Employs interpolating functions and modified Poisson equations. Relativistic extensions (e.g. TeVeS) involve tensor-vector-scalar frameworks. Rigorous in parts, but lacks unified formalism. || ★★★☆☆
|}

'''Total: 28/40'''

=== '''8.8.4 Emergent Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Entropic_gravity Emergent / Entropic Gravity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Attempts to account for galactic rotation without dark matter by linking gravity to entropy and information. Some results match MOND-like behavior, but broad observational support remains limited. || ★★★☆☆
|-
| '''Internal Consistency''' || Theoretical framework draws from thermodynamics, holography, and information theory. Conceptually coherent, but not fully developed as a unified physical model. || ★★★☆☆
|-
| '''Predictive Power''' || Offers qualitative insights but lacks precise predictive capabilities in most contexts. No wide adoption for simulations or system modeling. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates ideas from black hole thermodynamics, quantum information, and spacetime geometry. Weak integration with observational astronomy or geology. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Abstract and speculative. Concepts like entropic forces and holographic screens are not intuitive for most readers. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates discussion about the nature of spacetime and gravity. Has inspired new theoretical directions in quantum gravity and information theory. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Philosophically intriguing: redefines gravity as emergent rather than fundamental. Links to ideas from Bekenstein and Hawking. || ★★★★☆
|-
| '''Mathematical Rigor''' || Relies on concepts from thermodynamics (e.g. entropy gradients), statistical mechanics, and quantum gravity. Uses integral relations and variational principles, but lacks a standardized set of equations for general use. || ★★★☆☆
|}

'''Total: 26/40'''

=== '''8.8.5 Big Bang – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strongly supported by CMB, redshift-distance relation, and light element abundances. However, JWST data revealing early, mature galaxies challenges the predicted timeline of structure formation. || ★★★★☆
|-
| '''Internal Consistency''' || Internally coherent within the ΛCDM framework. Logical structure is intact, though singularity and quantum-gravity transitions remain unresolved. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted CMB and nucleosynthesis. But recent observations (e.g. JWST galaxies at z &gt; 10) were not anticipated, requiring post-hoc model adjustments. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Strong integration with general relativity, quantum field theory, and thermodynamics. Limited links to geology or planetary evolution. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Conceptually complex genesis: singularity, inflation, and multiple postulated fields (inflaton, dark energy, dark matter). Relies on hypothetical constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulated massive observational and theoretical advances. Has driven decades of mission planning and cosmological interpretation. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Represented a paradigm shift from steady-state thinking. Raises deep ontological and metaphysical questions (e.g. time’s origin, creation ex nihilo). || ★★★★☆
|-
| '''Mathematical Rigor''' || Grounded in Einstein’s field equations, Friedmann dynamics, and thermodynamics. Offers well-defined, highly developed formalism. || ★★★★★
|}

'''Total: 34/40'''

=== '''8.8.6 Steady State Theory – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Cosmology]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Early successes with radio‐source counts, but contradicted by the cosmic microwave background, evolving galaxy populations, and quasar statistics. || ★★☆☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within the “perfect cosmological principle,” requiring continuous matter creation at a fixed rate. Logical but invokes an ad-hoc creation field (C-field). || ★★★☆☆
|-
| '''Predictive Power''' || Predicted constant large-scale density and specific radio‐source number counts; few successful novel predictions beyond its initial scope. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Limited overlap with modern astrophysics and particle physics; conflicts with nucleosynthesis and CMB observations. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively simple: Universe is homogeneous in space **and** time, avoiding an initial singularity. Minimal parameter set. || ★★★★☆
|-
| '''Heuristic Value''' || Historically spurred observational tests that ultimately favored Big Bang models; now mainly of pedagogical interest. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Embodies the perfect cosmological principle and continuous-creation idea, provoking debates on temporality and cosmological assumptions. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs Friedmann-like solutions with a creation term; uses relativistic field equations but lacks the richer formal development of ΛCDM or GR extensions. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.7 Big Crunch – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Once considered viable if cosmic density exceeded the critical value. Current observations (accelerating expansion, dark energy) contradict its key assumptions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretically consistent as a time-reversed Big Bang within general relativity. Requires high matter density and no (or reversing) dark energy. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts a decelerating expansion turning to collapse. Testable in principle, but not supported by current data. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with thermodynamic and relativistic models of entropy and time symmetry, but unsupported by astronomical data. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively mirrors Big Bang, offering closure and symmetry. Simple in concept, but difficult to reconcile with observed acceleration. || ★★★☆☆
|-
| '''Heuristic Value''' || Motivated theoretical discussion on cosmological fate and cyclic models. Limited influence in current cosmology. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Explores cosmological temporality and finitude. Once a philosophically compelling counterbalance to eternal expansion. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on time-reversible solutions to Friedmann equations and relativistic cosmology. Rigorous within GR but not extended in modern frameworks. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.8 Big Bounce – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || No direct observational evidence yet. Some loop quantum cosmology models suggest signatures in the CMB, but these remain speculative. || ★★☆☆☆
|-
| '''Internal Consistency''' || Offers a logically coherent alternative to singularity-based models. Dependent on quantum gravity frameworks (e.g. loop quantum gravity) that remain under development. || ★★★☆☆
|-
| '''Predictive Power''' || Provides potential testable differences in early universe structure and CMB fluctuations. Predictions are still uncertain and model-dependent. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges general relativity with quantum mechanics. Limited overlap with geology or observational astronomy. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex and abstract. The idea of a cyclical universe is conceptually appealing, but quantum corrections are not intuitive. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates exploration of singularity resolution and quantum gravity cosmologies. Encourages investigation of pre-Big Bang conditions. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Resonates with ancient cyclical cosmologies and philosophical ideas of eternal recurrence. Reframes the question of origins. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on extensions of Friedmann equations using loop quantum corrections or other quantum gravity approaches. Some models are mathematically formal, but the field is still unsettled. || ★★★☆☆
|}

'''Total: 24/40'''

=== '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' ===

''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆
|-
| '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆
|-
| '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆
|-
| '''Mathematical Rigor''' || Provides original equations (e.g. for \(D_{\text{pref}}\), \(G = (\gamma - 1)/4\pi\), \(\kappa = v_{\text{RMS}}^2 / c^4\)) and consistent dimensional analysis. Excel-based datasets link math to observations. Lacks field-theoretic formalism. || ★★★★☆
|}

'''Total: 34/40'''

=== '''8.8.10 Spiral Cosmology – AI Rating Summary''' ===

''Related link:'' [https://www.academia.edu/103005946/Cosmology_as_Spiral_Evolution Spiral Cosmology on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers visual and structural explanations for spiral galaxy morphology and cosmic rotation patterns. Less directly tied to quantitative data or tested predictions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Conceptually consistent in proposing self-similar spiral evolution at multiple scales, but lacks a developed dynamic or energetic framework. || ★★☆☆☆
|-
| '''Predictive Power''' || Suggests qualitative evolutionary stages and possible cyclic features, but does not provide specific numerical predictions. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Makes symbolic and philosophical connections across cosmology, biology, and culture. Scientific integration with physical fields is minimal. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Emphasizes intuitive and visual structures (e.g. spirals), which are accessible but may oversimplify physical complexity. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulates reflection on cosmic structure, symmetry, and recursion. Encourages reinterpretation of known forms (e.g. galaxies, DNA, hurricanes). || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Reconnects with ancient and Renaissance cosmologies linking form and function across scales. Offers metaphysical resonance. || ★★★★☆
|-
| '''Mathematical Rigor''' || Utilizes geometric symbolism (e.g. spiral ratios, golden mean) but lacks physical equations or dynamical systems modeling. No quantitative derivations. || ★★☆☆☆
|}

'''Total: 23/40'''

==== '''8.9 – Additional Alternative Cosmological Theories (Under Evaluation)''' ====
* '''Topological Field Framework (Hall)''' – Proposes that fundamental constants such as G, c, and Λ emerge from topological constraints in higher-dimensional field configurations. The theory has high internal logic, mathematical consistency, and geometric depth. Empirical validation depends on measurable predictions, but its interdisciplinary integration (e.g., quantum geometry, general relativity) offers high conceptual promise.

* '''Conformal Gravity (Mannheim–Kazanas)''' – Eliminates the need for dark matter by applying conformal symmetry to gravitational equations. It explains galactic rotation curves and lensing without exotic particles. Predictive power is strong on galactic scales, but it faces challenges with early-universe data. Internally consistent and testable, though its cosmological compatibility is debated.

* '''Quasi-Steady State Cosmology (QSSC)''' – A cyclic, non-Big Bang model incorporating continuous matter creation via a “C-field.” It accounts for redshift and some cosmic structure without expansion from a singularity. Empirical adequacy is mixed due to tension with CMB and elemental abundance observations. Still, its falsifiability and explanatory ambition support its inclusion in theoretical discourse.

* '''Dynamic Universe (Tuomo Suntola)''' – A model based on zero-energy balance and time-evolving geometry, predicting cosmic constants from dynamic curvature. Offers conceptual simplicity and mathematical consistency. Deviates from mainstream relativity but maintains coherence. Predictions related to H₀ and time-scaling allow for observational tests and empirical challenge.


'''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]'''</text>
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      <comment>/* 8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor) */ replaced the rating for the Big Bang theory related to the observations from JWST as explained in the Talkpage.</comment>
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      <text bytes="30216" sha1="knxvdzbp52pfxb3ut272tx4l9cdsvil" xml:space="preserve">== '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' =

== '''8.1 Purpose''' ==

This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated.

== '''8.2 Toolchain and Workflow''' ==

AI tools like ChatGPT are used to analyze, compare, and refine theories

Tables and frameworks are generated collaboratively using open formats

Contributors submit input via email or editing suggestions

Ratings and evaluations are dynamically updated based on ongoing analysis

== '''8.3 AI-Based Rating System: Motivation and Procedure''' ==

To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''.

This system is designed to be:

Transparent – Each rating is justified through AI’s large-scale reference analysis.

Dynamic – Contributors may submit additional materials to request re-evaluation.

Consistent – All evaluations are performed by the same AI logic, eliminating personal bias.

Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted.

This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate.

== '''8.4 Open Participation''' ==

This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to:

Describe their framework in terms of assumptions, predictions, and compatibility

Suggest how their model could be tested or falsified

Provide references or original materials for AI evaluation

All analysis is open, and contributors may propose improvements at any time.

== '''8.5 Understanding the Star Ratings''' ==

The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied.

'''8.5.1. Empirical Adequacy'''  
Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower.

'''8.5.2. Internal Consistency'''  
Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions.

'''8.5.3. Predictive Power'''  
Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings.

'''8.5.4. Cross-Disciplinary Compatibility'''  
Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score.

'''8.5.5. Conceptual Clarity and Simplicity'''  
Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification.

'''8.5.6. Heuristic Value'''  
Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential.

'''8.5.7. Historical and Philosophical Insight'''  
Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here.

'''8.5.8. Mathematical Rigor'''  
Does the theory provide clear mathematical formulations, derivations, and quantitative predictions? Theories are valued for their use of equations to express core principles, ensure internal consistency, and generate testable results.


Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail.


=== '''8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor)''' ===

''Note: In July 2025, an eighth evaluation criterion was added: '''Mathematical Rigor'''. The total score is now out of 40 stars instead of 35.  ''
''All ratings are expressed in whole stars (★), without fractional values, to ensure clarity in display and consistency with the visual format of this table.''  
''Theories are listed in the same order as in Section 8.8.''

{| class=&quot;wikitable&quot;
! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HP''' !! '''MR''' !! '''Total (★/40)'''
|-
| '''General Relativity''' || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || ★★★★★ || '''37'''
|-
| '''Newtonian Gravity''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''33'''
|-
| '''MOND''' || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || '''26'''
|-
| '''Emergent Gravity''' || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''24'''
|-
| '''Big Bang''' || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || '''34'''
|-
| '''Steady State Theory''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23'''
|-
| '''Big Crunch''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Big Bounce''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Cosmic Influx Theory (CIT)''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || '''33'''
|-
| '''Spiral Cosmology''' || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''21'''
|}

''Legend:''  
''EA = Empirical Adequacy IC = Internal Consistency PP = Predictive Power CC = Cross-Disciplinary Compatibility  ''
''CS = Conceptual Simplicity HV = Heuristic Value HP = Historical/Philosophical Insight MR = Mathematical Rigor''


&lt;!-- Add a blank line here --&gt;

== '''8.7 Requesting Detailed Justification''' ==

“Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by:

1. Visiting the '''discussion page''' of this Wikiversity chapter.
  
2. Mentioning the theory by name and explicitly asking for the detailed breakdown.
  
3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. 

These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented.

If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership.

'''Mainstream theories are subject to the same critical standard.'''  
If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed.

If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''.

== '''8.8 Detailed Evaluations of Theories''' ==

This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes.

=== '''8.8.1 General Relativity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Matches a wide range of observations: gravitational lensing, GPS corrections, perihelion precession, black hole dynamics, and gravitational waves. Supported by multiple experiments. || ★★★★★
|-
| '''Internal Consistency''' || Highly consistent within its differential geometric framework. Built upon Einstein's field equations with tensor calculus. Few internal contradictions, though extensions (e.g. quantum gravity) face challenges. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted gravitational redshift, time dilation, frame-dragging, and gravitational waves. Continues to guide observations in astrophysics. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with cosmology and astrophysics. Some tension with quantum theory. Less integrated with planetary geology or biology. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex mathematical structure makes it less intuitive. Conceptually abstract (spacetime curvature, geodesics). Clarity improves with education, but simplicity is low. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired vast developments in cosmology, black hole theory, and relativistic astrophysics. Foundation for modern gravitational physics. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Deep philosophical implications about space, time, and causality. Represents a major shift from Newtonian absolute space. Influenced 20th-century philosophy of science. || ★★★★★
|-
| '''Mathematical Rigor''' || Built upon advanced mathematics: Riemannian geometry, Einstein field equations, tensor calculus. Equations are precise, formal, and deeply embedded in differential geometry. || ★★★★★
|}

'''Total: 39/40'''

=== '''8.8.2 Newtonian Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Accurately describes gravitational interactions for most macroscopic systems (planets, satellites, projectiles) under low-speed, weak-field conditions. Deviates in extreme conditions (e.g. near black holes). || ★★★★☆
|-
| '''Internal Consistency''' || Mathematically self-consistent with inverse-square law and Newton's laws of motion. Assumes instantaneous action at a distance, which conflicts with relativity. || ★★★★☆
|-
| '''Predictive Power''' || Predicts planetary orbits, tides, escape velocities, and Keplerian motion. Fails for relativistic effects (e.g. Mercury’s precession, gravitational lensing). || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Well-integrated in classical mechanics, astronomy, and engineering. Less compatible with modern cosmology or relativistic frameworks. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple and intuitive: gravity as a force between masses. Easily grasped and widely taught. || ★★★★★
|-
| '''Heuristic Value''' || Inspired centuries of scientific discovery and classical mechanics. Still used in teaching and engineering. Limited in modern theoretical development. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Founded classical physics. Major leap in scientific method and mathematical modeling. Paved the way for Enlightenment-era science. || ★★★★★
|-
| '''Mathematical Rigor''' || Clear and elegant use of calculus and vector algebra (e.g. \(\displaystyle F = G \frac{m_1 m_2}{r^2}\)). Highly accessible and historically groundbreaking, but lacks deeper geometric or relativistic structures. || ★★★★☆
|}

'''Total: 33/40'''

=== '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Fits galactic rotation curves without invoking dark matter. Matches Tully-Fisher relation. Performance weakens at cluster and cosmological scales. || ★★★★☆
|-
| '''Internal Consistency''' || Original formulation is non-relativistic and phenomenological. Several relativistic extensions (e.g. TeVeS) exist but introduce complexity and fine-tuning. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts galaxy dynamics from baryonic matter alone. Less predictive at larger scales or in non-galactic contexts. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Primarily astrophysical. Some tension with cosmology, structure formation, and gravitational lensing. Not aligned with particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple at galactic scale: modifies acceleration below a threshold \(a_0\). Extensions are less intuitive. || ★★★★☆
|-
| '''Heuristic Value''' || Challenges dark matter paradigm and motivates alternate gravity models. Sparked theoretical and observational debate. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Offers a conceptual challenge to Newton/Einstein gravity. Philosophically provocative, but limited historical lineage. || ★★★☆☆
|-
| '''Mathematical Rigor''' || Employs interpolating functions and modified Poisson equations. Relativistic extensions (e.g. TeVeS) involve tensor-vector-scalar frameworks. Rigorous in parts, but lacks unified formalism. || ★★★☆☆
|}

'''Total: 28/40'''

=== '''8.8.4 Emergent Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Entropic_gravity Emergent / Entropic Gravity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Attempts to account for galactic rotation without dark matter by linking gravity to entropy and information. Some results match MOND-like behavior, but broad observational support remains limited. || ★★★☆☆
|-
| '''Internal Consistency''' || Theoretical framework draws from thermodynamics, holography, and information theory. Conceptually coherent, but not fully developed as a unified physical model. || ★★★☆☆
|-
| '''Predictive Power''' || Offers qualitative insights but lacks precise predictive capabilities in most contexts. No wide adoption for simulations or system modeling. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates ideas from black hole thermodynamics, quantum information, and spacetime geometry. Weak integration with observational astronomy or geology. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Abstract and speculative. Concepts like entropic forces and holographic screens are not intuitive for most readers. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates discussion about the nature of spacetime and gravity. Has inspired new theoretical directions in quantum gravity and information theory. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Philosophically intriguing: redefines gravity as emergent rather than fundamental. Links to ideas from Bekenstein and Hawking. || ★★★★☆
|-
| '''Mathematical Rigor''' || Relies on concepts from thermodynamics (e.g. entropy gradients), statistical mechanics, and quantum gravity. Uses integral relations and variational principles, but lacks a standardized set of equations for general use. || ★★★☆☆
|}

'''Total: 26/40'''

=== '''8.8.5 Big Bang – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strongly supported by CMB, redshift-distance relation, and light element abundances. However, JWST data revealing early, mature galaxies challenges the predicted timeline of structure formation. || ★★★★☆
|-
| '''Internal Consistency''' || Internally coherent within the ΛCDM framework. Logical structure is intact, though singularity and quantum-gravity transitions remain unresolved. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted CMB and nucleosynthesis. But recent observations (e.g. JWST galaxies at z &gt; 10) were not anticipated, requiring post-hoc model adjustments. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Strong integration with general relativity, quantum field theory, and thermodynamics. Limited links to geology or planetary evolution. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Conceptually complex genesis: singularity, inflation, and multiple postulated fields (inflaton, dark energy, dark matter). Relies on hypothetical constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulated massive observational and theoretical advances. Has driven decades of mission planning and cosmological interpretation. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Represented a paradigm shift from steady-state thinking. Raises deep ontological and metaphysical questions (e.g. time’s origin, creation ex nihilo). || ★★★★☆
|-
| '''Mathematical Rigor''' || Grounded in Einstein’s field equations, Friedmann dynamics, and thermodynamics. Offers well-defined, highly developed formalism. || ★★★★★
|}

'''Total: 34/40'''

=== '''8.8.6 Steady State Theory – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Cosmology]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Early successes with radio‐source counts, but contradicted by the cosmic microwave background, evolving galaxy populations, and quasar statistics. || ★★☆☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within the “perfect cosmological principle,” requiring continuous matter creation at a fixed rate. Logical but invokes an ad-hoc creation field (C-field). || ★★★☆☆
|-
| '''Predictive Power''' || Predicted constant large-scale density and specific radio‐source number counts; few successful novel predictions beyond its initial scope. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Limited overlap with modern astrophysics and particle physics; conflicts with nucleosynthesis and CMB observations. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively simple: Universe is homogeneous in space **and** time, avoiding an initial singularity. Minimal parameter set. || ★★★★☆
|-
| '''Heuristic Value''' || Historically spurred observational tests that ultimately favored Big Bang models; now mainly of pedagogical interest. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Embodies the perfect cosmological principle and continuous-creation idea, provoking debates on temporality and cosmological assumptions. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs Friedmann-like solutions with a creation term; uses relativistic field equations but lacks the richer formal development of ΛCDM or GR extensions. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.7 Big Crunch – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Once considered viable if cosmic density exceeded the critical value. Current observations (accelerating expansion, dark energy) contradict its key assumptions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretically consistent as a time-reversed Big Bang within general relativity. Requires high matter density and no (or reversing) dark energy. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts a decelerating expansion turning to collapse. Testable in principle, but not supported by current data. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with thermodynamic and relativistic models of entropy and time symmetry, but unsupported by astronomical data. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively mirrors Big Bang, offering closure and symmetry. Simple in concept, but difficult to reconcile with observed acceleration. || ★★★☆☆
|-
| '''Heuristic Value''' || Motivated theoretical discussion on cosmological fate and cyclic models. Limited influence in current cosmology. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Explores cosmological temporality and finitude. Once a philosophically compelling counterbalance to eternal expansion. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on time-reversible solutions to Friedmann equations and relativistic cosmology. Rigorous within GR but not extended in modern frameworks. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.8 Big Bounce – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || No direct observational evidence yet. Some loop quantum cosmology models suggest signatures in the CMB, but these remain speculative. || ★★☆☆☆
|-
| '''Internal Consistency''' || Offers a logically coherent alternative to singularity-based models. Dependent on quantum gravity frameworks (e.g. loop quantum gravity) that remain under development. || ★★★☆☆
|-
| '''Predictive Power''' || Provides potential testable differences in early universe structure and CMB fluctuations. Predictions are still uncertain and model-dependent. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges general relativity with quantum mechanics. Limited overlap with geology or observational astronomy. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex and abstract. The idea of a cyclical universe is conceptually appealing, but quantum corrections are not intuitive. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates exploration of singularity resolution and quantum gravity cosmologies. Encourages investigation of pre-Big Bang conditions. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Resonates with ancient cyclical cosmologies and philosophical ideas of eternal recurrence. Reframes the question of origins. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on extensions of Friedmann equations using loop quantum corrections or other quantum gravity approaches. Some models are mathematically formal, but the field is still unsettled. || ★★★☆☆
|}

'''Total: 24/40'''

=== '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' ===

''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆
|-
| '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆
|-
| '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆
|-
| '''Mathematical Rigor''' || Provides original equations (e.g. for \(D_{\text{pref}}\), \(G = (\gamma - 1)/4\pi\), \(\kappa = v_{\text{RMS}}^2 / c^4\)) and consistent dimensional analysis. Excel-based datasets link math to observations. Lacks field-theoretic formalism. || ★★★★☆
|}

'''Total: 34/40'''

=== '''8.8.10 Spiral Cosmology – AI Rating Summary''' ===

''Related link:'' [https://www.academia.edu/103005946/Cosmology_as_Spiral_Evolution Spiral Cosmology on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers visual and structural explanations for spiral galaxy morphology and cosmic rotation patterns. Less directly tied to quantitative data or tested predictions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Conceptually consistent in proposing self-similar spiral evolution at multiple scales, but lacks a developed dynamic or energetic framework. || ★★☆☆☆
|-
| '''Predictive Power''' || Suggests qualitative evolutionary stages and possible cyclic features, but does not provide specific numerical predictions. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Makes symbolic and philosophical connections across cosmology, biology, and culture. Scientific integration with physical fields is minimal. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Emphasizes intuitive and visual structures (e.g. spirals), which are accessible but may oversimplify physical complexity. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulates reflection on cosmic structure, symmetry, and recursion. Encourages reinterpretation of known forms (e.g. galaxies, DNA, hurricanes). || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Reconnects with ancient and Renaissance cosmologies linking form and function across scales. Offers metaphysical resonance. || ★★★★☆
|-
| '''Mathematical Rigor''' || Utilizes geometric symbolism (e.g. spiral ratios, golden mean) but lacks physical equations or dynamical systems modeling. No quantitative derivations. || ★★☆☆☆
|}

'''Total: 23/40'''

==== '''8.9 – Additional Alternative Cosmological Theories (Under Evaluation)''' ====
* '''Topological Field Framework (Hall)''' – Proposes that fundamental constants such as G, c, and Λ emerge from topological constraints in higher-dimensional field configurations. The theory has high internal logic, mathematical consistency, and geometric depth. Empirical validation depends on measurable predictions, but its interdisciplinary integration (e.g., quantum geometry, general relativity) offers high conceptual promise.

* '''Conformal Gravity (Mannheim–Kazanas)''' – Eliminates the need for dark matter by applying conformal symmetry to gravitational equations. It explains galactic rotation curves and lensing without exotic particles. Predictive power is strong on galactic scales, but it faces challenges with early-universe data. Internally consistent and testable, though its cosmological compatibility is debated.

* '''Quasi-Steady State Cosmology (QSSC)''' – A cyclic, non-Big Bang model incorporating continuous matter creation via a “C-field.” It accounts for redshift and some cosmic structure without expansion from a singularity. Empirical adequacy is mixed due to tension with CMB and elemental abundance observations. Still, its falsifiability and explanatory ambition support its inclusion in theoretical discourse.

* '''Dynamic Universe (Tuomo Suntola)''' – A model based on zero-energy balance and time-evolving geometry, predicting cosmic constants from dynamic curvature. Offers conceptual simplicity and mathematical consistency. Deviates from mainstream relativity but maintains coherence. Predictions related to H₀ and time-scaling allow for observational tests and empirical challenge.


'''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]'''</text>
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      <text bytes="30388" sha1="p9sgn9nvzz0nofo4dtj6ge61jhyckk8" xml:space="preserve">== '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' =

== '''8.1 Purpose''' ==

This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated.

== '''8.2 Toolchain and Workflow''' ==

AI tools like ChatGPT are used to analyze, compare, and refine theories

Tables and frameworks are generated collaboratively using open formats

Contributors submit input via email or editing suggestions

Ratings and evaluations are dynamically updated based on ongoing analysis

== '''8.3 AI-Based Rating System: Motivation and Procedure''' ==

To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''.

This system is designed to be:

Transparent – Each rating is justified through AI’s large-scale reference analysis.

Dynamic – Contributors may submit additional materials to request re-evaluation.

Consistent – All evaluations are performed by the same AI logic, eliminating personal bias.

Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted.

This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate.

== '''8.4 Open Participation''' ==

This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to:

Describe their framework in terms of assumptions, predictions, and compatibility

Suggest how their model could be tested or falsified

Provide references or original materials for AI evaluation

All analysis is open, and contributors may propose improvements at any time.

== '''8.5 Understanding the Star Ratings''' ==

The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied.

'''8.5.1. Empirical Adequacy'''  
Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower.

'''8.5.2. Internal Consistency'''  
Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions.

'''8.5.3. Predictive Power'''  
Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings.

'''8.5.4. Cross-Disciplinary Compatibility'''  
Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score.

'''8.5.5. Conceptual Clarity and Simplicity'''  
Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification.

'''8.5.6. Heuristic Value'''  
Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential.

'''8.5.7. Historical and Philosophical Insight'''  
Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here.

'''8.5.8. Mathematical Rigor'''  
Does the theory provide clear mathematical formulations, derivations, and quantitative predictions? Theories are valued for their use of equations to express core principles, ensure internal consistency, and generate testable results.


Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail.


=== '''8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor)''' ===

''Note: In July 2025, an eighth evaluation criterion was added: '''Mathematical Rigor'''. The total score is now out of 40 stars instead of 35.  ''
''All ratings are expressed in whole stars (★), without fractional values, to ensure clarity in display and consistency with the visual format of this table.''  
''Theories are listed in the same order as in Section 8.8.''

{| class=&quot;wikitable&quot;
! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HP''' !! '''MR''' !! '''Total (★/40)'''
|-
| '''General Relativity''' || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || ★★★★★ || '''37'''
|-
| '''Newtonian Gravity''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''33'''
|-
| '''MOND''' || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || '''26'''
|-
| '''Emergent Gravity''' || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''24'''
|-
| '''Big Bang''' || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || '''34'''
|-
| '''Steady State Theory''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23'''
|-
| '''Big Crunch''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Big Bounce''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Cosmic Influx Theory (CIT)''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || '''33'''
|-
| '''Spiral Cosmology''' || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''21'''
|}

''Legend:''  
''EA = Empirical Adequacy IC = Internal Consistency PP = Predictive Power CC = Cross-Disciplinary Compatibility  ''
''CS = Conceptual Simplicity HV = Heuristic Value HP = Historical/Philosophical Insight MR = Mathematical Rigor''


&lt;!-- Add a blank line here --&gt;

== '''8.7 Requesting Detailed Justification''' ==

“Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by:

1. Visiting the '''discussion page''' of this Wikiversity chapter.
  
2. Mentioning the theory by name and explicitly asking for the detailed breakdown.
  
3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. 

These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented.

If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership.

'''Mainstream theories are subject to the same critical standard.'''  
If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed.

If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''.

== '''8.8 Detailed Evaluations of Theories''' ==

This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes.

=== '''8.8.1 General Relativity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Matches a wide range of observations: gravitational lensing, GPS corrections, perihelion precession, black hole dynamics, and gravitational waves. Supported by multiple experiments. || ★★★★★
|-
| '''Internal Consistency''' || Highly consistent within its differential geometric framework. Built upon Einstein's field equations with tensor calculus. Few internal contradictions, though extensions (e.g. quantum gravity) face challenges. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted gravitational redshift, time dilation, frame-dragging, and gravitational waves. Continues to guide observations in astrophysics. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with cosmology and astrophysics. Some tension with quantum theory. Less integrated with planetary geology or biology. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex mathematical structure makes it less intuitive. Conceptually abstract (spacetime curvature, geodesics). Clarity improves with education, but simplicity is low. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired vast developments in cosmology, black hole theory, and relativistic astrophysics. Foundation for modern gravitational physics. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Deep philosophical implications about space, time, and causality. Represents a major shift from Newtonian absolute space. Influenced 20th-century philosophy of science. || ★★★★★
|-
| '''Mathematical Rigor''' || Built upon advanced mathematics: Riemannian geometry, Einstein field equations, tensor calculus. Equations are precise, formal, and deeply embedded in differential geometry. || ★★★★★
|}

'''Total: 39/40'''

=== '''8.8.2 Newtonian Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Accurately describes gravitational interactions for most macroscopic systems (planets, satellites, projectiles) under low-speed, weak-field conditions. Deviates in extreme conditions (e.g. near black holes). || ★★★★☆
|-
| '''Internal Consistency''' || Mathematically self-consistent with inverse-square law and Newton's laws of motion. Assumes instantaneous action at a distance, which conflicts with relativity. || ★★★★☆
|-
| '''Predictive Power''' || Predicts planetary orbits, tides, escape velocities, and Keplerian motion. Fails for relativistic effects (e.g. Mercury’s precession, gravitational lensing). || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Well-integrated in classical mechanics, astronomy, and engineering. Less compatible with modern cosmology or relativistic frameworks. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple and intuitive: gravity as a force between masses. Easily grasped and widely taught. || ★★★★★
|-
| '''Heuristic Value''' || Inspired centuries of scientific discovery and classical mechanics. Still used in teaching and engineering. Limited in modern theoretical development. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Founded classical physics. Major leap in scientific method and mathematical modeling. Paved the way for Enlightenment-era science. || ★★★★★
|-
| '''Mathematical Rigor''' || Clear and elegant use of calculus and vector algebra (e.g. \(\displaystyle F = G \frac{m_1 m_2}{r^2}\)). Highly accessible and historically groundbreaking, but lacks deeper geometric or relativistic structures. || ★★★★☆
|}

'''Total: 33/40'''

=== '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Fits galactic rotation curves without invoking dark matter. Matches Tully-Fisher relation. Performance weakens at cluster and cosmological scales. || ★★★★☆
|-
| '''Internal Consistency''' || Original formulation is non-relativistic and phenomenological. Several relativistic extensions (e.g. TeVeS) exist but introduce complexity and fine-tuning. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts galaxy dynamics from baryonic matter alone. Less predictive at larger scales or in non-galactic contexts. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Primarily astrophysical. Some tension with cosmology, structure formation, and gravitational lensing. Not aligned with particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple at galactic scale: modifies acceleration below a threshold \(a_0\). Extensions are less intuitive. || ★★★★☆
|-
| '''Heuristic Value''' || Challenges dark matter paradigm and motivates alternate gravity models. Sparked theoretical and observational debate. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Offers a conceptual challenge to Newton/Einstein gravity. Philosophically provocative, but limited historical lineage. || ★★★☆☆
|-
| '''Mathematical Rigor''' || Employs interpolating functions and modified Poisson equations. Relativistic extensions (e.g. TeVeS) involve tensor-vector-scalar frameworks. Rigorous in parts, but lacks unified formalism. || ★★★☆☆
|}

'''Total: 28/40'''

=== '''8.8.4 Emergent Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Entropic_gravity Emergent / Entropic Gravity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Attempts to account for galactic rotation without dark matter by linking gravity to entropy and information. Some results match MOND-like behavior, but broad observational support remains limited. || ★★★☆☆
|-
| '''Internal Consistency''' || Theoretical framework draws from thermodynamics, holography, and information theory. Conceptually coherent, but not fully developed as a unified physical model. || ★★★☆☆
|-
| '''Predictive Power''' || Offers qualitative insights but lacks precise predictive capabilities in most contexts. No wide adoption for simulations or system modeling. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates ideas from black hole thermodynamics, quantum information, and spacetime geometry. Weak integration with observational astronomy or geology. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Abstract and speculative. Concepts like entropic forces and holographic screens are not intuitive for most readers. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates discussion about the nature of spacetime and gravity. Has inspired new theoretical directions in quantum gravity and information theory. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Philosophically intriguing: redefines gravity as emergent rather than fundamental. Links to ideas from Bekenstein and Hawking. || ★★★★☆
|-
| '''Mathematical Rigor''' || Relies on concepts from thermodynamics (e.g. entropy gradients), statistical mechanics, and quantum gravity. Uses integral relations and variational principles, but lacks a standardized set of equations for general use. || ★★★☆☆
|}

'''Total: 26/40'''

=== '''8.8.5 Big Bang – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strongly supported by CMB, redshift-distance relation, and light element abundances. However, JWST data revealing early, mature galaxies challenges the predicted timeline of structure formation. || ★★★★☆
|-
| '''Internal Consistency''' || Internally coherent within the ΛCDM framework. Logical structure is intact, though singularity and quantum-gravity transitions remain unresolved. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted CMB and nucleosynthesis. But recent observations (e.g. JWST galaxies at z &gt; 10) were not anticipated, requiring post-hoc model adjustments. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Strong integration with general relativity, quantum field theory, and thermodynamics. Limited links to geology or planetary evolution. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Conceptually complex genesis: singularity, inflation, and multiple postulated fields (inflaton, dark energy, dark matter). Relies on hypothetical constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulated massive observational and theoretical advances. Has driven decades of mission planning and cosmological interpretation. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Represented a paradigm shift from steady-state thinking. Raises deep ontological and metaphysical questions (e.g. time’s origin, creation ex nihilo). || ★★★★☆
|-
| '''Mathematical Rigor''' || Grounded in Einstein’s field equations, Friedmann dynamics, and thermodynamics. Offers well-defined, highly developed formalism. || ★★★★★
|}

'''Total: 34/40'''

=== '''8.8.6 Steady State Theory – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Cosmology]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Early successes with radio‐source counts, but contradicted by the cosmic microwave background, evolving galaxy populations, and quasar statistics. || ★★☆☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within the “perfect cosmological principle,” requiring continuous matter creation at a fixed rate. Logical but invokes an ad-hoc creation field (C-field). || ★★★☆☆
|-
| '''Predictive Power''' || Predicted constant large-scale density and specific radio‐source number counts; few successful novel predictions beyond its initial scope. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Limited overlap with modern astrophysics and particle physics; conflicts with nucleosynthesis and CMB observations. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively simple: Universe is homogeneous in space **and** time, avoiding an initial singularity. Minimal parameter set. || ★★★★☆
|-
| '''Heuristic Value''' || Historically spurred observational tests that ultimately favored Big Bang models; now mainly of pedagogical interest. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Embodies the perfect cosmological principle and continuous-creation idea, provoking debates on temporality and cosmological assumptions. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs Friedmann-like solutions with a creation term; uses relativistic field equations but lacks the richer formal development of ΛCDM or GR extensions. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.7 Big Crunch – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Once considered viable if cosmic density exceeded the critical value. Current observations (accelerating expansion, dark energy) contradict its key assumptions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretically consistent as a time-reversed Big Bang within general relativity. Requires high matter density and no (or reversing) dark energy. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts a decelerating expansion turning to collapse. Testable in principle, but not supported by current data. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with thermodynamic and relativistic models of entropy and time symmetry, but unsupported by astronomical data. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively mirrors Big Bang, offering closure and symmetry. Simple in concept, but difficult to reconcile with observed acceleration. || ★★★☆☆
|-
| '''Heuristic Value''' || Motivated theoretical discussion on cosmological fate and cyclic models. Limited influence in current cosmology. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Explores cosmological temporality and finitude. Once a philosophically compelling counterbalance to eternal expansion. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on time-reversible solutions to Friedmann equations and relativistic cosmology. Rigorous within GR but not extended in modern frameworks. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.8 Big Bounce – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || No direct observational evidence yet. Some loop quantum cosmology models suggest signatures in the CMB, but these remain speculative. || ★★☆☆☆
|-
| '''Internal Consistency''' || Offers a logically coherent alternative to singularity-based models. Dependent on quantum gravity frameworks (e.g. loop quantum gravity) that remain under development. || ★★★☆☆
|-
| '''Predictive Power''' || Provides potential testable differences in early universe structure and CMB fluctuations. Predictions are still uncertain and model-dependent. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges general relativity with quantum mechanics. Limited overlap with geology or observational astronomy. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex and abstract. The idea of a cyclical universe is conceptually appealing, but quantum corrections are not intuitive. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates exploration of singularity resolution and quantum gravity cosmologies. Encourages investigation of pre-Big Bang conditions. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Resonates with ancient cyclical cosmologies and philosophical ideas of eternal recurrence. Reframes the question of origins. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on extensions of Friedmann equations using loop quantum corrections or other quantum gravity approaches. Some models are mathematically formal, but the field is still unsettled. || ★★★☆☆
|}

'''Total: 24/40'''

=== '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' ===

''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆
|-
| '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆
|-
| '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆
|-
| '''Mathematical Rigor''' || Provides original equations (e.g. for \(D_{\text{pref}}\), \(G = (\gamma - 1)/4\pi\), \(\kappa = v_{\text{RMS}}^2 / c^4\)) and consistent dimensional analysis. Excel-based datasets link math to observations. Lacks field-theoretic formalism. || ★★★★☆
|}

'''Total: 34/40'''

=== '''8.8.10 Spiral Cosmology – AI Rating Summary''' ===

''Related link:'' [https://www.academia.edu/103005946/Cosmology_as_Spiral_Evolution Spiral Cosmology on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers visual and structural explanations for spiral galaxy morphology and cosmic rotation patterns. Less directly tied to quantitative data or tested predictions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Conceptually consistent in proposing self-similar spiral evolution at multiple scales, but lacks a developed dynamic or energetic framework. || ★★☆☆☆
|-
| '''Predictive Power''' || Suggests qualitative evolutionary stages and possible cyclic features, but does not provide specific numerical predictions. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Makes symbolic and philosophical connections across cosmology, biology, and culture. Scientific integration with physical fields is minimal. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Emphasizes intuitive and visual structures (e.g. spirals), which are accessible but may oversimplify physical complexity. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulates reflection on cosmic structure, symmetry, and recursion. Encourages reinterpretation of known forms (e.g. galaxies, DNA, hurricanes). || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Reconnects with ancient and Renaissance cosmologies linking form and function across scales. Offers metaphysical resonance. || ★★★★☆
|-
| '''Mathematical Rigor''' || Utilizes geometric symbolism (e.g. spiral ratios, golden mean) but lacks physical equations or dynamical systems modeling. No quantitative derivations. || ★★☆☆☆
|}

'''Total: 23/40'''

=== '''8.9 – Additional Alternative Cosmological Theories (Under Evaluation)''' ===

* '''[https://arxiv.org/abs/physics/0003045 Topological Field Framework]''' (Hall) – Proposes that fundamental constants such as G, c, and Λ emerge from topological constraints in higher-dimensional field configurations. The theory has high internal logic, mathematical consistency, and geometric depth. Empirical validation depends on measurable predictions, but its interdisciplinary integration (e.g., quantum geometry, general relativity) offers high conceptual promise.

* '''[https://arxiv.org/abs/astro-ph/0409117 Conformal Gravity]''' (Mannheim–Kazanas) – Eliminates the need for dark matter by applying conformal symmetry to gravitational equations. It explains galactic rotation curves and lensing without exotic particles. Predictive power is strong on galactic scales, but it faces challenges with early-universe data. Internally consistent and testable, though its cosmological compatibility is debated.

* '''[https://arxiv.org/abs/astro-ph/9801196 Quasi-Steady State Cosmology (QSSC)]''' – A cyclic, non-Big Bang model incorporating continuous matter creation via a “C-field.” It accounts for redshift and some cosmic structure without expansion from a singularity. Empirical adequacy is mixed due to tension with CMB and elemental abundance observations. Still, its falsifiability and explanatory ambition support its inclusion in theoretical discourse.

* '''[https://tuomas.suntola.fi/the-dynamic-universe/ Dynamic Universe]''' (Tuomo Suntola) – A model based on zero-energy balance and time-evolving geometry, predicting cosmic constants from dynamic curvature. Offers conceptual simplicity and mathematical consistency. Deviates from mainstream relativity but maintains coherence. Predictions related to H₀ and time-scaling allow for observational tests and empirical challenge.


'''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]'''</text>
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      <text bytes="30699" sha1="57tmy5q8li9pz6uegxy7rny3lpzqn6t" xml:space="preserve">== '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' =

== '''8.1 Purpose''' ==

This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated.

== '''8.2 Toolchain and Workflow''' ==

AI tools like ChatGPT are used to analyze, compare, and refine theories

Tables and frameworks are generated collaboratively using open formats

Contributors submit input via email or editing suggestions

Ratings and evaluations are dynamically updated based on ongoing analysis

== '''8.3 AI-Based Rating System: Motivation and Procedure''' ==

To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''.

This system is designed to be:

Transparent – Each rating is justified through AI’s large-scale reference analysis.

Dynamic – Contributors may submit additional materials to request re-evaluation.

Consistent – All evaluations are performed by the same AI logic, eliminating personal bias.

Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted.

This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate.

== '''8.4 Open Participation''' ==

This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to:

Describe their framework in terms of assumptions, predictions, and compatibility

Suggest how their model could be tested or falsified

Provide references or original materials for AI evaluation

All analysis is open, and contributors may propose improvements at any time.

== '''8.5 Understanding the Star Ratings''' ==

The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied.

'''8.5.1. Empirical Adequacy'''  
Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower.

'''8.5.2. Internal Consistency'''  
Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions.

'''8.5.3. Predictive Power'''  
Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings.

'''8.5.4. Cross-Disciplinary Compatibility'''  
Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score.

'''8.5.5. Conceptual Clarity and Simplicity'''  
Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification.

'''8.5.6. Heuristic Value'''  
Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential.

'''8.5.7. Historical and Philosophical Insight'''  
Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here.

'''8.5.8. Mathematical Rigor'''  
Does the theory provide clear mathematical formulations, derivations, and quantitative predictions? Theories are valued for their use of equations to express core principles, ensure internal consistency, and generate testable results.


Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail.


=== '''8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor)''' ===

''Note: In July 2025, an eighth evaluation criterion was added: '''Mathematical Rigor'''. The total score is now out of 40 stars instead of 35.  ''
''All ratings are expressed in whole stars (★), without fractional values, to ensure clarity in display and consistency with the visual format of this table.''  
''Theories are listed in the same order as in Section 8.8.''

{| class=&quot;wikitable&quot;
! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HP''' !! '''MR''' !! '''Total (★/40)'''
|-
| '''General Relativity''' || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || ★★★★★ || '''37'''
|-
| '''Newtonian Gravity''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''33'''
|-
| '''MOND''' || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || '''26'''
|-
| '''Emergent Gravity''' || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''24'''
|-
| '''Big Bang''' || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || '''34'''
|-
| '''Steady State Theory''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23'''
|-
| '''Big Crunch''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Big Bounce''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Cosmic Influx Theory (CIT)''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || '''33'''
|-
| '''Spiral Cosmology''' || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''21'''
|}

''Legend:''  
''EA = Empirical Adequacy IC = Internal Consistency PP = Predictive Power CC = Cross-Disciplinary Compatibility  ''
''CS = Conceptual Simplicity HV = Heuristic Value HP = Historical/Philosophical Insight MR = Mathematical Rigor''


&lt;!-- Add a blank line here --&gt;

== '''8.7 Requesting Detailed Justification''' ==

“Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by:

1. Visiting the '''discussion page''' of this Wikiversity chapter.
  
2. Mentioning the theory by name and explicitly asking for the detailed breakdown.
  
3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. 

These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented.

If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership.

'''Mainstream theories are subject to the same critical standard.'''  
If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed.

If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''.

== '''8.8 Detailed Evaluations of Theories''' ==

This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes.

=== '''8.8.1 General Relativity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Matches a wide range of observations: gravitational lensing, GPS corrections, perihelion precession, black hole dynamics, and gravitational waves. Supported by multiple experiments. || ★★★★★
|-
| '''Internal Consistency''' || Highly consistent within its differential geometric framework. Built upon Einstein's field equations with tensor calculus. Few internal contradictions, though extensions (e.g. quantum gravity) face challenges. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted gravitational redshift, time dilation, frame-dragging, and gravitational waves. Continues to guide observations in astrophysics. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with cosmology and astrophysics. Some tension with quantum theory. Less integrated with planetary geology or biology. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex mathematical structure makes it less intuitive. Conceptually abstract (spacetime curvature, geodesics). Clarity improves with education, but simplicity is low. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired vast developments in cosmology, black hole theory, and relativistic astrophysics. Foundation for modern gravitational physics. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Deep philosophical implications about space, time, and causality. Represents a major shift from Newtonian absolute space. Influenced 20th-century philosophy of science. || ★★★★★
|-
| '''Mathematical Rigor''' || Built upon advanced mathematics: Riemannian geometry, Einstein field equations, tensor calculus. Equations are precise, formal, and deeply embedded in differential geometry. || ★★★★★
|}

'''Total: 39/40'''

=== '''8.8.2 Newtonian Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Accurately describes gravitational interactions for most macroscopic systems (planets, satellites, projectiles) under low-speed, weak-field conditions. Deviates in extreme conditions (e.g. near black holes). || ★★★★☆
|-
| '''Internal Consistency''' || Mathematically self-consistent with inverse-square law and Newton's laws of motion. Assumes instantaneous action at a distance, which conflicts with relativity. || ★★★★☆
|-
| '''Predictive Power''' || Predicts planetary orbits, tides, escape velocities, and Keplerian motion. Fails for relativistic effects (e.g. Mercury’s precession, gravitational lensing). || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Well-integrated in classical mechanics, astronomy, and engineering. Less compatible with modern cosmology or relativistic frameworks. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple and intuitive: gravity as a force between masses. Easily grasped and widely taught. || ★★★★★
|-
| '''Heuristic Value''' || Inspired centuries of scientific discovery and classical mechanics. Still used in teaching and engineering. Limited in modern theoretical development. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Founded classical physics. Major leap in scientific method and mathematical modeling. Paved the way for Enlightenment-era science. || ★★★★★
|-
| '''Mathematical Rigor''' || Clear and elegant use of calculus and vector algebra (e.g. \(\displaystyle F = G \frac{m_1 m_2}{r^2}\)). Highly accessible and historically groundbreaking, but lacks deeper geometric or relativistic structures. || ★★★★☆
|}

'''Total: 33/40'''

=== '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Fits galactic rotation curves without invoking dark matter. Matches Tully-Fisher relation. Performance weakens at cluster and cosmological scales. || ★★★★☆
|-
| '''Internal Consistency''' || Original formulation is non-relativistic and phenomenological. Several relativistic extensions (e.g. TeVeS) exist but introduce complexity and fine-tuning. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts galaxy dynamics from baryonic matter alone. Less predictive at larger scales or in non-galactic contexts. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Primarily astrophysical. Some tension with cosmology, structure formation, and gravitational lensing. Not aligned with particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple at galactic scale: modifies acceleration below a threshold \(a_0\). Extensions are less intuitive. || ★★★★☆
|-
| '''Heuristic Value''' || Challenges dark matter paradigm and motivates alternate gravity models. Sparked theoretical and observational debate. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Offers a conceptual challenge to Newton/Einstein gravity. Philosophically provocative, but limited historical lineage. || ★★★☆☆
|-
| '''Mathematical Rigor''' || Employs interpolating functions and modified Poisson equations. Relativistic extensions (e.g. TeVeS) involve tensor-vector-scalar frameworks. Rigorous in parts, but lacks unified formalism. || ★★★☆☆
|}

'''Total: 28/40'''

=== '''8.8.4 Emergent Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Entropic_gravity Emergent / Entropic Gravity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Attempts to account for galactic rotation without dark matter by linking gravity to entropy and information. Some results match MOND-like behavior, but broad observational support remains limited. || ★★★☆☆
|-
| '''Internal Consistency''' || Theoretical framework draws from thermodynamics, holography, and information theory. Conceptually coherent, but not fully developed as a unified physical model. || ★★★☆☆
|-
| '''Predictive Power''' || Offers qualitative insights but lacks precise predictive capabilities in most contexts. No wide adoption for simulations or system modeling. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates ideas from black hole thermodynamics, quantum information, and spacetime geometry. Weak integration with observational astronomy or geology. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Abstract and speculative. Concepts like entropic forces and holographic screens are not intuitive for most readers. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates discussion about the nature of spacetime and gravity. Has inspired new theoretical directions in quantum gravity and information theory. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Philosophically intriguing: redefines gravity as emergent rather than fundamental. Links to ideas from Bekenstein and Hawking. || ★★★★☆
|-
| '''Mathematical Rigor''' || Relies on concepts from thermodynamics (e.g. entropy gradients), statistical mechanics, and quantum gravity. Uses integral relations and variational principles, but lacks a standardized set of equations for general use. || ★★★☆☆
|}

'''Total: 26/40'''

=== '''8.8.5 Big Bang – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strongly supported by CMB, redshift-distance relation, and light element abundances. However, JWST data revealing early, mature galaxies challenges the predicted timeline of structure formation. || ★★★★☆
|-
| '''Internal Consistency''' || Internally coherent within the ΛCDM framework. Logical structure is intact, though singularity and quantum-gravity transitions remain unresolved. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted CMB and nucleosynthesis. But recent observations (e.g. JWST galaxies at z &gt; 10) were not anticipated, requiring post-hoc model adjustments. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Strong integration with general relativity, quantum field theory, and thermodynamics. Limited links to geology or planetary evolution. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Conceptually complex genesis: singularity, inflation, and multiple postulated fields (inflaton, dark energy, dark matter). Relies on hypothetical constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulated massive observational and theoretical advances. Has driven decades of mission planning and cosmological interpretation. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Represented a paradigm shift from steady-state thinking. Raises deep ontological and metaphysical questions (e.g. time’s origin, creation ex nihilo). || ★★★★☆
|-
| '''Mathematical Rigor''' || Grounded in Einstein’s field equations, Friedmann dynamics, and thermodynamics. Offers well-defined, highly developed formalism. || ★★★★★
|}

'''Total: 34/40'''

=== '''8.8.6 Steady State Theory – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Cosmology]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Early successes with radio‐source counts, but contradicted by the cosmic microwave background, evolving galaxy populations, and quasar statistics. || ★★☆☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within the “perfect cosmological principle,” requiring continuous matter creation at a fixed rate. Logical but invokes an ad-hoc creation field (C-field). || ★★★☆☆
|-
| '''Predictive Power''' || Predicted constant large-scale density and specific radio‐source number counts; few successful novel predictions beyond its initial scope. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Limited overlap with modern astrophysics and particle physics; conflicts with nucleosynthesis and CMB observations. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively simple: Universe is homogeneous in space **and** time, avoiding an initial singularity. Minimal parameter set. || ★★★★☆
|-
| '''Heuristic Value''' || Historically spurred observational tests that ultimately favored Big Bang models; now mainly of pedagogical interest. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Embodies the perfect cosmological principle and continuous-creation idea, provoking debates on temporality and cosmological assumptions. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs Friedmann-like solutions with a creation term; uses relativistic field equations but lacks the richer formal development of ΛCDM or GR extensions. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.7 Big Crunch – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Once considered viable if cosmic density exceeded the critical value. Current observations (accelerating expansion, dark energy) contradict its key assumptions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretically consistent as a time-reversed Big Bang within general relativity. Requires high matter density and no (or reversing) dark energy. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts a decelerating expansion turning to collapse. Testable in principle, but not supported by current data. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with thermodynamic and relativistic models of entropy and time symmetry, but unsupported by astronomical data. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively mirrors Big Bang, offering closure and symmetry. Simple in concept, but difficult to reconcile with observed acceleration. || ★★★☆☆
|-
| '''Heuristic Value''' || Motivated theoretical discussion on cosmological fate and cyclic models. Limited influence in current cosmology. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Explores cosmological temporality and finitude. Once a philosophically compelling counterbalance to eternal expansion. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on time-reversible solutions to Friedmann equations and relativistic cosmology. Rigorous within GR but not extended in modern frameworks. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.8 Big Bounce – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || No direct observational evidence yet. Some loop quantum cosmology models suggest signatures in the CMB, but these remain speculative. || ★★☆☆☆
|-
| '''Internal Consistency''' || Offers a logically coherent alternative to singularity-based models. Dependent on quantum gravity frameworks (e.g. loop quantum gravity) that remain under development. || ★★★☆☆
|-
| '''Predictive Power''' || Provides potential testable differences in early universe structure and CMB fluctuations. Predictions are still uncertain and model-dependent. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges general relativity with quantum mechanics. Limited overlap with geology or observational astronomy. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex and abstract. The idea of a cyclical universe is conceptually appealing, but quantum corrections are not intuitive. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates exploration of singularity resolution and quantum gravity cosmologies. Encourages investigation of pre-Big Bang conditions. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Resonates with ancient cyclical cosmologies and philosophical ideas of eternal recurrence. Reframes the question of origins. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on extensions of Friedmann equations using loop quantum corrections or other quantum gravity approaches. Some models are mathematically formal, but the field is still unsettled. || ★★★☆☆
|}

'''Total: 24/40'''

=== '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' ===

''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆
|-
| '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆
|-
| '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆
|-
| '''Mathematical Rigor''' || Provides original equations (e.g. for \(D_{\text{pref}}\), \(G = (\gamma - 1)/4\pi\), \(\kappa = v_{\text{RMS}}^2 / c^4\)) and consistent dimensional analysis. Excel-based datasets link math to observations. Lacks field-theoretic formalism. || ★★★★☆
|}

'''Total: 34/40'''

=== '''8.8.10 Spiral Cosmology – AI Rating Summary''' ===

''Related link:'' [https://www.academia.edu/103005946/Cosmology_as_Spiral_Evolution Spiral Cosmology on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers visual and structural explanations for spiral galaxy morphology and cosmic rotation patterns. Less directly tied to quantitative data or tested predictions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Conceptually consistent in proposing self-similar spiral evolution at multiple scales, but lacks a developed dynamic or energetic framework. || ★★☆☆☆
|-
| '''Predictive Power''' || Suggests qualitative evolutionary stages and possible cyclic features, but does not provide specific numerical predictions. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Makes symbolic and philosophical connections across cosmology, biology, and culture. Scientific integration with physical fields is minimal. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Emphasizes intuitive and visual structures (e.g. spirals), which are accessible but may oversimplify physical complexity. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulates reflection on cosmic structure, symmetry, and recursion. Encourages reinterpretation of known forms (e.g. galaxies, DNA, hurricanes). || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Reconnects with ancient and Renaissance cosmologies linking form and function across scales. Offers metaphysical resonance. || ★★★★☆
|-
| '''Mathematical Rigor''' || Utilizes geometric symbolism (e.g. spiral ratios, golden mean) but lacks physical equations or dynamical systems modeling. No quantitative derivations. || ★★☆☆☆
|}

'''Total: 23/40'''

=== '''8.9 – Additional Alternative Cosmological Theories (Under Evaluation)''' ===

* '''[https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework]''' (Hall) – Proposes that fundamental constants such as G, c, and Λ emerge from topological constraints in higher-dimensional field configurations. The theory has high internal logic, mathematical consistency, and geometric depth. Empirical validation depends on measurable predictions, but its interdisciplinary integration (e.g., quantum geometry, general relativity) offers high conceptual promise.

* '''[https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]''' (Mannheim–Kazanas) – Eliminates the need for dark matter by applying conformal symmetry to gravitational equations. It explains galactic rotation curves and lensing without exotic particles. Predictive power is strong on galactic scales, but it faces challenges with early-universe data. Internally consistent and testable, though its cosmological compatibility is debated.

* '''[https://www.ias.ac.in/article/fulltext/pram/053/06/1093-1104 The Quasi-Steady State Cosmology: Theory and Observations]''' – A cyclic, non-Big Bang model incorporating continuous matter creation via a “C-field.” It accounts for redshift and some cosmic structure without expansion from a singularity. Empirical adequacy is mixed due to tension with CMB and elemental abundance observations. Still, its falsifiability and explanatory ambition support its inclusion in theoretical discourse.

* '''[https://physicsfoundations.org/suntola/dynamic-universe Dynamic Universe]''' (Tuomo Suntola) – A model based on zero-energy balance and time-evolving geometry, predicting cosmic constants from dynamic curvature. Offers conceptual simplicity and mathematical consistency. Deviates from mainstream relativity but maintains coherence. Predictions related to H₀ and time-scaling allow for observational tests and empirical challenge.  
{{#ev:youtube|n62WMdSYSjk|Tuomo Suntola: Introduction to the Dynamic Universe}}


'''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]'''</text>
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      <text bytes="32849" sha1="2epxbu7zzrcev70fgh66dirpqfxb7jm" xml:space="preserve">== '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' =

== '''8.1 Purpose''' ==

This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated.

== '''8.2 Toolchain and Workflow''' ==

AI tools like ChatGPT are used to analyze, compare, and refine theories

Tables and frameworks are generated collaboratively using open formats

Contributors submit input via email or editing suggestions

Ratings and evaluations are dynamically updated based on ongoing analysis

== '''8.3 AI-Based Rating System: Motivation and Procedure''' ==

To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''.

This system is designed to be:

Transparent – Each rating is justified through AI’s large-scale reference analysis.

Dynamic – Contributors may submit additional materials to request re-evaluation.

Consistent – All evaluations are performed by the same AI logic, eliminating personal bias.

Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted.

This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate.

== '''8.4 Open Participation''' ==

This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to:

Describe their framework in terms of assumptions, predictions, and compatibility

Suggest how their model could be tested or falsified

Provide references or original materials for AI evaluation

All analysis is open, and contributors may propose improvements at any time.

== '''8.5 Understanding the Star Ratings''' ==

The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied.

'''8.5.1. Empirical Adequacy'''  
Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower.

'''8.5.2. Internal Consistency'''  
Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions.

'''8.5.3. Predictive Power'''  
Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings.

'''8.5.4. Cross-Disciplinary Compatibility'''  
Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score.

'''8.5.5. Conceptual Clarity and Simplicity'''  
Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification.

'''8.5.6. Heuristic Value'''  
Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential.

'''8.5.7. Historical and Philosophical Insight'''  
Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here.

'''8.5.8. Mathematical Rigor'''  
Does the theory provide clear mathematical formulations, derivations, and quantitative predictions? Theories are valued for their use of equations to express core principles, ensure internal consistency, and generate testable results.


Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail.


=== '''8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor)''' ===

''Note: In July 2025, an eighth evaluation criterion was added: '''Mathematical Rigor'''. The total score is now out of 40 stars instead of 35.  ''
''All ratings are expressed in whole stars (★), without fractional values, to ensure clarity in display and consistency with the visual format of this table.''  
''Theories are listed in the same order as in Section 8.8.''

{| class=&quot;wikitable&quot;
! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HP''' !! '''MR''' !! '''Total (★/40)'''
|-
| '''General Relativity''' || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || ★★★★★ || '''37'''
|-
| '''Newtonian Gravity''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''33'''
|-
| '''MOND''' || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || '''26'''
|-
| '''Emergent Gravity''' || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''24'''
|-
| '''Big Bang''' || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || '''34'''
|-
| '''Steady State Theory''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23'''
|-
| '''Big Crunch''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Big Bounce''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Cosmic Influx Theory (CIT)''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || '''33'''
|-
| '''Spiral Cosmology''' || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''21'''
|}

''Legend:''  
''EA = Empirical Adequacy IC = Internal Consistency PP = Predictive Power CC = Cross-Disciplinary Compatibility  ''
''CS = Conceptual Simplicity HV = Heuristic Value HP = Historical/Philosophical Insight MR = Mathematical Rigor''


&lt;!-- Add a blank line here --&gt;

== '''8.7 Requesting Detailed Justification''' ==

“Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by:

1. Visiting the '''discussion page''' of this Wikiversity chapter.
  
2. Mentioning the theory by name and explicitly asking for the detailed breakdown.
  
3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. 

These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented.

If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership.

'''Mainstream theories are subject to the same critical standard.'''  
If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed.

If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''.

== '''8.8 Detailed Evaluations of Theories''' ==

This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes.

=== '''8.8.1 General Relativity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Matches a wide range of observations: gravitational lensing, GPS corrections, perihelion precession, black hole dynamics, and gravitational waves. Supported by multiple experiments. || ★★★★★
|-
| '''Internal Consistency''' || Highly consistent within its differential geometric framework. Built upon Einstein's field equations with tensor calculus. Few internal contradictions, though extensions (e.g. quantum gravity) face challenges. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted gravitational redshift, time dilation, frame-dragging, and gravitational waves. Continues to guide observations in astrophysics. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with cosmology and astrophysics. Some tension with quantum theory. Less integrated with planetary geology or biology. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex mathematical structure makes it less intuitive. Conceptually abstract (spacetime curvature, geodesics). Clarity improves with education, but simplicity is low. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired vast developments in cosmology, black hole theory, and relativistic astrophysics. Foundation for modern gravitational physics. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Deep philosophical implications about space, time, and causality. Represents a major shift from Newtonian absolute space. Influenced 20th-century philosophy of science. || ★★★★★
|-
| '''Mathematical Rigor''' || Built upon advanced mathematics: Riemannian geometry, Einstein field equations, tensor calculus. Equations are precise, formal, and deeply embedded in differential geometry. || ★★★★★
|}

'''Total: 39/40'''

=== '''8.8.2 Newtonian Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Accurately describes gravitational interactions for most macroscopic systems (planets, satellites, projectiles) under low-speed, weak-field conditions. Deviates in extreme conditions (e.g. near black holes). || ★★★★☆
|-
| '''Internal Consistency''' || Mathematically self-consistent with inverse-square law and Newton's laws of motion. Assumes instantaneous action at a distance, which conflicts with relativity. || ★★★★☆
|-
| '''Predictive Power''' || Predicts planetary orbits, tides, escape velocities, and Keplerian motion. Fails for relativistic effects (e.g. Mercury’s precession, gravitational lensing). || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Well-integrated in classical mechanics, astronomy, and engineering. Less compatible with modern cosmology or relativistic frameworks. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple and intuitive: gravity as a force between masses. Easily grasped and widely taught. || ★★★★★
|-
| '''Heuristic Value''' || Inspired centuries of scientific discovery and classical mechanics. Still used in teaching and engineering. Limited in modern theoretical development. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Founded classical physics. Major leap in scientific method and mathematical modeling. Paved the way for Enlightenment-era science. || ★★★★★
|-
| '''Mathematical Rigor''' || Clear and elegant use of calculus and vector algebra (e.g. \(\displaystyle F = G \frac{m_1 m_2}{r^2}\)). Highly accessible and historically groundbreaking, but lacks deeper geometric or relativistic structures. || ★★★★☆
|}

'''Total: 33/40'''

=== '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Fits galactic rotation curves without invoking dark matter. Matches Tully-Fisher relation. Performance weakens at cluster and cosmological scales. || ★★★★☆
|-
| '''Internal Consistency''' || Original formulation is non-relativistic and phenomenological. Several relativistic extensions (e.g. TeVeS) exist but introduce complexity and fine-tuning. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts galaxy dynamics from baryonic matter alone. Less predictive at larger scales or in non-galactic contexts. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Primarily astrophysical. Some tension with cosmology, structure formation, and gravitational lensing. Not aligned with particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple at galactic scale: modifies acceleration below a threshold \(a_0\). Extensions are less intuitive. || ★★★★☆
|-
| '''Heuristic Value''' || Challenges dark matter paradigm and motivates alternate gravity models. Sparked theoretical and observational debate. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Offers a conceptual challenge to Newton/Einstein gravity. Philosophically provocative, but limited historical lineage. || ★★★☆☆
|-
| '''Mathematical Rigor''' || Employs interpolating functions and modified Poisson equations. Relativistic extensions (e.g. TeVeS) involve tensor-vector-scalar frameworks. Rigorous in parts, but lacks unified formalism. || ★★★☆☆
|}

'''Total: 28/40'''

=== '''8.8.4 Emergent Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Entropic_gravity Emergent / Entropic Gravity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Attempts to account for galactic rotation without dark matter by linking gravity to entropy and information. Some results match MOND-like behavior, but broad observational support remains limited. || ★★★☆☆
|-
| '''Internal Consistency''' || Theoretical framework draws from thermodynamics, holography, and information theory. Conceptually coherent, but not fully developed as a unified physical model. || ★★★☆☆
|-
| '''Predictive Power''' || Offers qualitative insights but lacks precise predictive capabilities in most contexts. No wide adoption for simulations or system modeling. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates ideas from black hole thermodynamics, quantum information, and spacetime geometry. Weak integration with observational astronomy or geology. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Abstract and speculative. Concepts like entropic forces and holographic screens are not intuitive for most readers. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates discussion about the nature of spacetime and gravity. Has inspired new theoretical directions in quantum gravity and information theory. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Philosophically intriguing: redefines gravity as emergent rather than fundamental. Links to ideas from Bekenstein and Hawking. || ★★★★☆
|-
| '''Mathematical Rigor''' || Relies on concepts from thermodynamics (e.g. entropy gradients), statistical mechanics, and quantum gravity. Uses integral relations and variational principles, but lacks a standardized set of equations for general use. || ★★★☆☆
|}

'''Total: 26/40'''

=== '''8.8.5 Big Bang – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strongly supported by CMB, redshift-distance relation, and light element abundances. However, JWST data revealing early, mature galaxies challenges the predicted timeline of structure formation. || ★★★★☆
|-
| '''Internal Consistency''' || Internally coherent within the ΛCDM framework. Logical structure is intact, though singularity and quantum-gravity transitions remain unresolved. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted CMB and nucleosynthesis. But recent observations (e.g. JWST galaxies at z &gt; 10) were not anticipated, requiring post-hoc model adjustments. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Strong integration with general relativity, quantum field theory, and thermodynamics. Limited links to geology or planetary evolution. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Conceptually complex genesis: singularity, inflation, and multiple postulated fields (inflaton, dark energy, dark matter). Relies on hypothetical constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulated massive observational and theoretical advances. Has driven decades of mission planning and cosmological interpretation. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Represented a paradigm shift from steady-state thinking. Raises deep ontological and metaphysical questions (e.g. time’s origin, creation ex nihilo). || ★★★★☆
|-
| '''Mathematical Rigor''' || Grounded in Einstein’s field equations, Friedmann dynamics, and thermodynamics. Offers well-defined, highly developed formalism. || ★★★★★
|}

'''Total: 34/40'''

=== '''8.8.6 Steady State Theory – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Cosmology]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Early successes with radio‐source counts, but contradicted by the cosmic microwave background, evolving galaxy populations, and quasar statistics. || ★★☆☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within the “perfect cosmological principle,” requiring continuous matter creation at a fixed rate. Logical but invokes an ad-hoc creation field (C-field). || ★★★☆☆
|-
| '''Predictive Power''' || Predicted constant large-scale density and specific radio‐source number counts; few successful novel predictions beyond its initial scope. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Limited overlap with modern astrophysics and particle physics; conflicts with nucleosynthesis and CMB observations. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively simple: Universe is homogeneous in space **and** time, avoiding an initial singularity. Minimal parameter set. || ★★★★☆
|-
| '''Heuristic Value''' || Historically spurred observational tests that ultimately favored Big Bang models; now mainly of pedagogical interest. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Embodies the perfect cosmological principle and continuous-creation idea, provoking debates on temporality and cosmological assumptions. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs Friedmann-like solutions with a creation term; uses relativistic field equations but lacks the richer formal development of ΛCDM or GR extensions. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.7 Big Crunch – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Once considered viable if cosmic density exceeded the critical value. Current observations (accelerating expansion, dark energy) contradict its key assumptions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretically consistent as a time-reversed Big Bang within general relativity. Requires high matter density and no (or reversing) dark energy. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts a decelerating expansion turning to collapse. Testable in principle, but not supported by current data. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with thermodynamic and relativistic models of entropy and time symmetry, but unsupported by astronomical data. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively mirrors Big Bang, offering closure and symmetry. Simple in concept, but difficult to reconcile with observed acceleration. || ★★★☆☆
|-
| '''Heuristic Value''' || Motivated theoretical discussion on cosmological fate and cyclic models. Limited influence in current cosmology. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Explores cosmological temporality and finitude. Once a philosophically compelling counterbalance to eternal expansion. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on time-reversible solutions to Friedmann equations and relativistic cosmology. Rigorous within GR but not extended in modern frameworks. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.8 Big Bounce – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || No direct observational evidence yet. Some loop quantum cosmology models suggest signatures in the CMB, but these remain speculative. || ★★☆☆☆
|-
| '''Internal Consistency''' || Offers a logically coherent alternative to singularity-based models. Dependent on quantum gravity frameworks (e.g. loop quantum gravity) that remain under development. || ★★★☆☆
|-
| '''Predictive Power''' || Provides potential testable differences in early universe structure and CMB fluctuations. Predictions are still uncertain and model-dependent. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges general relativity with quantum mechanics. Limited overlap with geology or observational astronomy. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex and abstract. The idea of a cyclical universe is conceptually appealing, but quantum corrections are not intuitive. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates exploration of singularity resolution and quantum gravity cosmologies. Encourages investigation of pre-Big Bang conditions. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Resonates with ancient cyclical cosmologies and philosophical ideas of eternal recurrence. Reframes the question of origins. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on extensions of Friedmann equations using loop quantum corrections or other quantum gravity approaches. Some models are mathematically formal, but the field is still unsettled. || ★★★☆☆
|}

'''Total: 24/40'''

=== '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' ===

''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆
|-
| '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆
|-
| '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆
|-
| '''Mathematical Rigor''' || Provides original equations (e.g. for \(D_{\text{pref}}\), \(G = (\gamma - 1)/4\pi\), \(\kappa = v_{\text{RMS}}^2 / c^4\)) and consistent dimensional analysis. Excel-based datasets link math to observations. Lacks field-theoretic formalism. || ★★★★☆
|}

'''Total: 34/40'''

=== '''8.8.10 Spiral Cosmology – AI Rating Summary''' ===

''Related link:'' [https://www.academia.edu/103005946/Cosmology_as_Spiral_Evolution Spiral Cosmology on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers visual and structural explanations for spiral galaxy morphology and cosmic rotation patterns. Less directly tied to quantitative data or tested predictions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Conceptually consistent in proposing self-similar spiral evolution at multiple scales, but lacks a developed dynamic or energetic framework. || ★★☆☆☆
|-
| '''Predictive Power''' || Suggests qualitative evolutionary stages and possible cyclic features, but does not provide specific numerical predictions. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Makes symbolic and philosophical connections across cosmology, biology, and culture. Scientific integration with physical fields is minimal. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Emphasizes intuitive and visual structures (e.g. spirals), which are accessible but may oversimplify physical complexity. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulates reflection on cosmic structure, symmetry, and recursion. Encourages reinterpretation of known forms (e.g. galaxies, DNA, hurricanes). || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Reconnects with ancient and Renaissance cosmologies linking form and function across scales. Offers metaphysical resonance. || ★★★★☆
|-
| '''Mathematical Rigor''' || Utilizes geometric symbolism (e.g. spiral ratios, golden mean) but lacks physical equations or dynamical systems modeling. No quantitative derivations. || ★★☆☆☆
|}

'''Total: 23/40'''

=== '''8.8.11 Topological Field Framework – AI Rating Summary''' ===

''Related link:'' [https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework on ResearchGate]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Proposes a geometric origin of particle properties and fundamental constants, but lacks direct comparison with observational or experimental datasets. Empirical testing is suggested but not yet demonstrated. || ★★☆☆☆
|-
| '''Internal Consistency''' || Builds a coherent and logically structured model grounded in topology and pressure gradients. Concepts are well integrated, with minimal contradictions. || ★★★★☆
|-
| '''Predictive Power''' || Offers a pathway to derive constants such as G, c, and Λ from topology and boundary conditions. However, quantitative predictions are still under development or pending validation. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges gravitational theory, particle physics, and topology. Aligns with ideas in quantum geometry, though not yet embedded in mainstream formulations. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Dense but conceptually focused. Uses field and pressure analogies to unify gravity and gauge interactions, though the abstract nature may limit accessibility. || ★★★☆☆
|-
| '''Heuristic Value''' || Provides an original and stimulating approach to unify physical constants via geometry. Encourages rethinking of foundational assumptions in physics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Revives geometrical unification ideals from early 20th-century physics and connects them to modern field-based ontology. Philosophically grounded. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs differential geometry, topological mapping, and field pressure modeling. Mathematical structure is present, but derivations are at a conceptual stage. || ★★★☆☆
|}

'''Total: 27/40'''


=== '''8.9 – Additional Alternative Cosmological Theories (Under Evaluation)''' ===

* '''[https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework]''' (Hall) – Proposes that fundamental constants such as G, c, and Λ emerge from topological constraints in higher-dimensional field configurations. The theory has high internal logic, mathematical consistency, and geometric depth. Empirical validation depends on measurable predictions, but its interdisciplinary integration (e.g., quantum geometry, general relativity) offers high conceptual promise.

* '''[https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]''' (Mannheim–Kazanas) – Eliminates the need for dark matter by applying conformal symmetry to gravitational equations. It explains galactic rotation curves and lensing without exotic particles. Predictive power is strong on galactic scales, but it faces challenges with early-universe data. Internally consistent and testable, though its cosmological compatibility is debated.

* '''[https://www.ias.ac.in/article/fulltext/pram/053/06/1093-1104 The Quasi-Steady State Cosmology: Theory and Observations]''' – A cyclic, non-Big Bang model incorporating continuous matter creation via a “C-field.” It accounts for redshift and some cosmic structure without expansion from a singularity. Empirical adequacy is mixed due to tension with CMB and elemental abundance observations. Still, its falsifiability and explanatory ambition support its inclusion in theoretical discourse.

* '''[https://physicsfoundations.org/suntola/dynamic-universe Dynamic Universe]''' (Tuomo Suntola) – A model based on zero-energy balance and time-evolving geometry, predicting cosmic constants from dynamic curvature. Offers conceptual simplicity and mathematical consistency. Deviates from mainstream relativity but maintains coherence. Predictions related to H₀ and time-scaling allow for observational tests and empirical challenge.  
{{#ev:youtube|n62WMdSYSjk|Tuomo Suntola: Introduction to the Dynamic Universe}}


'''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]'''</text>
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      <text bytes="36740" sha1="7l2w6ls9cpco2c7epiae5mz6m78snah" xml:space="preserve">== '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' =

== '''8.1 Purpose''' ==

This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated.

== '''8.2 Toolchain and Workflow''' ==

AI tools like ChatGPT are used to analyze, compare, and refine theories

Tables and frameworks are generated collaboratively using open formats

Contributors submit input via email or editing suggestions

Ratings and evaluations are dynamically updated based on ongoing analysis

== '''8.3 AI-Based Rating System: Motivation and Procedure''' ==

To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''.

This system is designed to be:

Transparent – Each rating is justified through AI’s large-scale reference analysis.

Dynamic – Contributors may submit additional materials to request re-evaluation.

Consistent – All evaluations are performed by the same AI logic, eliminating personal bias.

Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted.

This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate.

== '''8.4 Open Participation''' ==

This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to:

Describe their framework in terms of assumptions, predictions, and compatibility

Suggest how their model could be tested or falsified

Provide references or original materials for AI evaluation

All analysis is open, and contributors may propose improvements at any time.

== '''8.5 Understanding the Star Ratings''' ==

The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied.

'''8.5.1. Empirical Adequacy'''  
Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower.

'''8.5.2. Internal Consistency'''  
Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions.

'''8.5.3. Predictive Power'''  
Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings.

'''8.5.4. Cross-Disciplinary Compatibility'''  
Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score.

'''8.5.5. Conceptual Clarity and Simplicity'''  
Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification.

'''8.5.6. Heuristic Value'''  
Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential.

'''8.5.7. Historical and Philosophical Insight'''  
Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here.

'''8.5.8. Mathematical Rigor'''  
Does the theory provide clear mathematical formulations, derivations, and quantitative predictions? Theories are valued for their use of equations to express core principles, ensure internal consistency, and generate testable results.


Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail.


=== '''8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor)''' ===

''Note: In July 2025, an eighth evaluation criterion was added: '''Mathematical Rigor'''. The total score is now out of 40 stars instead of 35.  ''
''All ratings are expressed in whole stars (★), without fractional values, to ensure clarity in display and consistency with the visual format of this table.''  
''Theories are listed in the same order as in Section 8.8.''

{| class=&quot;wikitable&quot;
! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HP''' !! '''MR''' !! '''Total (★/40)'''
|-
| '''General Relativity''' || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || ★★★★★ || '''37'''
|-
| '''Newtonian Gravity''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''33'''
|-
| '''MOND''' || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || '''26'''
|-
| '''Emergent Gravity''' || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''24'''
|-
| '''Big Bang''' || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || '''34'''
|-
| '''Steady State Theory''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23'''
|-
| '''Big Crunch''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Big Bounce''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Cosmic Influx Theory (CIT)''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || '''33'''
|-
| '''Spiral Cosmology''' || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''21'''
|}

''Legend:''  
''EA = Empirical Adequacy IC = Internal Consistency PP = Predictive Power CC = Cross-Disciplinary Compatibility  ''
''CS = Conceptual Simplicity HV = Heuristic Value HP = Historical/Philosophical Insight MR = Mathematical Rigor''


&lt;!-- Add a blank line here --&gt;

== '''8.7 Requesting Detailed Justification''' ==

“Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by:

1. Visiting the '''discussion page''' of this Wikiversity chapter.
  
2. Mentioning the theory by name and explicitly asking for the detailed breakdown.
  
3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. 

These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented.

If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership.

'''Mainstream theories are subject to the same critical standard.'''  
If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed.

If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''.

== '''8.8 Detailed Evaluations of Theories''' ==

This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes.

=== '''8.8.1 General Relativity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Matches a wide range of observations: gravitational lensing, GPS corrections, perihelion precession, black hole dynamics, and gravitational waves. Supported by multiple experiments. || ★★★★★
|-
| '''Internal Consistency''' || Highly consistent within its differential geometric framework. Built upon Einstein's field equations with tensor calculus. Few internal contradictions, though extensions (e.g. quantum gravity) face challenges. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted gravitational redshift, time dilation, frame-dragging, and gravitational waves. Continues to guide observations in astrophysics. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with cosmology and astrophysics. Some tension with quantum theory. Less integrated with planetary geology or biology. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex mathematical structure makes it less intuitive. Conceptually abstract (spacetime curvature, geodesics). Clarity improves with education, but simplicity is low. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired vast developments in cosmology, black hole theory, and relativistic astrophysics. Foundation for modern gravitational physics. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Deep philosophical implications about space, time, and causality. Represents a major shift from Newtonian absolute space. Influenced 20th-century philosophy of science. || ★★★★★
|-
| '''Mathematical Rigor''' || Built upon advanced mathematics: Riemannian geometry, Einstein field equations, tensor calculus. Equations are precise, formal, and deeply embedded in differential geometry. || ★★★★★
|}

'''Total: 39/40'''

=== '''8.8.2 Newtonian Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Accurately describes gravitational interactions for most macroscopic systems (planets, satellites, projectiles) under low-speed, weak-field conditions. Deviates in extreme conditions (e.g. near black holes). || ★★★★☆
|-
| '''Internal Consistency''' || Mathematically self-consistent with inverse-square law and Newton's laws of motion. Assumes instantaneous action at a distance, which conflicts with relativity. || ★★★★☆
|-
| '''Predictive Power''' || Predicts planetary orbits, tides, escape velocities, and Keplerian motion. Fails for relativistic effects (e.g. Mercury’s precession, gravitational lensing). || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Well-integrated in classical mechanics, astronomy, and engineering. Less compatible with modern cosmology or relativistic frameworks. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple and intuitive: gravity as a force between masses. Easily grasped and widely taught. || ★★★★★
|-
| '''Heuristic Value''' || Inspired centuries of scientific discovery and classical mechanics. Still used in teaching and engineering. Limited in modern theoretical development. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Founded classical physics. Major leap in scientific method and mathematical modeling. Paved the way for Enlightenment-era science. || ★★★★★
|-
| '''Mathematical Rigor''' || Clear and elegant use of calculus and vector algebra (e.g. \(\displaystyle F = G \frac{m_1 m_2}{r^2}\)). Highly accessible and historically groundbreaking, but lacks deeper geometric or relativistic structures. || ★★★★☆
|}

'''Total: 33/40'''

=== '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Fits galactic rotation curves without invoking dark matter. Matches Tully-Fisher relation. Performance weakens at cluster and cosmological scales. || ★★★★☆
|-
| '''Internal Consistency''' || Original formulation is non-relativistic and phenomenological. Several relativistic extensions (e.g. TeVeS) exist but introduce complexity and fine-tuning. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts galaxy dynamics from baryonic matter alone. Less predictive at larger scales or in non-galactic contexts. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Primarily astrophysical. Some tension with cosmology, structure formation, and gravitational lensing. Not aligned with particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple at galactic scale: modifies acceleration below a threshold \(a_0\). Extensions are less intuitive. || ★★★★☆
|-
| '''Heuristic Value''' || Challenges dark matter paradigm and motivates alternate gravity models. Sparked theoretical and observational debate. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Offers a conceptual challenge to Newton/Einstein gravity. Philosophically provocative, but limited historical lineage. || ★★★☆☆
|-
| '''Mathematical Rigor''' || Employs interpolating functions and modified Poisson equations. Relativistic extensions (e.g. TeVeS) involve tensor-vector-scalar frameworks. Rigorous in parts, but lacks unified formalism. || ★★★☆☆
|}

'''Total: 28/40'''

=== '''8.8.4 Emergent Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Entropic_gravity Emergent / Entropic Gravity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Attempts to account for galactic rotation without dark matter by linking gravity to entropy and information. Some results match MOND-like behavior, but broad observational support remains limited. || ★★★☆☆
|-
| '''Internal Consistency''' || Theoretical framework draws from thermodynamics, holography, and information theory. Conceptually coherent, but not fully developed as a unified physical model. || ★★★☆☆
|-
| '''Predictive Power''' || Offers qualitative insights but lacks precise predictive capabilities in most contexts. No wide adoption for simulations or system modeling. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates ideas from black hole thermodynamics, quantum information, and spacetime geometry. Weak integration with observational astronomy or geology. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Abstract and speculative. Concepts like entropic forces and holographic screens are not intuitive for most readers. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates discussion about the nature of spacetime and gravity. Has inspired new theoretical directions in quantum gravity and information theory. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Philosophically intriguing: redefines gravity as emergent rather than fundamental. Links to ideas from Bekenstein and Hawking. || ★★★★☆
|-
| '''Mathematical Rigor''' || Relies on concepts from thermodynamics (e.g. entropy gradients), statistical mechanics, and quantum gravity. Uses integral relations and variational principles, but lacks a standardized set of equations for general use. || ★★★☆☆
|}

'''Total: 26/40'''

=== '''8.8.5 Big Bang – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strongly supported by CMB, redshift-distance relation, and light element abundances. However, JWST data revealing early, mature galaxies challenges the predicted timeline of structure formation. || ★★★★☆
|-
| '''Internal Consistency''' || Internally coherent within the ΛCDM framework. Logical structure is intact, though singularity and quantum-gravity transitions remain unresolved. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted CMB and nucleosynthesis. But recent observations (e.g. JWST galaxies at z &gt; 10) were not anticipated, requiring post-hoc model adjustments. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Strong integration with general relativity, quantum field theory, and thermodynamics. Limited links to geology or planetary evolution. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Conceptually complex genesis: singularity, inflation, and multiple postulated fields (inflaton, dark energy, dark matter). Relies on hypothetical constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulated massive observational and theoretical advances. Has driven decades of mission planning and cosmological interpretation. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Represented a paradigm shift from steady-state thinking. Raises deep ontological and metaphysical questions (e.g. time’s origin, creation ex nihilo). || ★★★★☆
|-
| '''Mathematical Rigor''' || Grounded in Einstein’s field equations, Friedmann dynamics, and thermodynamics. Offers well-defined, highly developed formalism. || ★★★★★
|}

'''Total: 34/40'''

=== '''8.8.6 Steady State Theory – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Cosmology]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Early successes with radio‐source counts, but contradicted by the cosmic microwave background, evolving galaxy populations, and quasar statistics. || ★★☆☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within the “perfect cosmological principle,” requiring continuous matter creation at a fixed rate. Logical but invokes an ad-hoc creation field (C-field). || ★★★☆☆
|-
| '''Predictive Power''' || Predicted constant large-scale density and specific radio‐source number counts; few successful novel predictions beyond its initial scope. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Limited overlap with modern astrophysics and particle physics; conflicts with nucleosynthesis and CMB observations. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively simple: Universe is homogeneous in space **and** time, avoiding an initial singularity. Minimal parameter set. || ★★★★☆
|-
| '''Heuristic Value''' || Historically spurred observational tests that ultimately favored Big Bang models; now mainly of pedagogical interest. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Embodies the perfect cosmological principle and continuous-creation idea, provoking debates on temporality and cosmological assumptions. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs Friedmann-like solutions with a creation term; uses relativistic field equations but lacks the richer formal development of ΛCDM or GR extensions. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.7 Big Crunch – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Once considered viable if cosmic density exceeded the critical value. Current observations (accelerating expansion, dark energy) contradict its key assumptions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretically consistent as a time-reversed Big Bang within general relativity. Requires high matter density and no (or reversing) dark energy. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts a decelerating expansion turning to collapse. Testable in principle, but not supported by current data. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with thermodynamic and relativistic models of entropy and time symmetry, but unsupported by astronomical data. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively mirrors Big Bang, offering closure and symmetry. Simple in concept, but difficult to reconcile with observed acceleration. || ★★★☆☆
|-
| '''Heuristic Value''' || Motivated theoretical discussion on cosmological fate and cyclic models. Limited influence in current cosmology. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Explores cosmological temporality and finitude. Once a philosophically compelling counterbalance to eternal expansion. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on time-reversible solutions to Friedmann equations and relativistic cosmology. Rigorous within GR but not extended in modern frameworks. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.8 Big Bounce – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || No direct observational evidence yet. Some loop quantum cosmology models suggest signatures in the CMB, but these remain speculative. || ★★☆☆☆
|-
| '''Internal Consistency''' || Offers a logically coherent alternative to singularity-based models. Dependent on quantum gravity frameworks (e.g. loop quantum gravity) that remain under development. || ★★★☆☆
|-
| '''Predictive Power''' || Provides potential testable differences in early universe structure and CMB fluctuations. Predictions are still uncertain and model-dependent. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges general relativity with quantum mechanics. Limited overlap with geology or observational astronomy. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex and abstract. The idea of a cyclical universe is conceptually appealing, but quantum corrections are not intuitive. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates exploration of singularity resolution and quantum gravity cosmologies. Encourages investigation of pre-Big Bang conditions. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Resonates with ancient cyclical cosmologies and philosophical ideas of eternal recurrence. Reframes the question of origins. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on extensions of Friedmann equations using loop quantum corrections or other quantum gravity approaches. Some models are mathematically formal, but the field is still unsettled. || ★★★☆☆
|}

'''Total: 24/40'''

=== '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' ===

''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆
|-
| '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆
|-
| '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆
|-
| '''Mathematical Rigor''' || Provides original equations (e.g. for \(D_{\text{pref}}\), \(G = (\gamma - 1)/4\pi\), \(\kappa = v_{\text{RMS}}^2 / c^4\)) and consistent dimensional analysis. Excel-based datasets link math to observations. Lacks field-theoretic formalism. || ★★★★☆
|}

'''Total: 34/40'''

=== '''8.8.10 Spiral Cosmology – AI Rating Summary''' ===

''Related link:'' [https://www.academia.edu/103005946/Cosmology_as_Spiral_Evolution Spiral Cosmology on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers visual and structural explanations for spiral galaxy morphology and cosmic rotation patterns. Less directly tied to quantitative data or tested predictions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Conceptually consistent in proposing self-similar spiral evolution at multiple scales, but lacks a developed dynamic or energetic framework. || ★★☆☆☆
|-
| '''Predictive Power''' || Suggests qualitative evolutionary stages and possible cyclic features, but does not provide specific numerical predictions. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Makes symbolic and philosophical connections across cosmology, biology, and culture. Scientific integration with physical fields is minimal. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Emphasizes intuitive and visual structures (e.g. spirals), which are accessible but may oversimplify physical complexity. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulates reflection on cosmic structure, symmetry, and recursion. Encourages reinterpretation of known forms (e.g. galaxies, DNA, hurricanes). || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Reconnects with ancient and Renaissance cosmologies linking form and function across scales. Offers metaphysical resonance. || ★★★★☆
|-
| '''Mathematical Rigor''' || Utilizes geometric symbolism (e.g. spiral ratios, golden mean) but lacks physical equations or dynamical systems modeling. No quantitative derivations. || ★★☆☆☆
|}

'''Total: 23/40'''

=== '''8.8.11 Topological Field Framework – AI Rating Summary''' ===

''Related link:'' [https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework on ResearchGate]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Proposes a geometric origin of particle properties and fundamental constants, but lacks direct comparison with observational or experimental datasets. Empirical testing is suggested but not yet demonstrated. || ★★☆☆☆
|-
| '''Internal Consistency''' || Builds a coherent and logically structured model grounded in topology and pressure gradients. Concepts are well integrated, with minimal contradictions. || ★★★★☆
|-
| '''Predictive Power''' || Offers a pathway to derive constants such as G, c, and Λ from topology and boundary conditions. However, quantitative predictions are still under development or pending validation. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges gravitational theory, particle physics, and topology. Aligns with ideas in quantum geometry, though not yet embedded in mainstream formulations. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Dense but conceptually focused. Uses field and pressure analogies to unify gravity and gauge interactions, though the abstract nature may limit accessibility. || ★★★☆☆
|-
| '''Heuristic Value''' || Provides an original and stimulating approach to unify physical constants via geometry. Encourages rethinking of foundational assumptions in physics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Revives geometrical unification ideals from early 20th-century physics and connects them to modern field-based ontology. Philosophically grounded. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs differential geometry, topological mapping, and field pressure modeling. Mathematical structure is present, but derivations are at a conceptual stage. || ★★★☆☆
|}

'''Total: 27/40'''

=== '''8.8.12 Conformal Gravity – AI Rating Summary''' ===

''Related link:'' [https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Successfully models galactic rotation curves and lensing effects without invoking dark matter. However, challenges remain regarding early-universe phenomena and the CMB. || ★★★☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within its conformal symmetry framework. Gravitational dynamics are derived cleanly from a fourth-order field equation. || ★★★★☆
|-
| '''Predictive Power''' || Accurately predicts galaxy-scale observations. However, extrapolations to cosmological scales require further development and empirical testing. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Intersects with quantum field theory through conformal invariance and offers alternatives to ΛCDM. Limited overlap with standard model particle physics. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Builds from a well-defined symmetry principle (conformal invariance). Some complexity arises due to fourth-order derivatives and unfamiliar constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Encourages reconsideration of gravitational assumptions and dark matter. Inspires new theoretical directions and alternative metrics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Connects with earlier Weyl geometry and symmetry-based models. Philosophically significant as a symmetry-driven alternative to general relativity. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs rigorous derivations based on conformal symmetry and higher-order field equations. Technically sophisticated. || ★★★★☆
|}

'''Total: 28/40'''

=== '''8.8.12 Conformal Gravity – AI Rating Summary''' ===

''Related link:'' [https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Successfully models galactic rotation curves and lensing effects without invoking dark matter. However, challenges remain regarding early-universe phenomena and the CMB. || ★★★☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within its conformal symmetry framework. Gravitational dynamics are derived cleanly from a fourth-order field equation. || ★★★★☆
|-
| '''Predictive Power''' || Accurately predicts galaxy-scale observations. However, extrapolations to cosmological scales require further development and empirical testing. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Intersects with quantum field theory through conformal invariance and offers alternatives to ΛCDM. Limited overlap with standard model particle physics. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Builds from a well-defined symmetry principle (conformal invariance). Some complexity arises due to fourth-order derivatives and unfamiliar constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Encourages reconsideration of gravitational assumptions and dark matter. Inspires new theoretical directions and alternative metrics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Connects with earlier Weyl geometry and symmetry-based models. Philosophically significant as a symmetry-driven alternative to general relativity. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs rigorous derivations based on conformal symmetry and higher-order field equations. Technically sophisticated. || ★★★★☆
|}

'''Total: 28/40'''


=== '''8.9 – Additional Alternative Cosmological Theories (Under Evaluation)''' ===

* '''[https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework]''' (Hall) – Proposes that fundamental constants such as G, c, and Λ emerge from topological constraints in higher-dimensional field configurations. The theory has high internal logic, mathematical consistency, and geometric depth. Empirical validation depends on measurable predictions, but its interdisciplinary integration (e.g., quantum geometry, general relativity) offers high conceptual promise.

* '''[https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]''' (Mannheim–Kazanas) – Eliminates the need for dark matter by applying conformal symmetry to gravitational equations. It explains galactic rotation curves and lensing without exotic particles. Predictive power is strong on galactic scales, but it faces challenges with early-universe data. Internally consistent and testable, though its cosmological compatibility is debated.

* '''[https://www.ias.ac.in/article/fulltext/pram/053/06/1093-1104 The Quasi-Steady State Cosmology: Theory and Observations]''' – A cyclic, non-Big Bang model incorporating continuous matter creation via a “C-field.” It accounts for redshift and some cosmic structure without expansion from a singularity. Empirical adequacy is mixed due to tension with CMB and elemental abundance observations. Still, its falsifiability and explanatory ambition support its inclusion in theoretical discourse.

* '''[https://physicsfoundations.org/suntola/dynamic-universe Dynamic Universe]''' (Tuomo Suntola) – A model based on zero-energy balance and time-evolving geometry, predicting cosmic constants from dynamic curvature. Offers conceptual simplicity and mathematical consistency. Deviates from mainstream relativity but maintains coherence. Predictions related to H₀ and time-scaling allow for observational tests and empirical challenge.  
{{#ev:youtube|n62WMdSYSjk|Tuomo Suntola: Introduction to the Dynamic Universe}}


'''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]'''</text>
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      <text bytes="34793" sha1="ayni2oe4n4z81t1c7x71i7n84b6y6mm" xml:space="preserve">== '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' =

== '''8.1 Purpose''' ==

This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated.

== '''8.2 Toolchain and Workflow''' ==

AI tools like ChatGPT are used to analyze, compare, and refine theories

Tables and frameworks are generated collaboratively using open formats

Contributors submit input via email or editing suggestions

Ratings and evaluations are dynamically updated based on ongoing analysis

== '''8.3 AI-Based Rating System: Motivation and Procedure''' ==

To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''.

This system is designed to be:

Transparent – Each rating is justified through AI’s large-scale reference analysis.

Dynamic – Contributors may submit additional materials to request re-evaluation.

Consistent – All evaluations are performed by the same AI logic, eliminating personal bias.

Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted.

This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate.

== '''8.4 Open Participation''' ==

This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to:

Describe their framework in terms of assumptions, predictions, and compatibility

Suggest how their model could be tested or falsified

Provide references or original materials for AI evaluation

All analysis is open, and contributors may propose improvements at any time.

== '''8.5 Understanding the Star Ratings''' ==

The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied.

'''8.5.1. Empirical Adequacy'''  
Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower.

'''8.5.2. Internal Consistency'''  
Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions.

'''8.5.3. Predictive Power'''  
Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings.

'''8.5.4. Cross-Disciplinary Compatibility'''  
Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score.

'''8.5.5. Conceptual Clarity and Simplicity'''  
Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification.

'''8.5.6. Heuristic Value'''  
Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential.

'''8.5.7. Historical and Philosophical Insight'''  
Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here.

'''8.5.8. Mathematical Rigor'''  
Does the theory provide clear mathematical formulations, derivations, and quantitative predictions? Theories are valued for their use of equations to express core principles, ensure internal consistency, and generate testable results.


Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail.


=== '''8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor)''' ===

''Note: In July 2025, an eighth evaluation criterion was added: '''Mathematical Rigor'''. The total score is now out of 40 stars instead of 35.  ''
''All ratings are expressed in whole stars (★), without fractional values, to ensure clarity in display and consistency with the visual format of this table.''  
''Theories are listed in the same order as in Section 8.8.''

{| class=&quot;wikitable&quot;
! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HP''' !! '''MR''' !! '''Total (★/40)'''
|-
| '''General Relativity''' || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || ★★★★★ || '''37'''
|-
| '''Newtonian Gravity''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''33'''
|-
| '''MOND''' || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || '''26'''
|-
| '''Emergent Gravity''' || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''24'''
|-
| '''Big Bang''' || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || '''34'''
|-
| '''Steady State Theory''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23'''
|-
| '''Big Crunch''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Big Bounce''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Cosmic Influx Theory (CIT)''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || '''33'''
|-
| '''Spiral Cosmology''' || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''21'''
|}

''Legend:''  
''EA = Empirical Adequacy IC = Internal Consistency PP = Predictive Power CC = Cross-Disciplinary Compatibility  ''
''CS = Conceptual Simplicity HV = Heuristic Value HP = Historical/Philosophical Insight MR = Mathematical Rigor''


&lt;!-- Add a blank line here --&gt;

== '''8.7 Requesting Detailed Justification''' ==

“Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by:

1. Visiting the '''discussion page''' of this Wikiversity chapter.
  
2. Mentioning the theory by name and explicitly asking for the detailed breakdown.
  
3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. 

These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented.

If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership.

'''Mainstream theories are subject to the same critical standard.'''  
If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed.

If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''.

== '''8.8 Detailed Evaluations of Theories''' ==

This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes.

=== '''8.8.1 General Relativity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Matches a wide range of observations: gravitational lensing, GPS corrections, perihelion precession, black hole dynamics, and gravitational waves. Supported by multiple experiments. || ★★★★★
|-
| '''Internal Consistency''' || Highly consistent within its differential geometric framework. Built upon Einstein's field equations with tensor calculus. Few internal contradictions, though extensions (e.g. quantum gravity) face challenges. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted gravitational redshift, time dilation, frame-dragging, and gravitational waves. Continues to guide observations in astrophysics. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with cosmology and astrophysics. Some tension with quantum theory. Less integrated with planetary geology or biology. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex mathematical structure makes it less intuitive. Conceptually abstract (spacetime curvature, geodesics). Clarity improves with education, but simplicity is low. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired vast developments in cosmology, black hole theory, and relativistic astrophysics. Foundation for modern gravitational physics. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Deep philosophical implications about space, time, and causality. Represents a major shift from Newtonian absolute space. Influenced 20th-century philosophy of science. || ★★★★★
|-
| '''Mathematical Rigor''' || Built upon advanced mathematics: Riemannian geometry, Einstein field equations, tensor calculus. Equations are precise, formal, and deeply embedded in differential geometry. || ★★★★★
|}

'''Total: 39/40'''

=== '''8.8.2 Newtonian Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Accurately describes gravitational interactions for most macroscopic systems (planets, satellites, projectiles) under low-speed, weak-field conditions. Deviates in extreme conditions (e.g. near black holes). || ★★★★☆
|-
| '''Internal Consistency''' || Mathematically self-consistent with inverse-square law and Newton's laws of motion. Assumes instantaneous action at a distance, which conflicts with relativity. || ★★★★☆
|-
| '''Predictive Power''' || Predicts planetary orbits, tides, escape velocities, and Keplerian motion. Fails for relativistic effects (e.g. Mercury’s precession, gravitational lensing). || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Well-integrated in classical mechanics, astronomy, and engineering. Less compatible with modern cosmology or relativistic frameworks. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple and intuitive: gravity as a force between masses. Easily grasped and widely taught. || ★★★★★
|-
| '''Heuristic Value''' || Inspired centuries of scientific discovery and classical mechanics. Still used in teaching and engineering. Limited in modern theoretical development. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Founded classical physics. Major leap in scientific method and mathematical modeling. Paved the way for Enlightenment-era science. || ★★★★★
|-
| '''Mathematical Rigor''' || Clear and elegant use of calculus and vector algebra (e.g. \(\displaystyle F = G \frac{m_1 m_2}{r^2}\)). Highly accessible and historically groundbreaking, but lacks deeper geometric or relativistic structures. || ★★★★☆
|}

'''Total: 33/40'''

=== '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Fits galactic rotation curves without invoking dark matter. Matches Tully-Fisher relation. Performance weakens at cluster and cosmological scales. || ★★★★☆
|-
| '''Internal Consistency''' || Original formulation is non-relativistic and phenomenological. Several relativistic extensions (e.g. TeVeS) exist but introduce complexity and fine-tuning. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts galaxy dynamics from baryonic matter alone. Less predictive at larger scales or in non-galactic contexts. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Primarily astrophysical. Some tension with cosmology, structure formation, and gravitational lensing. Not aligned with particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple at galactic scale: modifies acceleration below a threshold \(a_0\). Extensions are less intuitive. || ★★★★☆
|-
| '''Heuristic Value''' || Challenges dark matter paradigm and motivates alternate gravity models. Sparked theoretical and observational debate. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Offers a conceptual challenge to Newton/Einstein gravity. Philosophically provocative, but limited historical lineage. || ★★★☆☆
|-
| '''Mathematical Rigor''' || Employs interpolating functions and modified Poisson equations. Relativistic extensions (e.g. TeVeS) involve tensor-vector-scalar frameworks. Rigorous in parts, but lacks unified formalism. || ★★★☆☆
|}

'''Total: 28/40'''

=== '''8.8.4 Emergent Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Entropic_gravity Emergent / Entropic Gravity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Attempts to account for galactic rotation without dark matter by linking gravity to entropy and information. Some results match MOND-like behavior, but broad observational support remains limited. || ★★★☆☆
|-
| '''Internal Consistency''' || Theoretical framework draws from thermodynamics, holography, and information theory. Conceptually coherent, but not fully developed as a unified physical model. || ★★★☆☆
|-
| '''Predictive Power''' || Offers qualitative insights but lacks precise predictive capabilities in most contexts. No wide adoption for simulations or system modeling. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates ideas from black hole thermodynamics, quantum information, and spacetime geometry. Weak integration with observational astronomy or geology. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Abstract and speculative. Concepts like entropic forces and holographic screens are not intuitive for most readers. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates discussion about the nature of spacetime and gravity. Has inspired new theoretical directions in quantum gravity and information theory. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Philosophically intriguing: redefines gravity as emergent rather than fundamental. Links to ideas from Bekenstein and Hawking. || ★★★★☆
|-
| '''Mathematical Rigor''' || Relies on concepts from thermodynamics (e.g. entropy gradients), statistical mechanics, and quantum gravity. Uses integral relations and variational principles, but lacks a standardized set of equations for general use. || ★★★☆☆
|}

'''Total: 26/40'''

=== '''8.8.5 Big Bang – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strongly supported by CMB, redshift-distance relation, and light element abundances. However, JWST data revealing early, mature galaxies challenges the predicted timeline of structure formation. || ★★★★☆
|-
| '''Internal Consistency''' || Internally coherent within the ΛCDM framework. Logical structure is intact, though singularity and quantum-gravity transitions remain unresolved. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted CMB and nucleosynthesis. But recent observations (e.g. JWST galaxies at z &gt; 10) were not anticipated, requiring post-hoc model adjustments. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Strong integration with general relativity, quantum field theory, and thermodynamics. Limited links to geology or planetary evolution. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Conceptually complex genesis: singularity, inflation, and multiple postulated fields (inflaton, dark energy, dark matter). Relies on hypothetical constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulated massive observational and theoretical advances. Has driven decades of mission planning and cosmological interpretation. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Represented a paradigm shift from steady-state thinking. Raises deep ontological and metaphysical questions (e.g. time’s origin, creation ex nihilo). || ★★★★☆
|-
| '''Mathematical Rigor''' || Grounded in Einstein’s field equations, Friedmann dynamics, and thermodynamics. Offers well-defined, highly developed formalism. || ★★★★★
|}

'''Total: 34/40'''

=== '''8.8.6 Steady State Theory – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Cosmology]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Early successes with radio‐source counts, but contradicted by the cosmic microwave background, evolving galaxy populations, and quasar statistics. || ★★☆☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within the “perfect cosmological principle,” requiring continuous matter creation at a fixed rate. Logical but invokes an ad-hoc creation field (C-field). || ★★★☆☆
|-
| '''Predictive Power''' || Predicted constant large-scale density and specific radio‐source number counts; few successful novel predictions beyond its initial scope. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Limited overlap with modern astrophysics and particle physics; conflicts with nucleosynthesis and CMB observations. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively simple: Universe is homogeneous in space **and** time, avoiding an initial singularity. Minimal parameter set. || ★★★★☆
|-
| '''Heuristic Value''' || Historically spurred observational tests that ultimately favored Big Bang models; now mainly of pedagogical interest. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Embodies the perfect cosmological principle and continuous-creation idea, provoking debates on temporality and cosmological assumptions. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs Friedmann-like solutions with a creation term; uses relativistic field equations but lacks the richer formal development of ΛCDM or GR extensions. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.7 Big Crunch – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Once considered viable if cosmic density exceeded the critical value. Current observations (accelerating expansion, dark energy) contradict its key assumptions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretically consistent as a time-reversed Big Bang within general relativity. Requires high matter density and no (or reversing) dark energy. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts a decelerating expansion turning to collapse. Testable in principle, but not supported by current data. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with thermodynamic and relativistic models of entropy and time symmetry, but unsupported by astronomical data. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively mirrors Big Bang, offering closure and symmetry. Simple in concept, but difficult to reconcile with observed acceleration. || ★★★☆☆
|-
| '''Heuristic Value''' || Motivated theoretical discussion on cosmological fate and cyclic models. Limited influence in current cosmology. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Explores cosmological temporality and finitude. Once a philosophically compelling counterbalance to eternal expansion. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on time-reversible solutions to Friedmann equations and relativistic cosmology. Rigorous within GR but not extended in modern frameworks. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.8 Big Bounce – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || No direct observational evidence yet. Some loop quantum cosmology models suggest signatures in the CMB, but these remain speculative. || ★★☆☆☆
|-
| '''Internal Consistency''' || Offers a logically coherent alternative to singularity-based models. Dependent on quantum gravity frameworks (e.g. loop quantum gravity) that remain under development. || ★★★☆☆
|-
| '''Predictive Power''' || Provides potential testable differences in early universe structure and CMB fluctuations. Predictions are still uncertain and model-dependent. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges general relativity with quantum mechanics. Limited overlap with geology or observational astronomy. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex and abstract. The idea of a cyclical universe is conceptually appealing, but quantum corrections are not intuitive. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates exploration of singularity resolution and quantum gravity cosmologies. Encourages investigation of pre-Big Bang conditions. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Resonates with ancient cyclical cosmologies and philosophical ideas of eternal recurrence. Reframes the question of origins. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on extensions of Friedmann equations using loop quantum corrections or other quantum gravity approaches. Some models are mathematically formal, but the field is still unsettled. || ★★★☆☆
|}

'''Total: 24/40'''

=== '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' ===

''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆
|-
| '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆
|-
| '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆
|-
| '''Mathematical Rigor''' || Provides original equations (e.g. for \(D_{\text{pref}}\), \(G = (\gamma - 1)/4\pi\), \(\kappa = v_{\text{RMS}}^2 / c^4\)) and consistent dimensional analysis. Excel-based datasets link math to observations. Lacks field-theoretic formalism. || ★★★★☆
|}

'''Total: 34/40'''

=== '''8.8.10 Spiral Cosmology – AI Rating Summary''' ===

''Related link:'' [https://www.academia.edu/103005946/Cosmology_as_Spiral_Evolution Spiral Cosmology on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers visual and structural explanations for spiral galaxy morphology and cosmic rotation patterns. Less directly tied to quantitative data or tested predictions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Conceptually consistent in proposing self-similar spiral evolution at multiple scales, but lacks a developed dynamic or energetic framework. || ★★☆☆☆
|-
| '''Predictive Power''' || Suggests qualitative evolutionary stages and possible cyclic features, but does not provide specific numerical predictions. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Makes symbolic and philosophical connections across cosmology, biology, and culture. Scientific integration with physical fields is minimal. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Emphasizes intuitive and visual structures (e.g. spirals), which are accessible but may oversimplify physical complexity. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulates reflection on cosmic structure, symmetry, and recursion. Encourages reinterpretation of known forms (e.g. galaxies, DNA, hurricanes). || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Reconnects with ancient and Renaissance cosmologies linking form and function across scales. Offers metaphysical resonance. || ★★★★☆
|-
| '''Mathematical Rigor''' || Utilizes geometric symbolism (e.g. spiral ratios, golden mean) but lacks physical equations or dynamical systems modeling. No quantitative derivations. || ★★☆☆☆
|}

'''Total: 23/40'''

=== '''8.8.11 Topological Field Framework – AI Rating Summary''' ===

''Related link:'' [https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework on ResearchGate]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Proposes a geometric origin of particle properties and fundamental constants, but lacks direct comparison with observational or experimental datasets. Empirical testing is suggested but not yet demonstrated. || ★★☆☆☆
|-
| '''Internal Consistency''' || Builds a coherent and logically structured model grounded in topology and pressure gradients. Concepts are well integrated, with minimal contradictions. || ★★★★☆
|-
| '''Predictive Power''' || Offers a pathway to derive constants such as G, c, and Λ from topology and boundary conditions. However, quantitative predictions are still under development or pending validation. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges gravitational theory, particle physics, and topology. Aligns with ideas in quantum geometry, though not yet embedded in mainstream formulations. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Dense but conceptually focused. Uses field and pressure analogies to unify gravity and gauge interactions, though the abstract nature may limit accessibility. || ★★★☆☆
|-
| '''Heuristic Value''' || Provides an original and stimulating approach to unify physical constants via geometry. Encourages rethinking of foundational assumptions in physics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Revives geometrical unification ideals from early 20th-century physics and connects them to modern field-based ontology. Philosophically grounded. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs differential geometry, topological mapping, and field pressure modeling. Mathematical structure is present, but derivations are at a conceptual stage. || ★★★☆☆
|}

'''Total: 27/40'''

=== '''8.8.12 Conformal Gravity – AI Rating Summary''' ===

''Related link:'' [https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Successfully models galactic rotation curves and lensing effects without invoking dark matter. However, challenges remain regarding early-universe phenomena and the CMB. || ★★★☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within its conformal symmetry framework. Gravitational dynamics are derived cleanly from a fourth-order field equation. || ★★★★☆
|-
| '''Predictive Power''' || Accurately predicts galaxy-scale observations. However, extrapolations to cosmological scales require further development and empirical testing. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Intersects with quantum field theory through conformal invariance and offers alternatives to ΛCDM. Limited overlap with standard model particle physics. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Builds from a well-defined symmetry principle (conformal invariance). Some complexity arises due to fourth-order derivatives and unfamiliar constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Encourages reconsideration of gravitational assumptions and dark matter. Inspires new theoretical directions and alternative metrics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Connects with earlier Weyl geometry and symmetry-based models. Philosophically significant as a symmetry-driven alternative to general relativity. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs rigorous derivations based on conformal symmetry and higher-order field equations. Technically sophisticated. || ★★★★☆
|}

'''Total: 28/40'''

=== '''8.9 – Additional Alternative Cosmological Theories (Under Evaluation)''' ===

* '''[https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework]''' (Hall) – Proposes that fundamental constants such as G, c, and Λ emerge from topological constraints in higher-dimensional field configurations. The theory has high internal logic, mathematical consistency, and geometric depth. Empirical validation depends on measurable predictions, but its interdisciplinary integration (e.g., quantum geometry, general relativity) offers high conceptual promise.

* '''[https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]''' (Mannheim–Kazanas) – Eliminates the need for dark matter by applying conformal symmetry to gravitational equations. It explains galactic rotation curves and lensing without exotic particles. Predictive power is strong on galactic scales, but it faces challenges with early-universe data. Internally consistent and testable, though its cosmological compatibility is debated.

* '''[https://www.ias.ac.in/article/fulltext/pram/053/06/1093-1104 The Quasi-Steady State Cosmology: Theory and Observations]''' – A cyclic, non-Big Bang model incorporating continuous matter creation via a “C-field.” It accounts for redshift and some cosmic structure without expansion from a singularity. Empirical adequacy is mixed due to tension with CMB and elemental abundance observations. Still, its falsifiability and explanatory ambition support its inclusion in theoretical discourse.

* '''[https://physicsfoundations.org/suntola/dynamic-universe Dynamic Universe]''' (Tuomo Suntola) – A model based on zero-energy balance and time-evolving geometry, predicting cosmic constants from dynamic curvature. Offers conceptual simplicity and mathematical consistency. Deviates from mainstream relativity but maintains coherence. Predictions related to H₀ and time-scaling allow for observational tests and empirical challenge.  
{{#ev:youtube|n62WMdSYSjk|Tuomo Suntola: Introduction to the Dynamic Universe}}


'''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]'''</text>
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      <text bytes="36811" sha1="415c0grzzdvy7nbhtfr0ezwfdwae7nw" xml:space="preserve">== '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' =

== '''8.1 Purpose''' ==

This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated.

== '''8.2 Toolchain and Workflow''' ==

AI tools like ChatGPT are used to analyze, compare, and refine theories

Tables and frameworks are generated collaboratively using open formats

Contributors submit input via email or editing suggestions

Ratings and evaluations are dynamically updated based on ongoing analysis

== '''8.3 AI-Based Rating System: Motivation and Procedure''' ==

To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''.

This system is designed to be:

Transparent – Each rating is justified through AI’s large-scale reference analysis.

Dynamic – Contributors may submit additional materials to request re-evaluation.

Consistent – All evaluations are performed by the same AI logic, eliminating personal bias.

Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted.

This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate.

== '''8.4 Open Participation''' ==

This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to:

Describe their framework in terms of assumptions, predictions, and compatibility

Suggest how their model could be tested or falsified

Provide references or original materials for AI evaluation

All analysis is open, and contributors may propose improvements at any time.

== '''8.5 Understanding the Star Ratings''' ==

The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied.

'''8.5.1. Empirical Adequacy'''  
Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower.

'''8.5.2. Internal Consistency'''  
Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions.

'''8.5.3. Predictive Power'''  
Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings.

'''8.5.4. Cross-Disciplinary Compatibility'''  
Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score.

'''8.5.5. Conceptual Clarity and Simplicity'''  
Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification.

'''8.5.6. Heuristic Value'''  
Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential.

'''8.5.7. Historical and Philosophical Insight'''  
Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here.

'''8.5.8. Mathematical Rigor'''  
Does the theory provide clear mathematical formulations, derivations, and quantitative predictions? Theories are valued for their use of equations to express core principles, ensure internal consistency, and generate testable results.


Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail.


=== '''8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor)''' ===

''Note: In July 2025, an eighth evaluation criterion was added: '''Mathematical Rigor'''. The total score is now out of 40 stars instead of 35.  ''
''All ratings are expressed in whole stars (★), without fractional values, to ensure clarity in display and consistency with the visual format of this table.''  
''Theories are listed in the same order as in Section 8.8.''

{| class=&quot;wikitable&quot;
! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HP''' !! '''MR''' !! '''Total (★/40)'''
|-
| '''General Relativity''' || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || ★★★★★ || '''37'''
|-
| '''Newtonian Gravity''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''33'''
|-
| '''MOND''' || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || '''26'''
|-
| '''Emergent Gravity''' || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''24'''
|-
| '''Big Bang''' || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || '''34'''
|-
| '''Steady State Theory''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23'''
|-
| '''Big Crunch''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Big Bounce''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Cosmic Influx Theory (CIT)''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || '''33'''
|-
| '''Spiral Cosmology''' || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''21'''
|}

''Legend:''  
''EA = Empirical Adequacy IC = Internal Consistency PP = Predictive Power CC = Cross-Disciplinary Compatibility  ''
''CS = Conceptual Simplicity HV = Heuristic Value HP = Historical/Philosophical Insight MR = Mathematical Rigor''


&lt;!-- Add a blank line here --&gt;

== '''8.7 Requesting Detailed Justification''' ==

“Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by:

1. Visiting the '''discussion page''' of this Wikiversity chapter.
  
2. Mentioning the theory by name and explicitly asking for the detailed breakdown.
  
3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. 

These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented.

If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership.

'''Mainstream theories are subject to the same critical standard.'''  
If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed.

If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''.

== '''8.8 Detailed Evaluations of Theories''' ==

This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes.

=== '''8.8.1 General Relativity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Matches a wide range of observations: gravitational lensing, GPS corrections, perihelion precession, black hole dynamics, and gravitational waves. Supported by multiple experiments. || ★★★★★
|-
| '''Internal Consistency''' || Highly consistent within its differential geometric framework. Built upon Einstein's field equations with tensor calculus. Few internal contradictions, though extensions (e.g. quantum gravity) face challenges. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted gravitational redshift, time dilation, frame-dragging, and gravitational waves. Continues to guide observations in astrophysics. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with cosmology and astrophysics. Some tension with quantum theory. Less integrated with planetary geology or biology. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex mathematical structure makes it less intuitive. Conceptually abstract (spacetime curvature, geodesics). Clarity improves with education, but simplicity is low. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired vast developments in cosmology, black hole theory, and relativistic astrophysics. Foundation for modern gravitational physics. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Deep philosophical implications about space, time, and causality. Represents a major shift from Newtonian absolute space. Influenced 20th-century philosophy of science. || ★★★★★
|-
| '''Mathematical Rigor''' || Built upon advanced mathematics: Riemannian geometry, Einstein field equations, tensor calculus. Equations are precise, formal, and deeply embedded in differential geometry. || ★★★★★
|}

'''Total: 39/40'''

=== '''8.8.2 Newtonian Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Accurately describes gravitational interactions for most macroscopic systems (planets, satellites, projectiles) under low-speed, weak-field conditions. Deviates in extreme conditions (e.g. near black holes). || ★★★★☆
|-
| '''Internal Consistency''' || Mathematically self-consistent with inverse-square law and Newton's laws of motion. Assumes instantaneous action at a distance, which conflicts with relativity. || ★★★★☆
|-
| '''Predictive Power''' || Predicts planetary orbits, tides, escape velocities, and Keplerian motion. Fails for relativistic effects (e.g. Mercury’s precession, gravitational lensing). || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Well-integrated in classical mechanics, astronomy, and engineering. Less compatible with modern cosmology or relativistic frameworks. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple and intuitive: gravity as a force between masses. Easily grasped and widely taught. || ★★★★★
|-
| '''Heuristic Value''' || Inspired centuries of scientific discovery and classical mechanics. Still used in teaching and engineering. Limited in modern theoretical development. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Founded classical physics. Major leap in scientific method and mathematical modeling. Paved the way for Enlightenment-era science. || ★★★★★
|-
| '''Mathematical Rigor''' || Clear and elegant use of calculus and vector algebra (e.g. \(\displaystyle F = G \frac{m_1 m_2}{r^2}\)). Highly accessible and historically groundbreaking, but lacks deeper geometric or relativistic structures. || ★★★★☆
|}

'''Total: 33/40'''

=== '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Fits galactic rotation curves without invoking dark matter. Matches Tully-Fisher relation. Performance weakens at cluster and cosmological scales. || ★★★★☆
|-
| '''Internal Consistency''' || Original formulation is non-relativistic and phenomenological. Several relativistic extensions (e.g. TeVeS) exist but introduce complexity and fine-tuning. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts galaxy dynamics from baryonic matter alone. Less predictive at larger scales or in non-galactic contexts. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Primarily astrophysical. Some tension with cosmology, structure formation, and gravitational lensing. Not aligned with particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple at galactic scale: modifies acceleration below a threshold \(a_0\). Extensions are less intuitive. || ★★★★☆
|-
| '''Heuristic Value''' || Challenges dark matter paradigm and motivates alternate gravity models. Sparked theoretical and observational debate. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Offers a conceptual challenge to Newton/Einstein gravity. Philosophically provocative, but limited historical lineage. || ★★★☆☆
|-
| '''Mathematical Rigor''' || Employs interpolating functions and modified Poisson equations. Relativistic extensions (e.g. TeVeS) involve tensor-vector-scalar frameworks. Rigorous in parts, but lacks unified formalism. || ★★★☆☆
|}

'''Total: 28/40'''

=== '''8.8.4 Emergent Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Entropic_gravity Emergent / Entropic Gravity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Attempts to account for galactic rotation without dark matter by linking gravity to entropy and information. Some results match MOND-like behavior, but broad observational support remains limited. || ★★★☆☆
|-
| '''Internal Consistency''' || Theoretical framework draws from thermodynamics, holography, and information theory. Conceptually coherent, but not fully developed as a unified physical model. || ★★★☆☆
|-
| '''Predictive Power''' || Offers qualitative insights but lacks precise predictive capabilities in most contexts. No wide adoption for simulations or system modeling. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates ideas from black hole thermodynamics, quantum information, and spacetime geometry. Weak integration with observational astronomy or geology. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Abstract and speculative. Concepts like entropic forces and holographic screens are not intuitive for most readers. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates discussion about the nature of spacetime and gravity. Has inspired new theoretical directions in quantum gravity and information theory. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Philosophically intriguing: redefines gravity as emergent rather than fundamental. Links to ideas from Bekenstein and Hawking. || ★★★★☆
|-
| '''Mathematical Rigor''' || Relies on concepts from thermodynamics (e.g. entropy gradients), statistical mechanics, and quantum gravity. Uses integral relations and variational principles, but lacks a standardized set of equations for general use. || ★★★☆☆
|}

'''Total: 26/40'''

=== '''8.8.5 Big Bang – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strongly supported by CMB, redshift-distance relation, and light element abundances. However, JWST data revealing early, mature galaxies challenges the predicted timeline of structure formation. || ★★★★☆
|-
| '''Internal Consistency''' || Internally coherent within the ΛCDM framework. Logical structure is intact, though singularity and quantum-gravity transitions remain unresolved. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted CMB and nucleosynthesis. But recent observations (e.g. JWST galaxies at z &gt; 10) were not anticipated, requiring post-hoc model adjustments. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Strong integration with general relativity, quantum field theory, and thermodynamics. Limited links to geology or planetary evolution. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Conceptually complex genesis: singularity, inflation, and multiple postulated fields (inflaton, dark energy, dark matter). Relies on hypothetical constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulated massive observational and theoretical advances. Has driven decades of mission planning and cosmological interpretation. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Represented a paradigm shift from steady-state thinking. Raises deep ontological and metaphysical questions (e.g. time’s origin, creation ex nihilo). || ★★★★☆
|-
| '''Mathematical Rigor''' || Grounded in Einstein’s field equations, Friedmann dynamics, and thermodynamics. Offers well-defined, highly developed formalism. || ★★★★★
|}

'''Total: 34/40'''

=== '''8.8.6 Steady State Theory – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Cosmology]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Early successes with radio‐source counts, but contradicted by the cosmic microwave background, evolving galaxy populations, and quasar statistics. || ★★☆☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within the “perfect cosmological principle,” requiring continuous matter creation at a fixed rate. Logical but invokes an ad-hoc creation field (C-field). || ★★★☆☆
|-
| '''Predictive Power''' || Predicted constant large-scale density and specific radio‐source number counts; few successful novel predictions beyond its initial scope. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Limited overlap with modern astrophysics and particle physics; conflicts with nucleosynthesis and CMB observations. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively simple: Universe is homogeneous in space **and** time, avoiding an initial singularity. Minimal parameter set. || ★★★★☆
|-
| '''Heuristic Value''' || Historically spurred observational tests that ultimately favored Big Bang models; now mainly of pedagogical interest. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Embodies the perfect cosmological principle and continuous-creation idea, provoking debates on temporality and cosmological assumptions. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs Friedmann-like solutions with a creation term; uses relativistic field equations but lacks the richer formal development of ΛCDM or GR extensions. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.7 Big Crunch – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Once considered viable if cosmic density exceeded the critical value. Current observations (accelerating expansion, dark energy) contradict its key assumptions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretically consistent as a time-reversed Big Bang within general relativity. Requires high matter density and no (or reversing) dark energy. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts a decelerating expansion turning to collapse. Testable in principle, but not supported by current data. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with thermodynamic and relativistic models of entropy and time symmetry, but unsupported by astronomical data. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively mirrors Big Bang, offering closure and symmetry. Simple in concept, but difficult to reconcile with observed acceleration. || ★★★☆☆
|-
| '''Heuristic Value''' || Motivated theoretical discussion on cosmological fate and cyclic models. Limited influence in current cosmology. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Explores cosmological temporality and finitude. Once a philosophically compelling counterbalance to eternal expansion. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on time-reversible solutions to Friedmann equations and relativistic cosmology. Rigorous within GR but not extended in modern frameworks. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.8 Big Bounce – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || No direct observational evidence yet. Some loop quantum cosmology models suggest signatures in the CMB, but these remain speculative. || ★★☆☆☆
|-
| '''Internal Consistency''' || Offers a logically coherent alternative to singularity-based models. Dependent on quantum gravity frameworks (e.g. loop quantum gravity) that remain under development. || ★★★☆☆
|-
| '''Predictive Power''' || Provides potential testable differences in early universe structure and CMB fluctuations. Predictions are still uncertain and model-dependent. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges general relativity with quantum mechanics. Limited overlap with geology or observational astronomy. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex and abstract. The idea of a cyclical universe is conceptually appealing, but quantum corrections are not intuitive. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates exploration of singularity resolution and quantum gravity cosmologies. Encourages investigation of pre-Big Bang conditions. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Resonates with ancient cyclical cosmologies and philosophical ideas of eternal recurrence. Reframes the question of origins. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on extensions of Friedmann equations using loop quantum corrections or other quantum gravity approaches. Some models are mathematically formal, but the field is still unsettled. || ★★★☆☆
|}

'''Total: 24/40'''

=== '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' ===

''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆
|-
| '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆
|-
| '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆
|-
| '''Mathematical Rigor''' || Provides original equations (e.g. for \(D_{\text{pref}}\), \(G = (\gamma - 1)/4\pi\), \(\kappa = v_{\text{RMS}}^2 / c^4\)) and consistent dimensional analysis. Excel-based datasets link math to observations. Lacks field-theoretic formalism. || ★★★★☆
|}

'''Total: 34/40'''

=== '''8.8.10 Spiral Cosmology – AI Rating Summary''' ===

''Related link:'' [https://www.academia.edu/103005946/Cosmology_as_Spiral_Evolution Spiral Cosmology on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers visual and structural explanations for spiral galaxy morphology and cosmic rotation patterns. Less directly tied to quantitative data or tested predictions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Conceptually consistent in proposing self-similar spiral evolution at multiple scales, but lacks a developed dynamic or energetic framework. || ★★☆☆☆
|-
| '''Predictive Power''' || Suggests qualitative evolutionary stages and possible cyclic features, but does not provide specific numerical predictions. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Makes symbolic and philosophical connections across cosmology, biology, and culture. Scientific integration with physical fields is minimal. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Emphasizes intuitive and visual structures (e.g. spirals), which are accessible but may oversimplify physical complexity. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulates reflection on cosmic structure, symmetry, and recursion. Encourages reinterpretation of known forms (e.g. galaxies, DNA, hurricanes). || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Reconnects with ancient and Renaissance cosmologies linking form and function across scales. Offers metaphysical resonance. || ★★★★☆
|-
| '''Mathematical Rigor''' || Utilizes geometric symbolism (e.g. spiral ratios, golden mean) but lacks physical equations or dynamical systems modeling. No quantitative derivations. || ★★☆☆☆
|}

'''Total: 23/40'''

=== '''8.8.11 Topological Field Framework – AI Rating Summary''' ===

''Related link:'' [https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework on ResearchGate]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Proposes a geometric origin of particle properties and fundamental constants, but lacks direct comparison with observational or experimental datasets. Empirical testing is suggested but not yet demonstrated. || ★★☆☆☆
|-
| '''Internal Consistency''' || Builds a coherent and logically structured model grounded in topology and pressure gradients. Concepts are well integrated, with minimal contradictions. || ★★★★☆
|-
| '''Predictive Power''' || Offers a pathway to derive constants such as G, c, and Λ from topology and boundary conditions. However, quantitative predictions are still under development or pending validation. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges gravitational theory, particle physics, and topology. Aligns with ideas in quantum geometry, though not yet embedded in mainstream formulations. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Dense but conceptually focused. Uses field and pressure analogies to unify gravity and gauge interactions, though the abstract nature may limit accessibility. || ★★★☆☆
|-
| '''Heuristic Value''' || Provides an original and stimulating approach to unify physical constants via geometry. Encourages rethinking of foundational assumptions in physics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Revives geometrical unification ideals from early 20th-century physics and connects them to modern field-based ontology. Philosophically grounded. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs differential geometry, topological mapping, and field pressure modeling. Mathematical structure is present, but derivations are at a conceptual stage. || ★★★☆☆
|}

'''Total: 27/40'''

=== '''8.8.12 Conformal Gravity – AI Rating Summary''' ===

''Related link:'' [https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Successfully models galactic rotation curves and lensing effects without invoking dark matter. However, challenges remain regarding early-universe phenomena and the CMB. || ★★★☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within its conformal symmetry framework. Gravitational dynamics are derived cleanly from a fourth-order field equation. || ★★★★☆
|-
| '''Predictive Power''' || Accurately predicts galaxy-scale observations. However, extrapolations to cosmological scales require further development and empirical testing. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Intersects with quantum field theory through conformal invariance and offers alternatives to ΛCDM. Limited overlap with standard model particle physics. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Builds from a well-defined symmetry principle (conformal invariance). Some complexity arises due to fourth-order derivatives and unfamiliar constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Encourages reconsideration of gravitational assumptions and dark matter. Inspires new theoretical directions and alternative metrics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Connects with earlier Weyl geometry and symmetry-based models. Philosophically significant as a symmetry-driven alternative to general relativity. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs rigorous derivations based on conformal symmetry and higher-order field equations. Technically sophisticated. || ★★★★☆
|}

'''Total: 28/40'''

=== '''8.8.13 Quasi-Steady State Cosmology (QSSC) – AI Rating Summary''' ===

''Related link:'' [https://www.ias.ac.in/article/fulltext/pram/053/06/1093-1104 The Quasi-Steady State Cosmology: Theory and Observations – Pramana Journal]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers explanations for redshift, large-scale structure, and quasar distributions. However, it faces difficulties matching the observed CMB spectrum and primordial element abundances. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretical foundations are logically constructed around a C-field and creation events. Internally coherent but relies on non-standard mechanisms not universally accepted. || ★★★☆☆
|-
| '''Predictive Power''' || Makes unique predictions about cosmic cycles, matter creation, and galaxy evolution. Some predictions remain qualitative or are difficult to test. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Attempts to integrate cosmology with continuous creation physics. However, the C-field concept is not aligned with standard field theory or particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Proposes an intuitive cyclical model of cosmic evolution. Some components, such as the C-field, are abstract and complex to formalize. || ★★★☆☆
|-
| '''Heuristic Value''' || Offers a provocative alternative to the Big Bang. Stimulates re-evaluation of singularity-based models and encourages cyclic interpretations. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Extends the steady-state philosophy of Hoyle. Challenges the singular origin narrative with philosophical depth and continuity. || ★★★★☆
|-
| '''Mathematical Rigor''' || Uses mathematical models for cyclic expansion and C-field dynamics. However, these are not widely adopted or fully developed in mainstream literature. || ★★☆☆☆
|}

'''Total: 23/40'''


=== '''8.9 – Additional Alternative Cosmological Theories (Under Evaluation)''' ===

* '''[https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework]''' (Hall) – Proposes that fundamental constants such as G, c, and Λ emerge from topological constraints in higher-dimensional field configurations. The theory has high internal logic, mathematical consistency, and geometric depth. Empirical validation depends on measurable predictions, but its interdisciplinary integration (e.g., quantum geometry, general relativity) offers high conceptual promise.

* '''[https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]''' (Mannheim–Kazanas) – Eliminates the need for dark matter by applying conformal symmetry to gravitational equations. It explains galactic rotation curves and lensing without exotic particles. Predictive power is strong on galactic scales, but it faces challenges with early-universe data. Internally consistent and testable, though its cosmological compatibility is debated.

* '''[https://www.ias.ac.in/article/fulltext/pram/053/06/1093-1104 The Quasi-Steady State Cosmology: Theory and Observations]''' – A cyclic, non-Big Bang model incorporating continuous matter creation via a “C-field.” It accounts for redshift and some cosmic structure without expansion from a singularity. Empirical adequacy is mixed due to tension with CMB and elemental abundance observations. Still, its falsifiability and explanatory ambition support its inclusion in theoretical discourse.

* '''[https://physicsfoundations.org/suntola/dynamic-universe Dynamic Universe]''' (Tuomo Suntola) – A model based on zero-energy balance and time-evolving geometry, predicting cosmic constants from dynamic curvature. Offers conceptual simplicity and mathematical consistency. Deviates from mainstream relativity but maintains coherence. Predictions related to H₀ and time-scaling allow for observational tests and empirical challenge.  
{{#ev:youtube|n62WMdSYSjk|Tuomo Suntola: Introduction to the Dynamic Universe}}


'''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]'''</text>
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      <text bytes="39003" sha1="8bizwm9snnqsbvhggk3asd8tjivd7zy" xml:space="preserve">== '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' =

== '''8.1 Purpose''' ==

This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated.

== '''8.2 Toolchain and Workflow''' ==

AI tools like ChatGPT are used to analyze, compare, and refine theories

Tables and frameworks are generated collaboratively using open formats

Contributors submit input via email or editing suggestions

Ratings and evaluations are dynamically updated based on ongoing analysis

== '''8.3 AI-Based Rating System: Motivation and Procedure''' ==

To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''.

This system is designed to be:

Transparent – Each rating is justified through AI’s large-scale reference analysis.

Dynamic – Contributors may submit additional materials to request re-evaluation.

Consistent – All evaluations are performed by the same AI logic, eliminating personal bias.

Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted.

This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate.

== '''8.4 Open Participation''' ==

This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to:

Describe their framework in terms of assumptions, predictions, and compatibility

Suggest how their model could be tested or falsified

Provide references or original materials for AI evaluation

All analysis is open, and contributors may propose improvements at any time.

== '''8.5 Understanding the Star Ratings''' ==

The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied.

'''8.5.1. Empirical Adequacy'''  
Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower.

'''8.5.2. Internal Consistency'''  
Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions.

'''8.5.3. Predictive Power'''  
Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings.

'''8.5.4. Cross-Disciplinary Compatibility'''  
Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score.

'''8.5.5. Conceptual Clarity and Simplicity'''  
Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification.

'''8.5.6. Heuristic Value'''  
Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential.

'''8.5.7. Historical and Philosophical Insight'''  
Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here.

'''8.5.8. Mathematical Rigor'''  
Does the theory provide clear mathematical formulations, derivations, and quantitative predictions? Theories are valued for their use of equations to express core principles, ensure internal consistency, and generate testable results.


Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail.


=== '''8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor)''' ===

''Note: In July 2025, an eighth evaluation criterion was added: '''Mathematical Rigor'''. The total score is now out of 40 stars instead of 35.  ''
''All ratings are expressed in whole stars (★), without fractional values, to ensure clarity in display and consistency with the visual format of this table.''  
''Theories are listed in the same order as in Section 8.8.''

{| class=&quot;wikitable&quot;
! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HP''' !! '''MR''' !! '''Total (★/40)'''
|-
| '''General Relativity''' || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || ★★★★★ || '''37'''
|-
| '''Newtonian Gravity''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''33'''
|-
| '''MOND''' || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || '''26'''
|-
| '''Emergent Gravity''' || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''24'''
|-
| '''Big Bang''' || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || '''34'''
|-
| '''Steady State Theory''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23'''
|-
| '''Big Crunch''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Big Bounce''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''Cosmic Influx Theory (CIT)''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || '''33'''
|-
| '''Spiral Cosmology''' || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''21'''
|}

''Legend:''  
''EA = Empirical Adequacy IC = Internal Consistency PP = Predictive Power CC = Cross-Disciplinary Compatibility  ''
''CS = Conceptual Simplicity HV = Heuristic Value HP = Historical/Philosophical Insight MR = Mathematical Rigor''


&lt;!-- Add a blank line here --&gt;

== '''8.7 Requesting Detailed Justification''' ==

“Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by:

1. Visiting the '''discussion page''' of this Wikiversity chapter.
  
2. Mentioning the theory by name and explicitly asking for the detailed breakdown.
  
3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. 

These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented.

If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership.

'''Mainstream theories are subject to the same critical standard.'''  
If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed.

If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''.

== '''8.8 Detailed Evaluations of Theories''' ==

This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes.

=== '''8.8.1 General Relativity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Matches a wide range of observations: gravitational lensing, GPS corrections, perihelion precession, black hole dynamics, and gravitational waves. Supported by multiple experiments. || ★★★★★
|-
| '''Internal Consistency''' || Highly consistent within its differential geometric framework. Built upon Einstein's field equations with tensor calculus. Few internal contradictions, though extensions (e.g. quantum gravity) face challenges. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted gravitational redshift, time dilation, frame-dragging, and gravitational waves. Continues to guide observations in astrophysics. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with cosmology and astrophysics. Some tension with quantum theory. Less integrated with planetary geology or biology. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex mathematical structure makes it less intuitive. Conceptually abstract (spacetime curvature, geodesics). Clarity improves with education, but simplicity is low. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired vast developments in cosmology, black hole theory, and relativistic astrophysics. Foundation for modern gravitational physics. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Deep philosophical implications about space, time, and causality. Represents a major shift from Newtonian absolute space. Influenced 20th-century philosophy of science. || ★★★★★
|-
| '''Mathematical Rigor''' || Built upon advanced mathematics: Riemannian geometry, Einstein field equations, tensor calculus. Equations are precise, formal, and deeply embedded in differential geometry. || ★★★★★
|}

'''Total: 39/40'''

=== '''8.8.2 Newtonian Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Accurately describes gravitational interactions for most macroscopic systems (planets, satellites, projectiles) under low-speed, weak-field conditions. Deviates in extreme conditions (e.g. near black holes). || ★★★★☆
|-
| '''Internal Consistency''' || Mathematically self-consistent with inverse-square law and Newton's laws of motion. Assumes instantaneous action at a distance, which conflicts with relativity. || ★★★★☆
|-
| '''Predictive Power''' || Predicts planetary orbits, tides, escape velocities, and Keplerian motion. Fails for relativistic effects (e.g. Mercury’s precession, gravitational lensing). || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Well-integrated in classical mechanics, astronomy, and engineering. Less compatible with modern cosmology or relativistic frameworks. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple and intuitive: gravity as a force between masses. Easily grasped and widely taught. || ★★★★★
|-
| '''Heuristic Value''' || Inspired centuries of scientific discovery and classical mechanics. Still used in teaching and engineering. Limited in modern theoretical development. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Founded classical physics. Major leap in scientific method and mathematical modeling. Paved the way for Enlightenment-era science. || ★★★★★
|-
| '''Mathematical Rigor''' || Clear and elegant use of calculus and vector algebra (e.g. \(\displaystyle F = G \frac{m_1 m_2}{r^2}\)). Highly accessible and historically groundbreaking, but lacks deeper geometric or relativistic structures. || ★★★★☆
|}

'''Total: 33/40'''

=== '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Fits galactic rotation curves without invoking dark matter. Matches Tully-Fisher relation. Performance weakens at cluster and cosmological scales. || ★★★★☆
|-
| '''Internal Consistency''' || Original formulation is non-relativistic and phenomenological. Several relativistic extensions (e.g. TeVeS) exist but introduce complexity and fine-tuning. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts galaxy dynamics from baryonic matter alone. Less predictive at larger scales or in non-galactic contexts. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Primarily astrophysical. Some tension with cosmology, structure formation, and gravitational lensing. Not aligned with particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple at galactic scale: modifies acceleration below a threshold \(a_0\). Extensions are less intuitive. || ★★★★☆
|-
| '''Heuristic Value''' || Challenges dark matter paradigm and motivates alternate gravity models. Sparked theoretical and observational debate. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Offers a conceptual challenge to Newton/Einstein gravity. Philosophically provocative, but limited historical lineage. || ★★★☆☆
|-
| '''Mathematical Rigor''' || Employs interpolating functions and modified Poisson equations. Relativistic extensions (e.g. TeVeS) involve tensor-vector-scalar frameworks. Rigorous in parts, but lacks unified formalism. || ★★★☆☆
|}

'''Total: 28/40'''

=== '''8.8.4 Emergent Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Entropic_gravity Emergent / Entropic Gravity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Attempts to account for galactic rotation without dark matter by linking gravity to entropy and information. Some results match MOND-like behavior, but broad observational support remains limited. || ★★★☆☆
|-
| '''Internal Consistency''' || Theoretical framework draws from thermodynamics, holography, and information theory. Conceptually coherent, but not fully developed as a unified physical model. || ★★★☆☆
|-
| '''Predictive Power''' || Offers qualitative insights but lacks precise predictive capabilities in most contexts. No wide adoption for simulations or system modeling. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates ideas from black hole thermodynamics, quantum information, and spacetime geometry. Weak integration with observational astronomy or geology. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Abstract and speculative. Concepts like entropic forces and holographic screens are not intuitive for most readers. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates discussion about the nature of spacetime and gravity. Has inspired new theoretical directions in quantum gravity and information theory. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Philosophically intriguing: redefines gravity as emergent rather than fundamental. Links to ideas from Bekenstein and Hawking. || ★★★★☆
|-
| '''Mathematical Rigor''' || Relies on concepts from thermodynamics (e.g. entropy gradients), statistical mechanics, and quantum gravity. Uses integral relations and variational principles, but lacks a standardized set of equations for general use. || ★★★☆☆
|}

'''Total: 26/40'''

=== '''8.8.5 Big Bang – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strongly supported by CMB, redshift-distance relation, and light element abundances. However, JWST data revealing early, mature galaxies challenges the predicted timeline of structure formation. || ★★★★☆
|-
| '''Internal Consistency''' || Internally coherent within the ΛCDM framework. Logical structure is intact, though singularity and quantum-gravity transitions remain unresolved. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted CMB and nucleosynthesis. But recent observations (e.g. JWST galaxies at z &gt; 10) were not anticipated, requiring post-hoc model adjustments. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Strong integration with general relativity, quantum field theory, and thermodynamics. Limited links to geology or planetary evolution. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Conceptually complex genesis: singularity, inflation, and multiple postulated fields (inflaton, dark energy, dark matter). Relies on hypothetical constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulated massive observational and theoretical advances. Has driven decades of mission planning and cosmological interpretation. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Represented a paradigm shift from steady-state thinking. Raises deep ontological and metaphysical questions (e.g. time’s origin, creation ex nihilo). || ★★★★☆
|-
| '''Mathematical Rigor''' || Grounded in Einstein’s field equations, Friedmann dynamics, and thermodynamics. Offers well-defined, highly developed formalism. || ★★★★★
|}

'''Total: 34/40'''

=== '''8.8.6 Steady State Theory – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Cosmology]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Early successes with radio‐source counts, but contradicted by the cosmic microwave background, evolving galaxy populations, and quasar statistics. || ★★☆☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within the “perfect cosmological principle,” requiring continuous matter creation at a fixed rate. Logical but invokes an ad-hoc creation field (C-field). || ★★★☆☆
|-
| '''Predictive Power''' || Predicted constant large-scale density and specific radio‐source number counts; few successful novel predictions beyond its initial scope. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Limited overlap with modern astrophysics and particle physics; conflicts with nucleosynthesis and CMB observations. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively simple: Universe is homogeneous in space **and** time, avoiding an initial singularity. Minimal parameter set. || ★★★★☆
|-
| '''Heuristic Value''' || Historically spurred observational tests that ultimately favored Big Bang models; now mainly of pedagogical interest. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Embodies the perfect cosmological principle and continuous-creation idea, provoking debates on temporality and cosmological assumptions. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs Friedmann-like solutions with a creation term; uses relativistic field equations but lacks the richer formal development of ΛCDM or GR extensions. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.7 Big Crunch – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Once considered viable if cosmic density exceeded the critical value. Current observations (accelerating expansion, dark energy) contradict its key assumptions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretically consistent as a time-reversed Big Bang within general relativity. Requires high matter density and no (or reversing) dark energy. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts a decelerating expansion turning to collapse. Testable in principle, but not supported by current data. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with thermodynamic and relativistic models of entropy and time symmetry, but unsupported by astronomical data. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively mirrors Big Bang, offering closure and symmetry. Simple in concept, but difficult to reconcile with observed acceleration. || ★★★☆☆
|-
| '''Heuristic Value''' || Motivated theoretical discussion on cosmological fate and cyclic models. Limited influence in current cosmology. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Explores cosmological temporality and finitude. Once a philosophically compelling counterbalance to eternal expansion. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on time-reversible solutions to Friedmann equations and relativistic cosmology. Rigorous within GR but not extended in modern frameworks. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.8 Big Bounce – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || No direct observational evidence yet. Some loop quantum cosmology models suggest signatures in the CMB, but these remain speculative. || ★★☆☆☆
|-
| '''Internal Consistency''' || Offers a logically coherent alternative to singularity-based models. Dependent on quantum gravity frameworks (e.g. loop quantum gravity) that remain under development. || ★★★☆☆
|-
| '''Predictive Power''' || Provides potential testable differences in early universe structure and CMB fluctuations. Predictions are still uncertain and model-dependent. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges general relativity with quantum mechanics. Limited overlap with geology or observational astronomy. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex and abstract. The idea of a cyclical universe is conceptually appealing, but quantum corrections are not intuitive. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates exploration of singularity resolution and quantum gravity cosmologies. Encourages investigation of pre-Big Bang conditions. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Resonates with ancient cyclical cosmologies and philosophical ideas of eternal recurrence. Reframes the question of origins. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on extensions of Friedmann equations using loop quantum corrections or other quantum gravity approaches. Some models are mathematically formal, but the field is still unsettled. || ★★★☆☆
|}

'''Total: 24/40'''

=== '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' ===

''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆
|-
| '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆
|-
| '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆
|-
| '''Mathematical Rigor''' || Provides original equations (e.g. for \(D_{\text{pref}}\), \(G = (\gamma - 1)/4\pi\), \(\kappa = v_{\text{RMS}}^2 / c^4\)) and consistent dimensional analysis. Excel-based datasets link math to observations. Lacks field-theoretic formalism. || ★★★★☆
|}

'''Total: 34/40'''

=== '''8.8.10 Spiral Cosmology – AI Rating Summary''' ===

''Related link:'' [https://www.academia.edu/103005946/Cosmology_as_Spiral_Evolution Spiral Cosmology on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers visual and structural explanations for spiral galaxy morphology and cosmic rotation patterns. Less directly tied to quantitative data or tested predictions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Conceptually consistent in proposing self-similar spiral evolution at multiple scales, but lacks a developed dynamic or energetic framework. || ★★☆☆☆
|-
| '''Predictive Power''' || Suggests qualitative evolutionary stages and possible cyclic features, but does not provide specific numerical predictions. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Makes symbolic and philosophical connections across cosmology, biology, and culture. Scientific integration with physical fields is minimal. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Emphasizes intuitive and visual structures (e.g. spirals), which are accessible but may oversimplify physical complexity. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulates reflection on cosmic structure, symmetry, and recursion. Encourages reinterpretation of known forms (e.g. galaxies, DNA, hurricanes). || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Reconnects with ancient and Renaissance cosmologies linking form and function across scales. Offers metaphysical resonance. || ★★★★☆
|-
| '''Mathematical Rigor''' || Utilizes geometric symbolism (e.g. spiral ratios, golden mean) but lacks physical equations or dynamical systems modeling. No quantitative derivations. || ★★☆☆☆
|}

'''Total: 23/40'''

=== '''8.8.11 Topological Field Framework – AI Rating Summary''' ===

''Related link:'' [https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework on ResearchGate]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Proposes a geometric origin of particle properties and fundamental constants, but lacks direct comparison with observational or experimental datasets. Empirical testing is suggested but not yet demonstrated. || ★★☆☆☆
|-
| '''Internal Consistency''' || Builds a coherent and logically structured model grounded in topology and pressure gradients. Concepts are well integrated, with minimal contradictions. || ★★★★☆
|-
| '''Predictive Power''' || Offers a pathway to derive constants such as G, c, and Λ from topology and boundary conditions. However, quantitative predictions are still under development or pending validation. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges gravitational theory, particle physics, and topology. Aligns with ideas in quantum geometry, though not yet embedded in mainstream formulations. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Dense but conceptually focused. Uses field and pressure analogies to unify gravity and gauge interactions, though the abstract nature may limit accessibility. || ★★★☆☆
|-
| '''Heuristic Value''' || Provides an original and stimulating approach to unify physical constants via geometry. Encourages rethinking of foundational assumptions in physics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Revives geometrical unification ideals from early 20th-century physics and connects them to modern field-based ontology. Philosophically grounded. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs differential geometry, topological mapping, and field pressure modeling. Mathematical structure is present, but derivations are at a conceptual stage. || ★★★☆☆
|}

'''Total: 27/40'''

=== '''8.8.12 Conformal Gravity – AI Rating Summary''' ===

''Related link:'' [https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Successfully models galactic rotation curves and lensing effects without invoking dark matter. However, challenges remain regarding early-universe phenomena and the CMB. || ★★★☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within its conformal symmetry framework. Gravitational dynamics are derived cleanly from a fourth-order field equation. || ★★★★☆
|-
| '''Predictive Power''' || Accurately predicts galaxy-scale observations. However, extrapolations to cosmological scales require further development and empirical testing. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Intersects with quantum field theory through conformal invariance and offers alternatives to ΛCDM. Limited overlap with standard model particle physics. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Builds from a well-defined symmetry principle (conformal invariance). Some complexity arises due to fourth-order derivatives and unfamiliar constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Encourages reconsideration of gravitational assumptions and dark matter. Inspires new theoretical directions and alternative metrics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Connects with earlier Weyl geometry and symmetry-based models. Philosophically significant as a symmetry-driven alternative to general relativity. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs rigorous derivations based on conformal symmetry and higher-order field equations. Technically sophisticated. || ★★★★☆
|}

'''Total: 28/40'''

=== '''8.8.13 Quasi-Steady State Cosmology (QSSC) – AI Rating Summary''' ===

''Related link:'' [https://www.ias.ac.in/article/fulltext/pram/053/06/1093-1104 The Quasi-Steady State Cosmology: Theory and Observations – Pramana Journal]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers explanations for redshift, large-scale structure, and quasar distributions. However, it faces difficulties matching the observed CMB spectrum and primordial element abundances. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretical foundations are logically constructed around a C-field and creation events. Internally coherent but relies on non-standard mechanisms not universally accepted. || ★★★☆☆
|-
| '''Predictive Power''' || Makes unique predictions about cosmic cycles, matter creation, and galaxy evolution. Some predictions remain qualitative or are difficult to test. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Attempts to integrate cosmology with continuous creation physics. However, the C-field concept is not aligned with standard field theory or particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Proposes an intuitive cyclical model of cosmic evolution. Some components, such as the C-field, are abstract and complex to formalize. || ★★★☆☆
|-
| '''Heuristic Value''' || Offers a provocative alternative to the Big Bang. Stimulates re-evaluation of singularity-based models and encourages cyclic interpretations. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Extends the steady-state philosophy of Hoyle. Challenges the singular origin narrative with philosophical depth and continuity. || ★★★★☆
|-
| '''Mathematical Rigor''' || Uses mathematical models for cyclic expansion and C-field dynamics. However, these are not widely adopted or fully developed in mainstream literature. || ★★☆☆☆
|}

'''Total: 23/40'''

=== '''8.8.14 Dynamic Universe (Tuomo Suntola) – AI Rating Summary''' ===

''Related link:'' [https://physicsfoundations.org/suntola/dynamic-universe Dynamic Universe – Physics Foundations Society]  
''Additional source:'' [https://www.academia.edu/37149633/The_Dynamic_Universe_Toward_a_unified_picture_of_physical_reality The Dynamic Universe on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Provides testable predictions for cosmological redshift, Hubble parameter, and time dilation without invoking dark energy. Several predictions align well with observational data, though not yet widely confirmed. || ★★★☆☆
|-
| '''Internal Consistency''' || The model is highly self-consistent, based on a single zero-energy principle and evolving 4-sphere geometry. Internally coherent and logically derived. || ★★★★☆
|-
| '''Predictive Power''' || Predicts cosmological parameters from first principles, including a time-evolving H₀ and expansion behavior. Some predictions differ from ΛCDM but remain observationally accessible. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Attempts unification of relativity, cosmology, and quantum phenomena under a geometric framework. Still under integration with conventional physics models. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Built on a single geometric principle with minimal assumptions. Clear in its physical logic, though unfamiliar to those trained in standard GR or QFT. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires a rethinking of time, space, and energy conservation. Offers a conceptually elegant reformulation of cosmic dynamics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Echoes Machian ideas and Einstein’s early search for balance models. Challenges the notion of spacetime curvature as fundamental. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs rigorous geometric derivations and differential equations. Mathematical structure is well-developed, though outside conventional formalisms. || ★★★★☆
|}

'''Total: 30/40'''


=== '''8.9 – Additional Alternative Cosmological Theories (Under Evaluation)''' ===

* '''[https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework]''' (Hall) – Proposes that fundamental constants such as G, c, and Λ emerge from topological constraints in higher-dimensional field configurations. The theory has high internal logic, mathematical consistency, and geometric depth. Empirical validation depends on measurable predictions, but its interdisciplinary integration (e.g., quantum geometry, general relativity) offers high conceptual promise.

* '''[https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]''' (Mannheim–Kazanas) – Eliminates the need for dark matter by applying conformal symmetry to gravitational equations. It explains galactic rotation curves and lensing without exotic particles. Predictive power is strong on galactic scales, but it faces challenges with early-universe data. Internally consistent and testable, though its cosmological compatibility is debated.

* '''[https://www.ias.ac.in/article/fulltext/pram/053/06/1093-1104 The Quasi-Steady State Cosmology: Theory and Observations]''' – A cyclic, non-Big Bang model incorporating continuous matter creation via a “C-field.” It accounts for redshift and some cosmic structure without expansion from a singularity. Empirical adequacy is mixed due to tension with CMB and elemental abundance observations. Still, its falsifiability and explanatory ambition support its inclusion in theoretical discourse.

* '''[https://physicsfoundations.org/suntola/dynamic-universe Dynamic Universe]''' (Tuomo Suntola) – A model based on zero-energy balance and time-evolving geometry, predicting cosmic constants from dynamic curvature. Offers conceptual simplicity and mathematical consistency. Deviates from mainstream relativity but maintains coherence. Predictions related to H₀ and time-scaling allow for observational tests and empirical challenge.  
{{#ev:youtube|n62WMdSYSjk|Tuomo Suntola: Introduction to the Dynamic Universe}}


'''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]'''</text>
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      <contributor>
        <username>Ruud Loeffen</username>
        <id>2998353</id>
      </contributor>
      <comment>/* 8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor) */  add 4 theories and add numbers for each theory in accordance withy the numbers of 8.8 for a clear reference</comment>
      <origin>2720883</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="39885" sha1="r9nfm15al81652l57osvhiix7vdub0d" xml:space="preserve">== '''Chapter 8: Methods, Tools, and AI-Assisted Evaluation''' =

== '''8.1 Purpose''' ==

This chapter describes the methodological foundations of the project, including the role of AI in evaluating theories, how contributors interact with the system, and how assessments are recorded, displayed, and updated.

== '''8.2 Toolchain and Workflow''' ==

AI tools like ChatGPT are used to analyze, compare, and refine theories

Tables and frameworks are generated collaboratively using open formats

Contributors submit input via email or editing suggestions

Ratings and evaluations are dynamically updated based on ongoing analysis

== '''8.3 AI-Based Rating System: Motivation and Procedure''' ==

To support comparative evaluation without personal or institutional bias, this project uses an AI-based rating system. ChatGPT acts as a neutral evaluator, analyzing each theory across clearly defined criteria in '''8.5 Understanding the Star Ratings'''.

This system is designed to be:

Transparent – Each rating is justified through AI’s large-scale reference analysis.

Dynamic – Contributors may submit additional materials to request re-evaluation.

Consistent – All evaluations are performed by the same AI logic, eliminating personal bias.

Contributors may ask ChatGPT to re-read specific articles, datasets, or theoretical arguments. If new insights are found, ratings will be updated and transparently noted.

This approach represents a shift toward evidence-driven, large-scale comparative review, using AI not as a gatekeeper but as a tool to synthesize and validate.

== '''8.4 Open Participation''' ==

This chapter is also where future documentation of the workflow and collaborative mechanisms will be expanded. Users who submit theories are encouraged to:

Describe their framework in terms of assumptions, predictions, and compatibility

Suggest how their model could be tested or falsified

Provide references or original materials for AI evaluation

All analysis is open, and contributors may propose improvements at any time.

== '''8.5 Understanding the Star Ratings''' ==

The AI Evaluation Table below rates theories across seven scientific criteria defined in '''Chapter 1.3'''. Here we provide a full explanation of what each criterion means and how it is applied.

'''8.5.1. Empirical Adequacy'''  
Does the theory fit known observations and experimental data? High scores require support from astronomy, cosmology, geology, or lab-based physics. Theories that contradict established measurements or lack empirical grounding score lower.

'''8.5.2. Internal Consistency'''  
Are the theory’s assumptions, mathematics, and logic self-coherent? A consistent theory does not contain contradictions, undefined steps, or ad hoc assumptions.

'''8.5.3. Predictive Power'''  
Does the theory make clear, testable predictions that distinguish it from others? Theories that anticipate new phenomena or retrodict known data gain higher ratings.

'''8.5.4. Cross-Disciplinary Compatibility'''  
Is the theory consistent with findings from other scientific fields, such as geology, chemistry, biology, or planetary science? The more compatible it is, the higher the score.

'''8.5.5. Conceptual Clarity and Simplicity'''  
Is the theory logically simple and intuitively understandable, without unnecessary complexity? This criterion rewards elegance, not oversimplification.

'''8.5.6. Heuristic Value'''  
Does the theory stimulate new questions, research directions, or rethinking of existing problems? A high score reflects creative scientific potential.

'''8.5.7. Historical and Philosophical Insight'''  
Does the theory connect meaningfully to the historical development of science or reflect philosophical depth? Theories grounded in tradition or conceptual evolution are valued here.

'''8.5.8. Mathematical Rigor'''  
Does the theory provide clear mathematical formulations, derivations, and quantitative predictions? Theories are valued for their use of equations to express core principles, ensure internal consistency, and generate testable results.


Each theory receives a rating from ★☆☆☆☆ to ★★★★★ per criterion. The total score (max 35) gives a general measure of its scientific coherence and reach. The reasoning behind the scores is available under each theory (subsection 8.8) or can be requested in more detail.


=== '''8.6 – Comparative Table of AI Ratings (Updated with Criterion 8: Mathematical Rigor)''' ===

''Note: In July 2025, an eighth evaluation criterion was added: '''Mathematical Rigor'''. The total score is now out of 40 stars instead of 35.  ''
''All ratings are expressed in whole stars (★), without fractional values, to ensure clarity in display and consistency with the visual format of this table.''  
''Theories are listed in the same order as in Section 8.8.''

{| class=&quot;wikitable&quot;
! '''Theory''' !! '''EA''' !! '''IC''' !! '''PP''' !! '''CC''' !! '''CS''' !! '''HV''' !! '''HP''' !! '''MR''' !! '''Total (★/40)'''
|-
| '''8.8.1 General Relativity''' || ★★★★★ || ★★★★★ || ★★★★★ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★★ || ★★★★★ || '''37'''
|-
| '''8.8.2 Newtonian Gravity''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || ★★★★☆ || '''33'''
|-
| '''8.8.3 MOND''' || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || '''26'''
|-
| '''8.8.4 Emergent Gravity''' || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''24'''
|-
| '''8.8.5 Big Bang''' || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★★ || ★★★★☆ || ★★★★★ || '''34'''
|-
| '''8.8.6 Steady State Theory''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''23'''
|-
| '''8.8.7 Big Crunch''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''8.8.8 Big Bounce''' || ★★☆☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''22'''
|-
| '''8.8.9 Cosmic Influx Theory (CIT)''' || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★★ || ★★★★☆ || ★★★★☆ || '''33'''
|-
| '''8.8.10 Spiral Cosmology''' || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''21'''
|-
| '''8.8.11 Topological Field Framework''' || ★★☆☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || '''27'''
|-
| '''8.8.12 Conformal Gravity''' || ★★★☆☆ || ★★★★☆ || ★★★☆☆ || ★★★☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || '''28'''
|-
| '''8.8.13 Quasi-Steady State Cosmology''' || ★★☆☆☆ || ★★★☆☆ || ★★★☆☆ || ★★☆☆☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★☆☆☆ || '''23'''
|-
| '''8.8.14 Dynamic Universe''' || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★★☆☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || ★★★★☆ || '''30'''

|}

''Legend:''  
''EA = Empirical Adequacy IC = Internal Consistency PP = Predictive Power CC = Cross-Disciplinary Compatibility  ''
''CS = Conceptual Simplicity HV = Heuristic Value HP = Historical/Philosophical Insight MR = Mathematical Rigor''


&lt;!-- Add a blank line here --&gt;

== '''8.7 Requesting Detailed Justification''' ==

“Somebody” interested in the full motivation for a theory’s score—criterion by criterion—can obtain this by:

1. Visiting the '''discussion page''' of this Wikiversity chapter.
  
2. Mentioning the theory by name and explicitly asking for the detailed breakdown.
  
3. Receiving an AI-generated or authored comment elaborating why each star rating was assigned. 

These ratings are transparent and intended to support critical evaluation and ongoing refinement of both established and alternative cosmological theories. Constructive feedback, new data, or arguments may lead to adjustments in the scores, provided clear reasoning is presented.

If a contributor or author does not agree with the evaluation or prefers not to have their theory represented under this framework, they may request that all related content and ratings for that theory be removed. This ensures that participation remains voluntary and respectful of intellectual ownership.

'''Mainstream theories are subject to the same critical standard.'''  
If someone presents a reasoned objection to the current star ratings of a widely accepted theory (e.g. General Relativity, Big Bang), their explanation will be reviewed. If the argument is well-founded, ChatGPT may generate a revised evaluation. Both the original and alternative viewpoints can be documented transparently if needed.

If you want to submit a '''Rating Rebuttal''', please use the template provided on the '''[[Talk:AI-Assisted Evaluation of Cosmological Theories|Discussion page]]'''.

== '''8.8 Detailed Evaluations of Theories''' ==

This section will be expanded progressively as new theories are added. Each evaluation is generated in collaboration with ChatGPT, based on a standardized set of seven criteria defined in Chapter 1. This approach allows for clear, consistent, and rapid assessment of both mainstream and non-mainstream cosmological theories within minutes.

=== '''8.8.1 General Relativity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/General_relativity General Relativity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Matches a wide range of observations: gravitational lensing, GPS corrections, perihelion precession, black hole dynamics, and gravitational waves. Supported by multiple experiments. || ★★★★★
|-
| '''Internal Consistency''' || Highly consistent within its differential geometric framework. Built upon Einstein's field equations with tensor calculus. Few internal contradictions, though extensions (e.g. quantum gravity) face challenges. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted gravitational redshift, time dilation, frame-dragging, and gravitational waves. Continues to guide observations in astrophysics. || ★★★★★
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with cosmology and astrophysics. Some tension with quantum theory. Less integrated with planetary geology or biology. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex mathematical structure makes it less intuitive. Conceptually abstract (spacetime curvature, geodesics). Clarity improves with education, but simplicity is low. || ★★★☆☆
|-
| '''Heuristic Value''' || Inspired vast developments in cosmology, black hole theory, and relativistic astrophysics. Foundation for modern gravitational physics. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Deep philosophical implications about space, time, and causality. Represents a major shift from Newtonian absolute space. Influenced 20th-century philosophy of science. || ★★★★★
|-
| '''Mathematical Rigor''' || Built upon advanced mathematics: Riemannian geometry, Einstein field equations, tensor calculus. Equations are precise, formal, and deeply embedded in differential geometry. || ★★★★★
|}

'''Total: 39/40'''

=== '''8.8.2 Newtonian Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation Newton's Law of Universal Gravitation]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Accurately describes gravitational interactions for most macroscopic systems (planets, satellites, projectiles) under low-speed, weak-field conditions. Deviates in extreme conditions (e.g. near black holes). || ★★★★☆
|-
| '''Internal Consistency''' || Mathematically self-consistent with inverse-square law and Newton's laws of motion. Assumes instantaneous action at a distance, which conflicts with relativity. || ★★★★☆
|-
| '''Predictive Power''' || Predicts planetary orbits, tides, escape velocities, and Keplerian motion. Fails for relativistic effects (e.g. Mercury’s precession, gravitational lensing). || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Well-integrated in classical mechanics, astronomy, and engineering. Less compatible with modern cosmology or relativistic frameworks. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple and intuitive: gravity as a force between masses. Easily grasped and widely taught. || ★★★★★
|-
| '''Heuristic Value''' || Inspired centuries of scientific discovery and classical mechanics. Still used in teaching and engineering. Limited in modern theoretical development. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Founded classical physics. Major leap in scientific method and mathematical modeling. Paved the way for Enlightenment-era science. || ★★★★★
|-
| '''Mathematical Rigor''' || Clear and elegant use of calculus and vector algebra (e.g. \(\displaystyle F = G \frac{m_1 m_2}{r^2}\)). Highly accessible and historically groundbreaking, but lacks deeper geometric or relativistic structures. || ★★★★☆
|}

'''Total: 33/40'''

=== '''8.8.3 MOND (Modified Newtonian Dynamics) – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics Modified Newtonian Dynamics (MOND)]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Fits galactic rotation curves without invoking dark matter. Matches Tully-Fisher relation. Performance weakens at cluster and cosmological scales. || ★★★★☆
|-
| '''Internal Consistency''' || Original formulation is non-relativistic and phenomenological. Several relativistic extensions (e.g. TeVeS) exist but introduce complexity and fine-tuning. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts galaxy dynamics from baryonic matter alone. Less predictive at larger scales or in non-galactic contexts. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Primarily astrophysical. Some tension with cosmology, structure formation, and gravitational lensing. Not aligned with particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Simple at galactic scale: modifies acceleration below a threshold \(a_0\). Extensions are less intuitive. || ★★★★☆
|-
| '''Heuristic Value''' || Challenges dark matter paradigm and motivates alternate gravity models. Sparked theoretical and observational debate. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Offers a conceptual challenge to Newton/Einstein gravity. Philosophically provocative, but limited historical lineage. || ★★★☆☆
|-
| '''Mathematical Rigor''' || Employs interpolating functions and modified Poisson equations. Relativistic extensions (e.g. TeVeS) involve tensor-vector-scalar frameworks. Rigorous in parts, but lacks unified formalism. || ★★★☆☆
|}

'''Total: 28/40'''

=== '''8.8.4 Emergent Gravity – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Entropic_gravity Emergent / Entropic Gravity]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Attempts to account for galactic rotation without dark matter by linking gravity to entropy and information. Some results match MOND-like behavior, but broad observational support remains limited. || ★★★☆☆
|-
| '''Internal Consistency''' || Theoretical framework draws from thermodynamics, holography, and information theory. Conceptually coherent, but not fully developed as a unified physical model. || ★★★☆☆
|-
| '''Predictive Power''' || Offers qualitative insights but lacks precise predictive capabilities in most contexts. No wide adoption for simulations or system modeling. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates ideas from black hole thermodynamics, quantum information, and spacetime geometry. Weak integration with observational astronomy or geology. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Abstract and speculative. Concepts like entropic forces and holographic screens are not intuitive for most readers. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates discussion about the nature of spacetime and gravity. Has inspired new theoretical directions in quantum gravity and information theory. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Philosophically intriguing: redefines gravity as emergent rather than fundamental. Links to ideas from Bekenstein and Hawking. || ★★★★☆
|-
| '''Mathematical Rigor''' || Relies on concepts from thermodynamics (e.g. entropy gradients), statistical mechanics, and quantum gravity. Uses integral relations and variational principles, but lacks a standardized set of equations for general use. || ★★★☆☆
|}

'''Total: 26/40'''

=== '''8.8.5 Big Bang – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bang Big Bang Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strongly supported by CMB, redshift-distance relation, and light element abundances. However, JWST data revealing early, mature galaxies challenges the predicted timeline of structure formation. || ★★★★☆
|-
| '''Internal Consistency''' || Internally coherent within the ΛCDM framework. Logical structure is intact, though singularity and quantum-gravity transitions remain unresolved. || ★★★★★
|-
| '''Predictive Power''' || Successfully predicted CMB and nucleosynthesis. But recent observations (e.g. JWST galaxies at z &gt; 10) were not anticipated, requiring post-hoc model adjustments. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Strong integration with general relativity, quantum field theory, and thermodynamics. Limited links to geology or planetary evolution. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Conceptually complex genesis: singularity, inflation, and multiple postulated fields (inflaton, dark energy, dark matter). Relies on hypothetical constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulated massive observational and theoretical advances. Has driven decades of mission planning and cosmological interpretation. || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Represented a paradigm shift from steady-state thinking. Raises deep ontological and metaphysical questions (e.g. time’s origin, creation ex nihilo). || ★★★★☆
|-
| '''Mathematical Rigor''' || Grounded in Einstein’s field equations, Friedmann dynamics, and thermodynamics. Offers well-defined, highly developed formalism. || ★★★★★
|}

'''Total: 34/40'''

=== '''8.8.6 Steady State Theory – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Steady_state_model Steady State Cosmology]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Early successes with radio‐source counts, but contradicted by the cosmic microwave background, evolving galaxy populations, and quasar statistics. || ★★☆☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within the “perfect cosmological principle,” requiring continuous matter creation at a fixed rate. Logical but invokes an ad-hoc creation field (C-field). || ★★★☆☆
|-
| '''Predictive Power''' || Predicted constant large-scale density and specific radio‐source number counts; few successful novel predictions beyond its initial scope. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Limited overlap with modern astrophysics and particle physics; conflicts with nucleosynthesis and CMB observations. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively simple: Universe is homogeneous in space **and** time, avoiding an initial singularity. Minimal parameter set. || ★★★★☆
|-
| '''Heuristic Value''' || Historically spurred observational tests that ultimately favored Big Bang models; now mainly of pedagogical interest. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Embodies the perfect cosmological principle and continuous-creation idea, provoking debates on temporality and cosmological assumptions. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs Friedmann-like solutions with a creation term; uses relativistic field equations but lacks the richer formal development of ΛCDM or GR extensions. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.7 Big Crunch – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Crunch Big Crunch]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Once considered viable if cosmic density exceeded the critical value. Current observations (accelerating expansion, dark energy) contradict its key assumptions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretically consistent as a time-reversed Big Bang within general relativity. Requires high matter density and no (or reversing) dark energy. || ★★★☆☆
|-
| '''Predictive Power''' || Predicts a decelerating expansion turning to collapse. Testable in principle, but not supported by current data. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Compatible with thermodynamic and relativistic models of entropy and time symmetry, but unsupported by astronomical data. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Intuitively mirrors Big Bang, offering closure and symmetry. Simple in concept, but difficult to reconcile with observed acceleration. || ★★★☆☆
|-
| '''Heuristic Value''' || Motivated theoretical discussion on cosmological fate and cyclic models. Limited influence in current cosmology. || ★★★☆☆
|-
| '''Historical and Philosophical Insight''' || Explores cosmological temporality and finitude. Once a philosophically compelling counterbalance to eternal expansion. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on time-reversible solutions to Friedmann equations and relativistic cosmology. Rigorous within GR but not extended in modern frameworks. || ★★★☆☆
|}

'''Total: 23/40'''

=== '''8.8.8 Big Bounce – AI Rating Summary''' ===

''Related link:'' [https://en.wikipedia.org/wiki/Big_Bounce Big Bounce]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || No direct observational evidence yet. Some loop quantum cosmology models suggest signatures in the CMB, but these remain speculative. || ★★☆☆☆
|-
| '''Internal Consistency''' || Offers a logically coherent alternative to singularity-based models. Dependent on quantum gravity frameworks (e.g. loop quantum gravity) that remain under development. || ★★★☆☆
|-
| '''Predictive Power''' || Provides potential testable differences in early universe structure and CMB fluctuations. Predictions are still uncertain and model-dependent. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges general relativity with quantum mechanics. Limited overlap with geology or observational astronomy. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Complex and abstract. The idea of a cyclical universe is conceptually appealing, but quantum corrections are not intuitive. || ★★☆☆☆
|-
| '''Heuristic Value''' || Stimulates exploration of singularity resolution and quantum gravity cosmologies. Encourages investigation of pre-Big Bang conditions. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Resonates with ancient cyclical cosmologies and philosophical ideas of eternal recurrence. Reframes the question of origins. || ★★★★☆
|-
| '''Mathematical Rigor''' || Based on extensions of Friedmann equations using loop quantum corrections or other quantum gravity approaches. Some models are mathematically formal, but the field is still unsettled. || ★★★☆☆
|}

'''Total: 24/40'''

=== '''8.8.9 Cosmic Influx Theory (CIT) – AI Rating Summary''' ===

''Related link:'' [https://en.wikiversity.org/wiki/Cosmic_Influx_Theory Cosmic Influx Theory]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Strong match with observed planetary structuring, VRMS-based system modeling, and geological trends like daylength and expansion. Supported by exoplanet data and disk morphology (e.g. HD 163296). || ★★★★☆
|-
| '''Internal Consistency''' || Equations and constants (e.g. κ₍CIT₎, (γ−1)/4π) are logically coherent. Internal derivations remain consistent across cosmological and planetary domains. || ★★★★☆
|-
| '''Predictive Power''' || Offers specific predictions (e.g. Trappist-1 preferred distance and orbital period). Some predictions still await observational confirmation. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Integrates cosmology, geology, biology, and observational astronomy. Compatible with expanding Earth, daylength data, and ring formation physics. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Introduces new yet intuitive ideas like influx and preferred distances. Avoids abstract constructs like dark matter/energy. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires re-evaluation of mainstream assumptions, links to overlooked or discarded theories (e.g. Le Sage, expansion tectonics). || ★★★★★
|-
| '''Historical and Philosophical Insight''' || Reconnects with early gravitational push models and continuous creation ideas, offering philosophical alternatives to entropy-based models. || ★★★★☆
|-
| '''Mathematical Rigor''' || Provides original equations (e.g. for \(D_{\text{pref}}\), \(G = (\gamma - 1)/4\pi\), \(\kappa = v_{\text{RMS}}^2 / c^4\)) and consistent dimensional analysis. Excel-based datasets link math to observations. Lacks field-theoretic formalism. || ★★★★☆
|}

'''Total: 34/40'''

=== '''8.8.10 Spiral Cosmology – AI Rating Summary''' ===

''Related link:'' [https://www.academia.edu/103005946/Cosmology_as_Spiral_Evolution Spiral Cosmology on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers visual and structural explanations for spiral galaxy morphology and cosmic rotation patterns. Less directly tied to quantitative data or tested predictions. || ★★☆☆☆
|-
| '''Internal Consistency''' || Conceptually consistent in proposing self-similar spiral evolution at multiple scales, but lacks a developed dynamic or energetic framework. || ★★☆☆☆
|-
| '''Predictive Power''' || Suggests qualitative evolutionary stages and possible cyclic features, but does not provide specific numerical predictions. || ★★☆☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Makes symbolic and philosophical connections across cosmology, biology, and culture. Scientific integration with physical fields is minimal. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Emphasizes intuitive and visual structures (e.g. spirals), which are accessible but may oversimplify physical complexity. || ★★★☆☆
|-
| '''Heuristic Value''' || Stimulates reflection on cosmic structure, symmetry, and recursion. Encourages reinterpretation of known forms (e.g. galaxies, DNA, hurricanes). || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Reconnects with ancient and Renaissance cosmologies linking form and function across scales. Offers metaphysical resonance. || ★★★★☆
|-
| '''Mathematical Rigor''' || Utilizes geometric symbolism (e.g. spiral ratios, golden mean) but lacks physical equations or dynamical systems modeling. No quantitative derivations. || ★★☆☆☆
|}

'''Total: 23/40'''

=== '''8.8.11 Topological Field Framework – AI Rating Summary''' ===

''Related link:'' [https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework on ResearchGate]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Proposes a geometric origin of particle properties and fundamental constants, but lacks direct comparison with observational or experimental datasets. Empirical testing is suggested but not yet demonstrated. || ★★☆☆☆
|-
| '''Internal Consistency''' || Builds a coherent and logically structured model grounded in topology and pressure gradients. Concepts are well integrated, with minimal contradictions. || ★★★★☆
|-
| '''Predictive Power''' || Offers a pathway to derive constants such as G, c, and Λ from topology and boundary conditions. However, quantitative predictions are still under development or pending validation. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Bridges gravitational theory, particle physics, and topology. Aligns with ideas in quantum geometry, though not yet embedded in mainstream formulations. || ★★★★☆
|-
| '''Conceptual Clarity and Simplicity''' || Dense but conceptually focused. Uses field and pressure analogies to unify gravity and gauge interactions, though the abstract nature may limit accessibility. || ★★★☆☆
|-
| '''Heuristic Value''' || Provides an original and stimulating approach to unify physical constants via geometry. Encourages rethinking of foundational assumptions in physics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Revives geometrical unification ideals from early 20th-century physics and connects them to modern field-based ontology. Philosophically grounded. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs differential geometry, topological mapping, and field pressure modeling. Mathematical structure is present, but derivations are at a conceptual stage. || ★★★☆☆
|}

'''Total: 27/40'''

=== '''8.8.12 Conformal Gravity – AI Rating Summary''' ===

''Related link:'' [https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Successfully models galactic rotation curves and lensing effects without invoking dark matter. However, challenges remain regarding early-universe phenomena and the CMB. || ★★★☆☆
|-
| '''Internal Consistency''' || Mathematically self-consistent within its conformal symmetry framework. Gravitational dynamics are derived cleanly from a fourth-order field equation. || ★★★★☆
|-
| '''Predictive Power''' || Accurately predicts galaxy-scale observations. However, extrapolations to cosmological scales require further development and empirical testing. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Intersects with quantum field theory through conformal invariance and offers alternatives to ΛCDM. Limited overlap with standard model particle physics. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Builds from a well-defined symmetry principle (conformal invariance). Some complexity arises due to fourth-order derivatives and unfamiliar constructs. || ★★★☆☆
|-
| '''Heuristic Value''' || Encourages reconsideration of gravitational assumptions and dark matter. Inspires new theoretical directions and alternative metrics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Connects with earlier Weyl geometry and symmetry-based models. Philosophically significant as a symmetry-driven alternative to general relativity. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs rigorous derivations based on conformal symmetry and higher-order field equations. Technically sophisticated. || ★★★★☆
|}

'''Total: 28/40'''

=== '''8.8.13 Quasi-Steady State Cosmology (QSSC) – AI Rating Summary''' ===

''Related link:'' [https://www.ias.ac.in/article/fulltext/pram/053/06/1093-1104 The Quasi-Steady State Cosmology: Theory and Observations – Pramana Journal]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Offers explanations for redshift, large-scale structure, and quasar distributions. However, it faces difficulties matching the observed CMB spectrum and primordial element abundances. || ★★☆☆☆
|-
| '''Internal Consistency''' || Theoretical foundations are logically constructed around a C-field and creation events. Internally coherent but relies on non-standard mechanisms not universally accepted. || ★★★☆☆
|-
| '''Predictive Power''' || Makes unique predictions about cosmic cycles, matter creation, and galaxy evolution. Some predictions remain qualitative or are difficult to test. || ★★★☆☆
|-
| '''Cross-Disciplinary Compatibility''' || Attempts to integrate cosmology with continuous creation physics. However, the C-field concept is not aligned with standard field theory or particle physics. || ★★☆☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Proposes an intuitive cyclical model of cosmic evolution. Some components, such as the C-field, are abstract and complex to formalize. || ★★★☆☆
|-
| '''Heuristic Value''' || Offers a provocative alternative to the Big Bang. Stimulates re-evaluation of singularity-based models and encourages cyclic interpretations. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Extends the steady-state philosophy of Hoyle. Challenges the singular origin narrative with philosophical depth and continuity. || ★★★★☆
|-
| '''Mathematical Rigor''' || Uses mathematical models for cyclic expansion and C-field dynamics. However, these are not widely adopted or fully developed in mainstream literature. || ★★☆☆☆
|}

'''Total: 23/40'''

=== '''8.8.14 Dynamic Universe (Tuomo Suntola) – AI Rating Summary''' ===

''Related link:'' [https://physicsfoundations.org/suntola/dynamic-universe Dynamic Universe – Physics Foundations Society]  
''Additional source:'' [https://www.academia.edu/37149633/The_Dynamic_Universe_Toward_a_unified_picture_of_physical_reality The Dynamic Universe on Academia.edu]

{| class=&quot;wikitable&quot;
! '''Criterion''' !! '''Description''' !! '''Rating'''
|-
| '''Empirical Adequacy''' || Provides testable predictions for cosmological redshift, Hubble parameter, and time dilation without invoking dark energy. Several predictions align well with observational data, though not yet widely confirmed. || ★★★☆☆
|-
| '''Internal Consistency''' || The model is highly self-consistent, based on a single zero-energy principle and evolving 4-sphere geometry. Internally coherent and logically derived. || ★★★★☆
|-
| '''Predictive Power''' || Predicts cosmological parameters from first principles, including a time-evolving H₀ and expansion behavior. Some predictions differ from ΛCDM but remain observationally accessible. || ★★★★☆
|-
| '''Cross-Disciplinary Compatibility''' || Attempts unification of relativity, cosmology, and quantum phenomena under a geometric framework. Still under integration with conventional physics models. || ★★★☆☆
|-
| '''Conceptual Clarity and Simplicity''' || Built on a single geometric principle with minimal assumptions. Clear in its physical logic, though unfamiliar to those trained in standard GR or QFT. || ★★★★☆
|-
| '''Heuristic Value''' || Inspires a rethinking of time, space, and energy conservation. Offers a conceptually elegant reformulation of cosmic dynamics. || ★★★★☆
|-
| '''Historical and Philosophical Insight''' || Echoes Machian ideas and Einstein’s early search for balance models. Challenges the notion of spacetime curvature as fundamental. || ★★★★☆
|-
| '''Mathematical Rigor''' || Employs rigorous geometric derivations and differential equations. Mathematical structure is well-developed, though outside conventional formalisms. || ★★★★☆
|}

'''Total: 30/40'''


=== '''8.9 – Additional Alternative Cosmological Theories (Under Evaluation)''' ===

* '''[https://www.researchgate.net/publication/393122856_A_Topological_Field_Framework_for_Particle_Mass_Gauge_Interactions_and_Emergent_Gravity A Topological Field Framework]''' (Hall) – Proposes that fundamental constants such as G, c, and Λ emerge from topological constraints in higher-dimensional field configurations. The theory has high internal logic, mathematical consistency, and geometric depth. Empirical validation depends on measurable predictions, but its interdisciplinary integration (e.g., quantum geometry, general relativity) offers high conceptual promise.

* '''[https://ui.adsabs.harvard.edu/abs/1989ApJ...342..635M Exact Vacuum Solution to Conformal Weyl Gravity and Galactic Rotation Curves]''' (Mannheim–Kazanas) – Eliminates the need for dark matter by applying conformal symmetry to gravitational equations. It explains galactic rotation curves and lensing without exotic particles. Predictive power is strong on galactic scales, but it faces challenges with early-universe data. Internally consistent and testable, though its cosmological compatibility is debated.

* '''[https://www.ias.ac.in/article/fulltext/pram/053/06/1093-1104 The Quasi-Steady State Cosmology: Theory and Observations]''' – A cyclic, non-Big Bang model incorporating continuous matter creation via a “C-field.” It accounts for redshift and some cosmic structure without expansion from a singularity. Empirical adequacy is mixed due to tension with CMB and elemental abundance observations. Still, its falsifiability and explanatory ambition support its inclusion in theoretical discourse.

* '''[https://physicsfoundations.org/suntola/dynamic-universe Dynamic Universe]''' (Tuomo Suntola) – A model based on zero-energy balance and time-evolving geometry, predicting cosmic constants from dynamic curvature. Offers conceptual simplicity and mathematical consistency. Deviates from mainstream relativity but maintains coherence. Predictions related to H₀ and time-scaling allow for observational tests and empirical challenge.  
{{#ev:youtube|n62WMdSYSjk|Tuomo Suntola: Introduction to the Dynamic Universe}}


'''◀ [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_7:_Cosmological_Parameters_and_Universal_Constants|Previous]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories|Main Page]] | [[AI-Assisted_Evaluation_of_Cosmological_Theories/Chapter_9:_Documentation_and_Transparency|Next ▶]]'''</text>
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    <title>The NKT Law on Position and Varying Inertia Interaction</title>
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      <text bytes="3447" sha1="ctsjfgpabygh9i4ddc1wa05j7dqu7qj" xml:space="preserve">== Introduction ==

This page presents an educational overview of the NKTg Law — a proposed theoretical framework that explores the interaction between position and varying inertia in physical systems. The formulation aims to extend traditional Newtonian dynamics by incorporating the possibility that inertia (mass) may not be constant, but can vary with position and time.

This page is intended for academic discussion, exploration, and critique within the spirit of open scientific learning.

== Theoretical Formulation ==

The NKT Law is based on two fundamental interaction terms:

:'''S₁ = x ⋅ p'''  
:'''S₂ = ṁ ⋅ p'''

Where:
- '''x''' is position,
- '''p''' is momentum,
- '''ṁ''' is the time derivative of mass (i.e., varying inertia),
- The dot (⋅) denotes scalar multiplication.

These two multiplicative interactions are proposed to represent:
- **S₁**: The classical coupling between position and momentum, echoing Hamiltonian intuition.
- **S₂**: A new term that models how changes in inertia might interact with momentum, a concept not found in Newtonian mechanics.

The total action-like expression is a sum of both interactions:  
:'''S = S₁ + S₂ = x⋅p + ṁ⋅p'''

This formulation is intentionally minimalistic, focusing on clarity and testability.

== Physical Motivation ==

Conventional physics assumes that mass (inertia) is constant in most cases. However, in scenarios like:
- **Rocket propulsion** (variable mass),
- **Gravitational collapse** (mass-energy distribution),
- **Cosmic expansion** (large-scale structure evolution),

mass may be effectively dynamic. The NKT Law hypothesizes that position-dependent inertia might lead to observable corrections in motion equations.

== Example Applications ==

Several hypothetical contexts where the NKT Law could be tested include:

* **Simple Harmonic Oscillator** – analyzing how variable inertia modifies periodic motion.
* **Rocket motion** – standard variable mass mechanics might gain additional terms.
* **Planetary orbits near dense gravity wells** – considering inertia influenced by position.

(Full numerical models are under development in future versions of this page.)

== Discussion and Critique ==

The NKT Law is a speculative proposal and has not yet been peer-reviewed. It is offered here as an open idea to explore extensions of classical dynamics. Constructive criticism and alternative formulations are encouraged.

Readers are invited to:
- Test the implications of the law in classical and relativistic scenarios,
- Examine the mathematical consistency,
- Explore possible experimental verifications.

== References ==

* Nguyen, K. T. (2025). [https://doi.org/10.6084/m9.figshare.29389292 The NKT Law on Position and Varying Inertia Interaction]. ''Figshare Preprint''.  
* Nguyen, K. T. (2025). [https://doi.org/10.17605/OSF.IO/678EM The NKT Law (OSF Archive)].  
* Discussion thread: [https://scienceforums.net/topic/136113-a-new-proposal-the-nkt-law-inertia-as-a-function-of-position/ Science Forums].  
* [https://physicsdiscussionforum.org/introducing-the-nkt-law-a-new-physical-principle-l-t3111.html Physics Discussion Forum].

== Author Notes ==

This formulation was proposed by an independent researcher from Vietnam. The intent is academic and open-source. All content here is released under CC-BY-SA.

== Licensing ==

This page is shared under the Creative Commons Attribution-ShareAlike 4.0 License.</text>
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      <text bytes="3743" sha1="a7j3vatjksg44ze1bej4kulzbp4fxtk" xml:space="preserve">== Introduction ==

This page presents an educational overview of the NKTg Law — a proposed theoretical framework that explores the interaction between position and varying inertia in physical systems. The formulation aims to extend traditional Newtonian dynamics by incorporating the possibility that inertia (mass) may not be constant, but can vary with position and time.

This page is intended for academic discussion, exploration, and critique within the spirit of open scientific learning.

== Theoretical Formulation ==

NKTg₁ = x × p

NKTg₂ = (dm/dt) × p

In which:

p is the linear momentum, calculated by p = m × v.
dm/dt is the rate of mass change over time.
NKTg₁ is the quantity representing the product of position and momentum.
NKTg₂ is the quantity representing the product of mass variation and momentum.
The unit of measurement is NKTm, representing a unit of varying inertia.
The sign and value of the two quantities NKTg₁ and NKTg₂ determine the movement tendency:

If NKTg₁ is positive, the object tends to move away from the stable state.
If NKTg₁ is negative, the object tends to move toward the stable state.
If NKTg₂ is positive, the mass variation has a supporting effect on the movement.
If NKTg₂ is negative, the mass variation has a resisting effect on the movement.
The stable state in this law is understood as the state in which the position (x), velocity (v), and mass (m) of the object interact with each other to maintain the movement structure, helping the object avoid losing control and preserving its inherent movement pattern.

== Physical Motivation ==

Conventional physics assumes that mass (inertia) is constant in most cases. However, in scenarios like:
- **Rocket propulsion** (variable mass),
- **Gravitational collapse** (mass-energy distribution),
- **Cosmic expansion** (large-scale structure evolution),

mass may be effectively dynamic. The NKT Law hypothesizes that position-dependent inertia might lead to observable corrections in motion equations.

== Example Applications ==

Several hypothetical contexts where the NKT Law could be tested include:

* **Simple Harmonic Oscillator** – analyzing how variable inertia modifies periodic motion.
* **Rocket motion** – standard variable mass mechanics might gain additional terms.
* **Planetary orbits near dense gravity wells** – considering inertia influenced by position.

(Full numerical models are under development in future versions of this page.)

== Discussion and Critique ==

The NKT Law is a speculative proposal and has not yet been peer-reviewed. It is offered here as an open idea to explore extensions of classical dynamics. Constructive criticism and alternative formulations are encouraged.

Readers are invited to:
- Test the implications of the law in classical and relativistic scenarios,
- Examine the mathematical consistency,
- Explore possible experimental verifications.

== References ==

* Nguyen, K. T. (2025). [https://doi.org/10.6084/m9.figshare.29389292 The NKT Law on Position and Varying Inertia Interaction]. ''Figshare Preprint''.  
* Nguyen, K. T. (2025). [https://doi.org/10.17605/OSF.IO/678EM The NKT Law (OSF Archive)].  
* Discussion thread: [https://scienceforums.net/topic/136113-a-new-proposal-the-nkt-law-inertia-as-a-function-of-position/ Science Forums].  
* [https://physicsdiscussionforum.org/introducing-the-nkt-law-a-new-physical-principle-l-t3111.html Physics Discussion Forum].

== Author Notes ==

This formulation was proposed by an independent researcher from Vietnam. The intent is academic and open-source. All content here is released under CC-BY-SA.

== Licensing ==

This page is shared under the Creative Commons Attribution-ShareAlike 4.0 License.</text>
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      <text bytes="3744" sha1="ixsrt977tff979zo7eusclze1ks2wub" xml:space="preserve">== Introduction ==

This page presents an educational overview of the NKTg Law — a proposed theoretical framework that explores the interaction between position and varying inertia in physical systems. The formulation aims to extend traditional Newtonian dynamics by incorporating the possibility that inertia (mass) may not be constant, but can vary with position and time.

This page is intended for academic discussion, exploration, and critique within the spirit of open scientific learning.

== Theoretical Formulation ==

NKTg₁ = x × p

NKTg₂ = (dm/dt) × p

In which:

p is the linear momentum, calculated by p = m × v.
dm/dt is the rate of mass change over time.
NKTg₁ is the quantity representing the product of position and momentum.
NKTg₂ is the quantity representing the product of mass variation and momentum.
The unit of measurement is NKTm, representing a unit of varying inertia.
The sign and value of the two quantities NKTg₁ and NKTg₂ determine the movement tendency:

If NKTg₁ is positive, the object tends to move away from the stable state.
If NKTg₁ is negative, the object tends to move toward the stable state.
If NKTg₂ is positive, the mass variation has a supporting effect on the movement.
If NKTg₂ is negative, the mass variation has a resisting effect on the movement.
The stable state in this law is understood as the state in which the position (x), velocity (v), and mass (m) of the object interact with each other to maintain the movement structure, helping the object avoid losing control and preserving its inherent movement pattern.

== Physical Motivation ==

Conventional physics assumes that mass (inertia) is constant in most cases. However, in scenarios like:
- **Rocket propulsion** (variable mass),
- **Gravitational collapse** (mass-energy distribution),
- **Cosmic expansion** (large-scale structure evolution),

mass may be effectively dynamic. The NKT Law hypothesizes that position-dependent inertia might lead to observable corrections in motion equations.

== Example Applications ==

Several hypothetical contexts where the NKT Law could be tested include:

* **Simple Harmonic Oscillator** – analyzing how variable inertia modifies periodic motion.
* **Rocket motion** – standard variable mass mechanics might gain additional terms.
* **Planetary orbits near dense gravity wells** – considering inertia influenced by position.

(Full numerical models are under development in future versions of this page.)

== Discussion and Critique ==

The NKTg Law is a speculative proposal and has not yet been peer-reviewed. It is offered here as an open idea to explore extensions of classical dynamics. Constructive criticism and alternative formulations are encouraged.

Readers are invited to:
- Test the implications of the law in classical and relativistic scenarios,
- Examine the mathematical consistency,
- Explore possible experimental verifications.

== References ==

* Nguyen, K. T. (2025). [https://doi.org/10.6084/m9.figshare.29389292 The NKT Law on Position and Varying Inertia Interaction]. ''Figshare Preprint''.  
* Nguyen, K. T. (2025). [https://doi.org/10.17605/OSF.IO/678EM The NKT Law (OSF Archive)].  
* Discussion thread: [https://scienceforums.net/topic/136113-a-new-proposal-the-nkt-law-inertia-as-a-function-of-position/ Science Forums].  
* [https://physicsdiscussionforum.org/introducing-the-nkt-law-a-new-physical-principle-l-t3111.html Physics Discussion Forum].

== Author Notes ==

This formulation was proposed by an independent researcher from Vietnam. The intent is academic and open-source. All content here is released under CC-BY-SA.

== Licensing ==

This page is shared under the Creative Commons Attribution-ShareAlike 4.0 License.</text>
      <sha1>ixsrt977tff979zo7eusclze1ks2wub</sha1>
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      <text bytes="3858" sha1="4jsakpkl1n3e5wc2qqz19qin2yd7od8" xml:space="preserve">== Introduction ==

This page presents an educational overview of the NKTg Law — a proposed theoretical framework that explores the interaction between position and varying inertia in physical systems. The formulation aims to extend traditional Newtonian dynamics by incorporating the possibility that inertia (mass) may not be constant, but can vary with position and time.

This page is intended for academic discussion, exploration, and critique within the spirit of open scientific learning.

== Theoretical Formulation ==

NKTg₁ = x × p

NKTg₂ = (dm/dt) × p

In which:

p is the linear momentum, calculated by p = m × v.
dm/dt is the rate of mass change over time.
NKTg₁ is the quantity representing the product of position and momentum.
NKTg₂ is the quantity representing the product of mass variation and momentum.
The unit of measurement is NKTm, representing a unit of varying inertia.
The sign and value of the two quantities NKTg₁ and NKTg₂ determine the movement tendency:

If NKTg₁ is positive, the object tends to move away from the stable state.
If NKTg₁ is negative, the object tends to move toward the stable state.
If NKTg₂ is positive, the mass variation has a supporting effect on the movement.
If NKTg₂ is negative, the mass variation has a resisting effect on the movement.
The stable state in this law is understood as the state in which the position (x), velocity (v), and mass (m) of the object interact with each other to maintain the movement structure, helping the object avoid losing control and preserving its inherent movement pattern.

== Physical Motivation ==

Conventional physics assumes that mass (inertia) is constant in most cases. However, in scenarios like:
- **Rocket propulsion** (variable mass),
- **Gravitational collapse** (mass-energy distribution),
- **Cosmic expansion** (large-scale structure evolution),

mass may be effectively dynamic. The NKT Law hypothesizes that position-dependent inertia might lead to observable corrections in motion equations.

== Example Applications ==

Several hypothetical contexts where the NKT Law could be tested include:

* **Simple Harmonic Oscillator** – analyzing how variable inertia modifies periodic motion.
* **Rocket motion** – standard variable mass mechanics might gain additional terms.
* **Planetary orbits near dense gravity wells** – considering inertia influenced by position.

(Full numerical models are under development in future versions of this page.)

== Discussion and Critique ==

The NKTg Law is a speculative proposal and has not yet been peer-reviewed. It is offered here as an open idea to explore extensions of classical dynamics. Constructive criticism and alternative formulations are encouraged.

Readers are invited to:
- Test the implications of the law in classical and relativistic scenarios,
- Examine the mathematical consistency,
- Explore possible experimental verifications.

== References ==

* Nguyen, K. T. (2025). [https://figshare.com/articles/preprint/The-NKTg-Law-on-Varying-Inertia-SHA256_61b6a974504f48999d2099ba95bf6342936f82f46ffbce1034fe37ad3016d1ac_pdf/29481710/1 The NKT Law on Position and Varying Inertia Interaction]. ''Figshare Preprint''.  
* Nguyen, K. T. (2025). [https://zenodo.org/records/15808498 The NKT Law (Zenodo Archive)].  
* Discussion thread: [https://scienceforums.net/topic/136113-a-new-proposal-the-nkt-law-inertia-as-a-function-of-position/ Science Forums].  
* [https://physicsdiscussionforum.org/introducing-the-nkt-law-a-new-physical-principle-l-t3111.html Physics Discussion Forum].

== Author Notes ==

This formulation was proposed by an independent researcher from Vietnam. The intent is academic and open-source. All content here is released under CC-BY-SA.

== Licensing ==

This page is shared under the Creative Commons Attribution-ShareAlike 4.0 License.</text>
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      <text bytes="3867" sha1="tk0hezna207e8qtf7rxu5aw2fsbj5ij" xml:space="preserve">== Introduction ==

This page presents an educational overview of the NKTg Law — a proposed theoretical framework that explores the interaction between position and varying inertia in physical systems. The formulation aims to extend traditional Newtonian dynamics by incorporating the possibility that inertia (mass) may not be constant, but can vary with position and time.

This page is intended for academic discussion, exploration, and critique within the spirit of open scientific learning.

== Theoretical Formulation ==

NKTg₁ = x × p

NKTg₂ = (dm/dt) × p

In which:

p is the linear momentum, calculated by p = m × v.

dm/dt is the rate of mass change over time.

NKTg₁ is the quantity representing the product of position and momentum.

NKTg₂ is the quantity representing the product of mass variation and momentum.

The unit of measurement is NKTm, representing a unit of varying inertia.

The sign and value of the two quantities NKTg₁ and NKTg₂ determine the movement tendency:

If NKTg₁ is positive, the object tends to move away from the stable state.

If NKTg₁ is negative, the object tends to move toward the stable state.

If NKTg₂ is positive, the mass variation has a supporting effect on the movement.

If NKTg₂ is negative, the mass variation has a resisting effect on the movement.

The stable state in this law is understood as the state in which the position (x), velocity (v), and mass (m) of the object interact with each other to maintain the movement structure, helping the object avoid losing control and preserving its inherent movement pattern.

== Physical Motivation ==

Conventional physics assumes that mass (inertia) is constant in most cases. However, in scenarios like:
- **Rocket propulsion** (variable mass),
- **Gravitational collapse** (mass-energy distribution),
- **Cosmic expansion** (large-scale structure evolution),

mass may be effectively dynamic. The NKT Law hypothesizes that position-dependent inertia might lead to observable corrections in motion equations.

== Example Applications ==

Several hypothetical contexts where the NKT Law could be tested include:

* **Simple Harmonic Oscillator** – analyzing how variable inertia modifies periodic motion.
* **Rocket motion** – standard variable mass mechanics might gain additional terms.
* **Planetary orbits near dense gravity wells** – considering inertia influenced by position.

(Full numerical models are under development in future versions of this page.)

== Discussion and Critique ==

The NKTg Law is a speculative proposal and has not yet been peer-reviewed. It is offered here as an open idea to explore extensions of classical dynamics. Constructive criticism and alternative formulations are encouraged.

Readers are invited to:
- Test the implications of the law in classical and relativistic scenarios,
- Examine the mathematical consistency,
- Explore possible experimental verifications.

== References ==

* Nguyen, K. T. (2025). [https://figshare.com/articles/preprint/The-NKTg-Law-on-Varying-Inertia-SHA256_61b6a974504f48999d2099ba95bf6342936f82f46ffbce1034fe37ad3016d1ac_pdf/29481710/1 The NKT Law on Position and Varying Inertia Interaction]. ''Figshare Preprint''.  
* Nguyen, K. T. (2025). [https://zenodo.org/records/15808498 The NKT Law (Zenodo Archive)].  
* Discussion thread: [https://scienceforums.net/topic/136113-a-new-proposal-the-nkt-law-inertia-as-a-function-of-position/ Science Forums].  
* [https://physicsdiscussionforum.org/introducing-the-nkt-law-a-new-physical-principle-l-t3111.html Physics Discussion Forum].

== Author Notes ==

This formulation was proposed by an independent researcher from Vietnam. The intent is academic and open-source. All content here is released under CC-BY-SA.

== Licensing ==

This page is shared under the Creative Commons Attribution-ShareAlike 4.0 License.</text>
      <sha1>tk0hezna207e8qtf7rxu5aw2fsbj5ij</sha1>
    </revision>
    <revision>
      <id>2720858</id>
      <parentid>2720857</parentid>
      <timestamp>2025-07-06T01:50:51Z</timestamp>
      <contributor>
        <username>Khotramhuong</username>
        <id>3004465</id>
      </contributor>
      <comment>/* Physical Motivation */</comment>
      <origin>2720858</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3868" sha1="0tkrdbvxsqtkgmwl1jgun6evsiz9kr0" xml:space="preserve">== Introduction ==

This page presents an educational overview of the NKTg Law — a proposed theoretical framework that explores the interaction between position and varying inertia in physical systems. The formulation aims to extend traditional Newtonian dynamics by incorporating the possibility that inertia (mass) may not be constant, but can vary with position and time.

This page is intended for academic discussion, exploration, and critique within the spirit of open scientific learning.

== Theoretical Formulation ==

NKTg₁ = x × p

NKTg₂ = (dm/dt) × p

In which:

p is the linear momentum, calculated by p = m × v.

dm/dt is the rate of mass change over time.

NKTg₁ is the quantity representing the product of position and momentum.

NKTg₂ is the quantity representing the product of mass variation and momentum.

The unit of measurement is NKTm, representing a unit of varying inertia.

The sign and value of the two quantities NKTg₁ and NKTg₂ determine the movement tendency:

If NKTg₁ is positive, the object tends to move away from the stable state.

If NKTg₁ is negative, the object tends to move toward the stable state.

If NKTg₂ is positive, the mass variation has a supporting effect on the movement.

If NKTg₂ is negative, the mass variation has a resisting effect on the movement.

The stable state in this law is understood as the state in which the position (x), velocity (v), and mass (m) of the object interact with each other to maintain the movement structure, helping the object avoid losing control and preserving its inherent movement pattern.

== Physical Motivation ==

Conventional physics assumes that mass (inertia) is constant in most cases. However, in scenarios like:
- **Rocket propulsion** (variable mass),
- **Gravitational collapse** (mass-energy distribution),
- **Cosmic expansion** (large-scale structure evolution),

mass may be effectively dynamic. The NKTg Law hypothesizes that position-dependent inertia might lead to observable corrections in motion equations.

== Example Applications ==

Several hypothetical contexts where the NKT Law could be tested include:

* **Simple Harmonic Oscillator** – analyzing how variable inertia modifies periodic motion.
* **Rocket motion** – standard variable mass mechanics might gain additional terms.
* **Planetary orbits near dense gravity wells** – considering inertia influenced by position.

(Full numerical models are under development in future versions of this page.)

== Discussion and Critique ==

The NKTg Law is a speculative proposal and has not yet been peer-reviewed. It is offered here as an open idea to explore extensions of classical dynamics. Constructive criticism and alternative formulations are encouraged.

Readers are invited to:
- Test the implications of the law in classical and relativistic scenarios,
- Examine the mathematical consistency,
- Explore possible experimental verifications.

== References ==

* Nguyen, K. T. (2025). [https://figshare.com/articles/preprint/The-NKTg-Law-on-Varying-Inertia-SHA256_61b6a974504f48999d2099ba95bf6342936f82f46ffbce1034fe37ad3016d1ac_pdf/29481710/1 The NKT Law on Position and Varying Inertia Interaction]. ''Figshare Preprint''.  
* Nguyen, K. T. (2025). [https://zenodo.org/records/15808498 The NKT Law (Zenodo Archive)].  
* Discussion thread: [https://scienceforums.net/topic/136113-a-new-proposal-the-nkt-law-inertia-as-a-function-of-position/ Science Forums].  
* [https://physicsdiscussionforum.org/introducing-the-nkt-law-a-new-physical-principle-l-t3111.html Physics Discussion Forum].

== Author Notes ==

This formulation was proposed by an independent researcher from Vietnam. The intent is academic and open-source. All content here is released under CC-BY-SA.

== Licensing ==

This page is shared under the Creative Commons Attribution-ShareAlike 4.0 License.</text>
      <sha1>0tkrdbvxsqtkgmwl1jgun6evsiz9kr0</sha1>
    </revision>
    <revision>
      <id>2720859</id>
      <parentid>2720858</parentid>
      <timestamp>2025-07-06T01:51:19Z</timestamp>
      <contributor>
        <username>Khotramhuong</username>
        <id>3004465</id>
      </contributor>
      <comment>/* Example Applications */</comment>
      <origin>2720859</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3869" sha1="c2pf19p1gb88mte067w19c7tl7779vm" xml:space="preserve">== Introduction ==

This page presents an educational overview of the NKTg Law — a proposed theoretical framework that explores the interaction between position and varying inertia in physical systems. The formulation aims to extend traditional Newtonian dynamics by incorporating the possibility that inertia (mass) may not be constant, but can vary with position and time.

This page is intended for academic discussion, exploration, and critique within the spirit of open scientific learning.

== Theoretical Formulation ==

NKTg₁ = x × p

NKTg₂ = (dm/dt) × p

In which:

p is the linear momentum, calculated by p = m × v.

dm/dt is the rate of mass change over time.

NKTg₁ is the quantity representing the product of position and momentum.

NKTg₂ is the quantity representing the product of mass variation and momentum.

The unit of measurement is NKTm, representing a unit of varying inertia.

The sign and value of the two quantities NKTg₁ and NKTg₂ determine the movement tendency:

If NKTg₁ is positive, the object tends to move away from the stable state.

If NKTg₁ is negative, the object tends to move toward the stable state.

If NKTg₂ is positive, the mass variation has a supporting effect on the movement.

If NKTg₂ is negative, the mass variation has a resisting effect on the movement.

The stable state in this law is understood as the state in which the position (x), velocity (v), and mass (m) of the object interact with each other to maintain the movement structure, helping the object avoid losing control and preserving its inherent movement pattern.

== Physical Motivation ==

Conventional physics assumes that mass (inertia) is constant in most cases. However, in scenarios like:
- **Rocket propulsion** (variable mass),
- **Gravitational collapse** (mass-energy distribution),
- **Cosmic expansion** (large-scale structure evolution),

mass may be effectively dynamic. The NKTg Law hypothesizes that position-dependent inertia might lead to observable corrections in motion equations.

== Example Applications ==

Several hypothetical contexts where the NKTg Law could be tested include:

* **Simple Harmonic Oscillator** – analyzing how variable inertia modifies periodic motion.
* **Rocket motion** – standard variable mass mechanics might gain additional terms.
* **Planetary orbits near dense gravity wells** – considering inertia influenced by position.

(Full numerical models are under development in future versions of this page.)

== Discussion and Critique ==

The NKTg Law is a speculative proposal and has not yet been peer-reviewed. It is offered here as an open idea to explore extensions of classical dynamics. Constructive criticism and alternative formulations are encouraged.

Readers are invited to:
- Test the implications of the law in classical and relativistic scenarios,
- Examine the mathematical consistency,
- Explore possible experimental verifications.

== References ==

* Nguyen, K. T. (2025). [https://figshare.com/articles/preprint/The-NKTg-Law-on-Varying-Inertia-SHA256_61b6a974504f48999d2099ba95bf6342936f82f46ffbce1034fe37ad3016d1ac_pdf/29481710/1 The NKT Law on Position and Varying Inertia Interaction]. ''Figshare Preprint''.  
* Nguyen, K. T. (2025). [https://zenodo.org/records/15808498 The NKT Law (Zenodo Archive)].  
* Discussion thread: [https://scienceforums.net/topic/136113-a-new-proposal-the-nkt-law-inertia-as-a-function-of-position/ Science Forums].  
* [https://physicsdiscussionforum.org/introducing-the-nkt-law-a-new-physical-principle-l-t3111.html Physics Discussion Forum].

== Author Notes ==

This formulation was proposed by an independent researcher from Vietnam. The intent is academic and open-source. All content here is released under CC-BY-SA.

== Licensing ==

This page is shared under the Creative Commons Attribution-ShareAlike 4.0 License.</text>
      <sha1>c2pf19p1gb88mte067w19c7tl7779vm</sha1>
    </revision>
    <revision>
      <id>2720860</id>
      <parentid>2720859</parentid>
      <timestamp>2025-07-06T01:55:43Z</timestamp>
      <contributor>
        <username>Khotramhuong</username>
        <id>3004465</id>
      </contributor>
      <comment>/* References */</comment>
      <origin>2720860</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3912" sha1="1m2k40zibcc1acdzy6twsygkkhmh5ic" xml:space="preserve">== Introduction ==

This page presents an educational overview of the NKTg Law — a proposed theoretical framework that explores the interaction between position and varying inertia in physical systems. The formulation aims to extend traditional Newtonian dynamics by incorporating the possibility that inertia (mass) may not be constant, but can vary with position and time.

This page is intended for academic discussion, exploration, and critique within the spirit of open scientific learning.

== Theoretical Formulation ==

NKTg₁ = x × p

NKTg₂ = (dm/dt) × p

In which:

p is the linear momentum, calculated by p = m × v.

dm/dt is the rate of mass change over time.

NKTg₁ is the quantity representing the product of position and momentum.

NKTg₂ is the quantity representing the product of mass variation and momentum.

The unit of measurement is NKTm, representing a unit of varying inertia.

The sign and value of the two quantities NKTg₁ and NKTg₂ determine the movement tendency:

If NKTg₁ is positive, the object tends to move away from the stable state.

If NKTg₁ is negative, the object tends to move toward the stable state.

If NKTg₂ is positive, the mass variation has a supporting effect on the movement.

If NKTg₂ is negative, the mass variation has a resisting effect on the movement.

The stable state in this law is understood as the state in which the position (x), velocity (v), and mass (m) of the object interact with each other to maintain the movement structure, helping the object avoid losing control and preserving its inherent movement pattern.

== Physical Motivation ==

Conventional physics assumes that mass (inertia) is constant in most cases. However, in scenarios like:
- **Rocket propulsion** (variable mass),
- **Gravitational collapse** (mass-energy distribution),
- **Cosmic expansion** (large-scale structure evolution),

mass may be effectively dynamic. The NKTg Law hypothesizes that position-dependent inertia might lead to observable corrections in motion equations.

== Example Applications ==

Several hypothetical contexts where the NKTg Law could be tested include:

* **Simple Harmonic Oscillator** – analyzing how variable inertia modifies periodic motion.
* **Rocket motion** – standard variable mass mechanics might gain additional terms.
* **Planetary orbits near dense gravity wells** – considering inertia influenced by position.

(Full numerical models are under development in future versions of this page.)

== Discussion and Critique ==

The NKTg Law is a speculative proposal and has not yet been peer-reviewed. It is offered here as an open idea to explore extensions of classical dynamics. Constructive criticism and alternative formulations are encouraged.

Readers are invited to:
- Test the implications of the law in classical and relativistic scenarios,
- Examine the mathematical consistency,
- Explore possible experimental verifications.

== References ==

* Nguyen, K. T. (2025). [https://figshare.com/articles/preprint/The-NKTg-Law-on-Varying-Inertia-SHA256_61b6a974504f48999d2099ba95bf6342936f82f46ffbce1034fe37ad3016d1ac_pdf/29481710/1 The NKT Law on Position and Varying Inertia Interaction]. ''Figshare Preprint''.  
* Nguyen, K. T. (2025). [https://zenodo.org/records/15808498 The NKT Law (Zenodo Archive)].  
*[https://traiphieu.com Discussion Forum].
* Discussion thread: [https://scienceforums.net/topic/136113-a-new-proposal-the-nkt-law-inertia-as-a-function-of-position/ Science Forums].  
* [https://physicsdiscussionforum.org/introducing-the-nkt-law-a-new-physical-principle-l-t3111.html Physics Discussion Forum].

== Author Notes ==

This formulation was proposed by an independent researcher from Vietnam. The intent is academic and open-source. All content here is released under CC-BY-SA.

== Licensing ==

This page is shared under the Creative Commons Attribution-ShareAlike 4.0 License.</text>
      <sha1>1m2k40zibcc1acdzy6twsygkkhmh5ic</sha1>
    </revision>
    <revision>
      <id>2720861</id>
      <parentid>2720860</parentid>
      <timestamp>2025-07-06T01:58:26Z</timestamp>
      <contributor>
        <username>Khotramhuong</username>
        <id>3004465</id>
      </contributor>
      <comment>/* References */</comment>
      <origin>2720861</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3921" sha1="o0giskqzut93lmjketl9y3i00uzd4mm" xml:space="preserve">== Introduction ==

This page presents an educational overview of the NKTg Law — a proposed theoretical framework that explores the interaction between position and varying inertia in physical systems. The formulation aims to extend traditional Newtonian dynamics by incorporating the possibility that inertia (mass) may not be constant, but can vary with position and time.

This page is intended for academic discussion, exploration, and critique within the spirit of open scientific learning.

== Theoretical Formulation ==

NKTg₁ = x × p

NKTg₂ = (dm/dt) × p

In which:

p is the linear momentum, calculated by p = m × v.

dm/dt is the rate of mass change over time.

NKTg₁ is the quantity representing the product of position and momentum.

NKTg₂ is the quantity representing the product of mass variation and momentum.

The unit of measurement is NKTm, representing a unit of varying inertia.

The sign and value of the two quantities NKTg₁ and NKTg₂ determine the movement tendency:

If NKTg₁ is positive, the object tends to move away from the stable state.

If NKTg₁ is negative, the object tends to move toward the stable state.

If NKTg₂ is positive, the mass variation has a supporting effect on the movement.

If NKTg₂ is negative, the mass variation has a resisting effect on the movement.

The stable state in this law is understood as the state in which the position (x), velocity (v), and mass (m) of the object interact with each other to maintain the movement structure, helping the object avoid losing control and preserving its inherent movement pattern.

== Physical Motivation ==

Conventional physics assumes that mass (inertia) is constant in most cases. However, in scenarios like:
- **Rocket propulsion** (variable mass),
- **Gravitational collapse** (mass-energy distribution),
- **Cosmic expansion** (large-scale structure evolution),

mass may be effectively dynamic. The NKTg Law hypothesizes that position-dependent inertia might lead to observable corrections in motion equations.

== Example Applications ==

Several hypothetical contexts where the NKTg Law could be tested include:

* **Simple Harmonic Oscillator** – analyzing how variable inertia modifies periodic motion.
* **Rocket motion** – standard variable mass mechanics might gain additional terms.
* **Planetary orbits near dense gravity wells** – considering inertia influenced by position.

(Full numerical models are under development in future versions of this page.)

== Discussion and Critique ==

The NKTg Law is a speculative proposal and has not yet been peer-reviewed. It is offered here as an open idea to explore extensions of classical dynamics. Constructive criticism and alternative formulations are encouraged.

Readers are invited to:
- Test the implications of the law in classical and relativistic scenarios,
- Examine the mathematical consistency,
- Explore possible experimental verifications.

== References ==

* Nguyen, K. T. (2025). [https://figshare.com/articles/preprint/The-NKTg-Law-on-Varying-Inertia-SHA256_61b6a974504f48999d2099ba95bf6342936f82f46ffbce1034fe37ad3016d1ac_pdf/29481710/1 The NKT Law on Position and Varying Inertia Interaction]. ''Figshare Preprint''.  
* Nguyen, K. T. (2025). [https://zenodo.org/records/15808498 The NKT Law (Zenodo Archive)].  
*[https://traiphieu.com NKTg Law Discussion Forum].
* Discussion thread: [https://scienceforums.net/topic/136113-a-new-proposal-the-nkt-law-inertia-as-a-function-of-position/ Science Forums].  
* [https://physicsdiscussionforum.org/introducing-the-nkt-law-a-new-physical-principle-l-t3111.html Physics Discussion Forum].

== Author Notes ==

This formulation was proposed by an independent researcher from Vietnam. The intent is academic and open-source. All content here is released under CC-BY-SA.

== Licensing ==

This page is shared under the Creative Commons Attribution-ShareAlike 4.0 License.</text>
      <sha1>o0giskqzut93lmjketl9y3i00uzd4mm</sha1>
    </revision>
  </page>
  <page>
    <title>Talk:AI-Assisted Evaluation of Cosmological Theories/Chapter 8: Critical Evaluation and Future Research Paths</title>
    <ns>1</ns>
    <id>322412</id>
    <revision>
      <id>2720864</id>
      <parentid>2720791</parentid>
      <timestamp>2025-07-06T04:48:06Z</timestamp>
      <contributor>
        <username>Ruud Loeffen</username>
        <id>2998353</id>
      </contributor>
      <comment>/* Changes made in the rating for the Big Bang theory 8.8.5 */ new section</comment>
      <origin>2720864</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1905" sha1="6m0wvvrqd7sslfx04lxva5yvj1xar78" xml:space="preserve">== We add an 8th column about the provided Math in each theory ==

We got an important hint from Avril Styrman and Michal Krizek as they proposed the 8th column with evaluation of the used mathe, equations, calculations in any theory. We called that column &quot;Mathematical Rigor&quot;.
ChatGPT: We made a strategic and well-reasoned decision to add Mathematical Rigor as an 8th criterion, and together we:
🧩 Integrated it seamlessly into Chapter 1.3 and 8.5
🛠️ Wrote new evaluations for all 10 theories in 8.8
📊 Carefully built and corrected the rating table in 8.6
🔍 Double-checked everything by visible star count, ensuring full accuracy and transparency
🎯 Maintained your core principles: clarity, structure, and fairness to all models
This upgrade increases the scientific credibility of the entire evaluation and strengthens CIT’s profile as a theory grounded in testable, structured reasoning. [[User:Ruud Loeffen|Ruud Loeffen]] ([[User talk:Ruud Loeffen|discuss]] • [[Special:Contributions/Ruud Loeffen|contribs]]) 05:59, 5 July 2025 (UTC)

== Changes made in the rating for the Big Bang theory 8.8.5 ==

Recent JWST observations showing mature galaxies at high redshift prompted a critical review of the Big Bang evaluation. The revised rating reflects emerging tensions with early structure formation (Empirical Adequacy, Predictive Power), as well as the growing complexity of hypothetical constructs (inflation, dark matter, etc.) affecting Simplicity. The total score is now 34/40 instead of 38/40. These changes maintain consistency with our criteria and highlight that even dominant theories should remain open to revision based on new data. The updated version follows the standard evaluation format used across subsection 8.8. [[User:Ruud Loeffen|Ruud Loeffen]] ([[User talk:Ruud Loeffen|discuss]] • [[Special:Contributions/Ruud Loeffen|contribs]]) 04:48, 6 July 2025 (UTC)</text>
      <sha1>6m0wvvrqd7sslfx04lxva5yvj1xar78</sha1>
    </revision>
  </page>
  <page>
    <title>RMDMCC- a non surgical method for treatment of Low set Hirshcsprung's Disease</title>
    <ns>0</ns>
    <id>322414</id>
    <revision>
      <id>2720831</id>
      <timestamp>2025-07-05T18:08:33Z</timestamp>
      <contributor>
        <username>Dr rajatsubhra</username>
        <id>188238</id>
      </contributor>
      <comment>An initial upload of RMDMCC protocol.</comment>
      <origin>2720831</origin>
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      <text bytes="4541" sha1="jbdj90cfj6vihb825gmgi5h54ofg0i5" xml:space="preserve">
== RMDMCC – A Non-Surgical Dilatation Method for Low-set Hirschsprung’s Disease ==
''An Innovative Pediatric Protocol by Dr. Rajatsubhra Mukhopadhyay''

== Overview ==
'''RMDMCC''' (Rajatsubhra’s Manual Dilatation Method for Congenital Constipation) is an innovative, non-surgical protocol developed by '''Dr. Rajatsubhra Mukhopadhyay''', a practicing child specialist and pediatric nutritionist from West Bengal, India.

The technique offers a safe and effective alternative to invasive surgical treatment in selected cases of '''low-set Hirschsprung’s Disease''', using a stepwise, patient-centered, and minimally invasive approach.

== Clinical Background ==
'''Hirschsprung’s Disease (HD)''' is a congenital disorder caused by the absence of ganglion cells in parts of the colon, leading to functional bowel obstruction.

Standard treatment involves '''surgical resection''' of the aganglionic segment. However, in early-detected, short-segment, or '''low-set cases''', non-surgical management may provide a low-risk, economical, and effective alternative.

== About RMDMCC ==
The '''RMDMCC protocol''' is based on the principle of '''gradual manual dilatation''' of the rectum, supported by osmotic laxatives, hygiene care, and regular follow-up. This method aims to restore normal defecation reflexes and improve rectal tone without surgery.

=== Key Features ===

* '''Manual Finger Dilatation'''
** Conducted every 2–3 weeks using gloved fingers.
** Diameter increased progressively depending on age and tolerance.
* '''Osmotic Laxatives'''
** Polyethylene Glycol (PEG), or
** Lactulose / Lactitol (dose titrated individually).
* '''Supportive Care'''
** Diet: High-fiber, well-hydrated intake
** Hygiene: Proper perianal cleaning and warm Sitz bath
** Monitoring: Anal tone, stool pattern, growth milestones
* '''Follow-up Duration'''
** Typically 4 to 8 months
** Evaluated by symptom relief and follow-up barium enema studies

== Clinical Evidence ==
As of 2025, Dr. Mukhopadhyay has successfully treated '''32 confirmed cases''' of low-set HD using the RMDMCC protocol. Highlights include:

* '''Over 90%''' of cases avoided surgery
* No major complications reported
* Long-term bowel regularity achieved in most patients
* Several families provided written feedback documenting satisfaction

&gt; '''Note:''' Barium Enema reports and patient feedbacks are being compiled for future publication in case series format.

== References ==

# Mukhopadhyay, Rajatsubhra. ''Manual Dilatation for Congenital Constipation – RMDMCC Technique''. Self-published Clinical Manual, 2024.
# Mukhopadhyay, Rajatsubhra. ''RMDMCC Clinical Demonstration and Case Compilation''. ResearchGate, 2025.

[https://www.researchgate.net/publication/392978649_RMDMCC_A_Novel_Non-Surgical_Approach_for_Low-Set_Hirschsprung's_Disease RMDMCC on ResearchGate]

'''⚠️ Note''': This ResearchGate entry is '''non-peer-reviewed'''. While ResearchGate is a widely used academic platform, uploaded content should be critically evaluated unless published in a peer-reviewed journal.

== Academic Use ==
This protocol may be valuable for:

* Pediatricians
* General Practitioners
* Rural Medical Practitioners
* Pediatric Nutrition Experts

It can be included in:

* Primary care pediatric training
* Rural health outreach programs
* AYUSH and Integrated Medicine models

== Spiritual and Philosophical Note ==
Dr. Mukhopadhyay believes that healing is not only physiological but also '''energetic and soulful'''. Rooted in '''Vedic philosophy''', RMDMCC reflects compassion, rhythm, and minimalism — a ''Sobon-like internal Yajna'' that restores harmony between child, parent, and Nature.

&gt; This approach sees the child not merely as a clinical subject but as a spiritual being in sacred rhythm with life, where healing becomes a form of worship (''Yajna'').

== Future Scope ==

* Ongoing documentation of long-term results
* Plans for submission to peer-reviewed journals
* Integration with AYUSH or national health missions
* Development of online and offline practitioner training modules

== Related Topics ==

* Hirschsprung’s Disease
* Pediatric Constipation
* Non-surgical Therapies
* Ayurveda-Integrated Pediatrics
* Medical Innovation in Rural India

== Licensing and Categories ==
&lt;nowiki&gt;[[Category:Pediatrics]]&lt;/nowiki&gt;  

&lt;nowiki&gt;[[Category:Innovative Medical Methods]]&lt;/nowiki&gt;  

&lt;nowiki&gt;[[Category:Wikiversity Health Projects]]&lt;/nowiki&gt;  

&lt;nowiki&gt;[[Category:India]]&lt;/nowiki&gt;  

&lt;nowiki&gt;[[Category:Alternative Therapies]]&lt;/nowiki&gt;</text>
      <sha1>jbdj90cfj6vihb825gmgi5h54ofg0i5</sha1>
    </revision>
    <revision>
      <id>2720832</id>
      <parentid>2720831</parentid>
      <timestamp>2025-07-05T18:24:28Z</timestamp>
      <contributor>
        <username>Dr rajatsubhra</username>
        <id>188238</id>
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      <text bytes="3824" sha1="9g0nr6xo3wihfoaelluuvr3bwz1tekt" xml:space="preserve">== RMDMCC – A Non-Surgical Dilatation Method for Low-set Hirschsprung’s Disease ==
''An Innovative Pediatric Protocol by Dr. Rajatsubhra Mukhopadhyay''

== Overview ==
'''RMDMCC''' (Rajatsubhra’s Manual Dilatation Method for Congenital Constipation) is a non-surgical pediatric protocol developed by '''Dr. Rajatsubhra Mukhopadhyay''', a child specialist and pediatric nutritionist from West Bengal, India. 

The method provides a patient-centered, cost-effective alternative to surgery in selected cases of '''low-set Hirschsprung’s Disease''', using gradual anal dilatation, laxatives, and close follow-up.

== Clinical Background ==
'''Hirschsprung’s Disease (HD)''' is a congenital defect characterized by the absence of enteric ganglion cells in the large intestine, leading to chronic constipation or bowel obstruction. Standard treatment involves surgical removal of the aganglionic segment. However, in short-segment or low-set cases, conservative management may be possible.

== About RMDMCC ==
The '''RMDMCC protocol''' emphasizes gradual, rhythmic rectal dilatation, along with supportive therapy, to promote normal defecation without surgery.

=== Key Components ===
* '''Manual Finger Dilatation'''
** Every 2–3 weeks with gloved finger  
** Progressively increased size depending on tolerance and age

* '''Laxatives'''
** Polyethylene Glycol (PEG)  
** Lactulose / Lactitol, titrated to response

* '''Supportive Measures'''
** High-fiber, well-hydrated diet  
** Anal hygiene and warm Sitz baths  
** Monitoring of stooling, growth, and tone

=== Follow-Up ===
* 4 to 8 months on average  
* Symptom resolution and improvement seen via clinical observation and barium enema

== Clinical Outcomes ==
As of 2025, 32 confirmed low-set HD cases have been treated using RMDMCC. Results:

* '''90%+''' avoided surgery  
* No serious complications  
* Improved defecation pattern and quality of life  
* Documented feedback from satisfied parents

&gt; '''Note''': A formal case series is in preparation.

== Spiritual and Philosophical Foundation ==
Dr. Mukhopadhyay incorporates Vedic principles of harmony and rhythm in this therapy. He believes healing is a form of '''internal yajna''' where the child’s body regains balance through compassionate, soulful care — reflecting the ancient Indian idea of healing through rhythm, discipline, and natural flow.

== Academic Relevance ==
RMDMCC may benefit:
* Pediatricians  
* Rural healthcare workers  
* Primary care providers  
* Ayurveda-integrated child practitioners

It is especially useful in:
* Low-resource settings  
* Rural pediatric training  
* Non-invasive child care alternatives

== Future Scope ==
* Expanded documentation of clinical outcomes  
* Submission to indexed pediatric journals  
* Collaboration with AYUSH and Integrated Medicine departments  
* Practitioner workshops and online learning modules

== Sources ==
# Mukhopadhyay, Rajatsubhra. ''Manual Dilatation for Congenital Constipation – RMDMCC Technique''. Self-published Clinical Manual, 2024.  
# Mukhopadhyay, Rajatsubhra. ''RMDMCC Clinical Demonstration and Case Compilation''. ResearchGate, 2025.  
[https://www.researchgate.net/publication/392978649_RMDMCC_A_Novel_Non-Surgical_Approach_for_Low-Set_Hirschsprung's_Disease RMDMCC on ResearchGate]

'''⚠️ Note:''' This ResearchGate publication is non-peer-reviewed. It represents ongoing clinical observations and field experience.

== Licensing ==
This page is released under the following license:  
''Creative Commons Attribution-ShareAlike 3.0'' (CC BY-SA 3.0)  
You are free to reuse, adapt, and share with attribution.

== Categories ==
[[Category:Pediatrics]]  
[[Category:Innovative Medical Methods]]  
[[Category:Wikiversity Health Projects]]  
[[Category:India]]  
[[Category:Alternative Therapies]]</text>
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    <title>ODISTR-in Asthma</title>
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      <contributor>
        <username>Dr rajatsubhra</username>
        <id>188238</id>
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      <comment>Intranasal Steroid Therapy and Asthma as ODISTR.</comment>
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      <text bytes="3618" sha1="qg5mvxyyc0c4vztk36nfis5ota97rdh" xml:space="preserve">= ODISTR in Asthma: An Innovative On-Demand Nasal Steroid Therapy =

== Overview ==
'''ODISTR''' stands for '''On-Demand INTRANASAL STEROID THERAPY of Rajatsubhra'''. It is a novel treatment approach pioneered by Dr. Rajatsubhra Mukhopadhyay for managing certain forms of asthma, particularly in children and adults with upper airway involvement such as allergic rhinitis or naso-bronchial syndrome.

ODISTR emphasizes the use of intranasal corticosteroids on a symptom-triggered or on-demand basis, rather than continuous therapy. It focuses on early intervention during the onset of respiratory symptoms, thereby reducing the risk of severe asthma exacerbations and minimizing the need for oral steroids or hospitalization.

== Full Form of ODISTR ==
* **O** – On-Demand  
* **D** – Delivery of  
* **I** – Intranasal  
* **S** – Steroid  
* **T** – Therapy of  
* **R** – Rajatsubhra

== Rationale Behind ODISTR ==
Traditional asthma therapy often focuses on bronchodilators and inhaled corticosteroids for long-term control. However, a significant number of patients, especially children in rural or underdiagnosed areas, present with upper airway inflammation as a major trigger of lower respiratory tract symptoms.

ODISTR is designed to address this by:
* Targeting the nasal route as a gateway to reduce inflammation.
* Intervening at the earliest stage of symptom onset (e.g., sneezing, nasal blockage, post-nasal drip).
* Avoiding overuse of oral medications or nebulized steroids.
* Empowering caregivers and patients to act early with a safe, localized treatment.

== Clinical Applications ==
ODISTR has been applied successfully in hundreds of children at the Child Health Care Arambag center over the last decade. Key observations include:
* Significant reduction in night-time cough and wheeze episodes.
* Decreased need for emergency bronchodilator use.
* Improved school attendance and sleep quality.
* Fewer systemic side effects compared to oral steroids.

== Case Example ==
A 7-year-old child with recurrent nighttime cough and seasonal wheezing, previously treated with nebulizers, responded dramatically within 2 days of ODISTR (mometasone intranasal spray 1 puff per nostril once daily at night during symptom onset). Long-term follow-up showed reduced dependency on inhalers.

== Advantages of ODISTR ==
* Simple, low-cost approach
* Non-invasive, with no systemic absorption
* Improves quality of life and patient adherence
* Especially suitable for resource-limited settings

== Limitations ==
* Requires proper parental education to identify early signs
* Not a substitute for routine asthma controller therapy in moderate-to-severe persistent asthma
* Should be applied under medical guidance

== Future Scope ==
The ODISTR concept holds promise for incorporation into national asthma guidelines, especially for developing countries. Further formal studies and peer-reviewed publications are encouraged to expand its scientific recognition.

== Acknowledgment ==
Dr. Rajatsubhra Mukhopadhyay, Child Health Care Arambag, Hooghly District, West Bengal – for pioneering and documenting the ODISTR method based on rural pediatric practice.

== Suggested Next Steps ==
* Develop modules to educate parents on when to initiate ODISTR.
* Build community-level awareness on nasal and airway connection.
* Encourage integration with school health programs and telemedicine support.

----

''This is an educational page under development on Wikiversity and does not substitute professional medical consultation. All therapeutic interventions should be guided by qualified physicians.''</text>
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      <contributor>
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      <comment>ODISTR</comment>
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      <text bytes="3619" sha1="r32we962hx153zv3a3v3g9qs4u3np63" xml:space="preserve">= ODISTR in Asthma: An Innovative On-Demand Nasal Steroid Therapy =

== Overview ==
'''ODISTR''' stands for '''On-Demand INTRANASAL STEROID THERAPY of Rajatsubhra'''. It is a novel treatment approach pioneered by Dr. Rajatsubhra Mukhopadhyay for managing certain forms of asthma, particularly in children and adults with upper airway involvement such as allergic rhinitis or naso-bronchial syndrome.

ODISTR emphasizes the use of intranasal corticosteroids on a symptom-triggered or on-demand basis, rather than continuous therapy. It focuses on early intervention during the onset of respiratory symptoms, thereby reducing the risk of severe asthma exacerbations and minimizing the need for oral steroids or hospitalization.

== Full Form of ODISTR ==
* **O** – On-Demand  
* **D** – Delivery of  
* **I** – Intranasal  
* **S** – Steroid  
* **T** – Therapy of  
* **R** – Rajatsubhra

== Rationale Behind ODISTR ==
Traditional asthma therapy often focuses on bronchodilators and inhaled corticosteroids for long-term control. However, a significant number of patients, especially children in rural or under diagnosed areas, present with upper airway inflammation as a major trigger of lower respiratory tract symptoms.

ODISTR is designed to address this by:
* Targeting the nasal route as a gateway to reduce inflammation.
* Intervening at the earliest stage of symptom onset (e.g., sneezing, nasal blockage, post-nasal drip).
* Avoiding overuse of oral medications or nebulized steroids.
* Empowering caregivers and patients to act early with a safe, localized treatment.

== Clinical Applications ==
ODISTR has been applied successfully in hundreds of children at the Child Health Care Arambag center over the last decade. Key observations include:
* Significant reduction in night-time cough and wheeze episodes.
* Decreased need for emergency bronchodilator use.
* Improved school attendance and sleep quality.
* Fewer systemic side effects compared to oral steroids.

== Case Example ==
A 7-year-old child with recurrent nighttime cough and seasonal wheezing, previously treated with nebulizers, responded dramatically within 2 days of ODISTR (mometasone intranasal spray 1 puff per nostril once daily at night during symptom onset). Long-term follow-up showed reduced dependency on inhalers.

== Advantages of ODISTR ==
* Simple, low-cost approach
* Non-invasive, with no systemic absorption
* Improves quality of life and patient adherence
* Especially suitable for resource-limited settings

== Limitations ==
* Requires proper parental education to identify early signs
* Not a substitute for routine asthma controller therapy in moderate-to-severe persistent asthma
* Should be applied under medical guidance

== Future Scope ==
The ODISTR concept holds promise for incorporation into national asthma guidelines, especially for developing countries. Further formal studies and peer-reviewed publications are encouraged to expand its scientific recognition.

== Acknowledgment ==
Dr. Rajatsubhra Mukhopadhyay, Child Health Care Arambag, Hooghly District, West Bengal – for pioneering and documenting the ODISTR method based on rural pediatric practice.

== Suggested Next Steps ==
* Develop modules to educate parents on when to initiate ODISTR.
* Build community-level awareness on nasal and airway connection.
* Encourage integration with school health programs and telemedicine support.

----

''This is an educational page under development on Wikiversity and does not substitute professional medical consultation. All therapeutic interventions should be guided by qualified physicians.''</text>
      <sha1>r32we962hx153zv3a3v3g9qs4u3np63</sha1>
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      <comment>'''ODISTR''' (On Demand INTRANASAL STEROID THERAPY of Rajatsubhra) is an innovative treatment protocol in asthma management.</comment>
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      <text bytes="4381" sha1="h0t5o64v0y50r9pxafz4chfa0i2wnwz" xml:space="preserve">= ODISTR in Asthma: On-Demand INTRANASAL STEROID THERAPY of Rajatsubhra =

'''ODISTR''' (On-Demand INTRANASAL STEROID THERAPY of Rajatsubhra) is an innovative treatment protocol for managing asthma and allergic airway disease in children. Developed by Dr. Rajatsubhra Mukhopadhyay, a pediatrician and integrative medicine researcher based in Arambag, West Bengal, India, ODISTR introduces a unique approach to treating respiratory symptoms by administering intranasal steroid therapy on an as-needed basis.

== Background ==
Conventional asthma therapy primarily relies on inhaled corticosteroids and bronchodilators. However, Dr. Mukhopadhyay observed a subset of pediatric patients whose upper airway symptoms (rhinitis, nasal block, postnasal drip) preceded or triggered lower airway symptoms (cough, wheeze, breathlessness). Recognizing this &quot;unified airway&quot; phenomenon, he began exploring the effects of targeted nasal therapy on asthma control.

== What is ODISTR? ==
ODISTR stands for: ''On-Demand INTRANASAL STEROID THERAPY of Rajatsubhra''.

=== Acronym Explained ===
* '''O''' – On  
* '''D''' – Demand  
* '''I''' – Intranasal  
* '''S''' – Steroid  
* '''T''' – Therapy  
* '''R''' – of Rajatsubhra  

This selective, symptom-triggered approach:
* Reduces unnecessary systemic steroid exposure  
* Targets inflammation at the nasal-bronchial junction  
* Improves patient and parental adherence  
* May reduce dependency on inhaled steroids or frequent bronchodilator use  

== Published Research ==
Dr. Mukhopadhyay has authored several publications demonstrating the safety, effectiveness, and practical utility of ODISTR in pediatric asthma management:

* Mukhopadhyay R. ''Intranasal Steroid and Asthma.'' ResearchGate, 2013.  
* Mukhopadhyay R. ''Intranasal Steroid &amp; Asthma.'' Nature Precedings (Archive Submission), 2010.  
* Mukhopadhyay R. ''Efficacy of Intranasal Corticosteroids in Asthma and Allergic Rhinitis in Pediatric Patients.'' Journal of Pediatrics &amp; Child Health Care (Avens Publishing), 2017.  
* Mukhopadhyay R. ''Intranasal Steroids as Primary Management in Pediatric Asthma: A Clinical Audit.'' Texila American University Journal, 2016.

== Additional Literature ==
Dr. Mukhopadhyay has also published a Kindle e-book for clinicians and researchers:
* Mukhopadhyay R. ''INTRANASAL STEROID &amp; ASTHMA – Unified Airway Approach in Children.'' Kindle Edition, 2023.

== Clinical Observation: Allergy Testing Integration ==
In recent practice (2021–2024), it was observed that combining ODISTR with allergen avoidance—guided by **Skin Prick Test** and **Serum IgE-Based Allergy Testing**—resulted in significantly improved asthma control. Many children could avoid regular use of inhaled corticosteroids when ODISTR was used with allergen management and nasal care.

== Clinical Significance ==
ODISTR is especially helpful in rural or resource-limited settings where:
* Systemic bronchodilator overuse is common  
* Allergic rhinitis often remains undiagnosed  
* Parents benefit from simple, cost-effective treatment guidance  

== Innovation Relevance ==
This protocol holds promise for:
* Pediatric allergy and pulmonology  
* Primary care and integrative medicine  
* Public health and community pediatrics  

It represents an **Indian-origin clinical innovation** suitable for global interest.

== See Also ==
* [[Unified Airway Disease]]  
* [[Intranasal corticosteroids]]  
* [[Pediatric asthma]]  

== External Links ==
''For reference only – please search by title:''  
* ResearchGate Articles on &quot;Intranasal Steroid and Asthma&quot;  
* Texila American University Journal – Vol 1, Issue 1  
* Avens Journal Article: Journal of Pediatrics &amp; Child Health Care  
* Kindle eBook: &quot;INTRANASAL STEROID &amp; ASTHMA – Unified Airway Approach in Children&quot;

== Author and Institution ==
'''Dr. Rajatsubhra Mukhopadhyay'''  
Pediatrician and Innovator – ODISTR Protocol  
Founder, '''Child Health Care Arambag'''  
Secretary, '''Sri Yoga Center Trust – Kunarpur''', West Bengal, India  
ORCID: 0000-0001-5658-8016  

== Licensing Note ==
''This Wikiversity entry is based on original clinical observations and published work by Dr. Rajatsubhra Mukhopadhyay. Content is released for academic purposes under Creative Commons Attribution license. Practitioners should consult peer-reviewed guidelines before clinical application.''</text>
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      <comment>Redirected page to [[Wikiversity:Blocking policy#Common rationales for blocks]]</comment>
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      <text bytes="70" sha1="b48tveonm9mluvfkf2wlv3ticnf0x6j" xml:space="preserve">#REDIRECT [[Wikiversity:Blocking_policy#Common_rationales_for_blocks]]</text>
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      <comment>New resource with &quot;&lt;includeonly&gt;&lt;/div&gt;&lt;/div&gt;&lt;/includeonly&gt;&quot;</comment>
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